A Multiscale Model for the World’s First Parasitic …downloads.hindawi.com/journals/cmmm/2017/1473287.pdftime of Guinea worm larvae𝐿𝑊(𝑡), susceptible copepods 𝑆 𝐸

Research ArticleA Multiscale Model for the Worldrsquos First Parasitic DiseaseTargeted for Eradication Guinea Worm Disease

Rendani Netshikweta andWinston Garira

Modelling Health and Environmental Linkages Research Group (MHELRG) Department of Mathematics and Applied MathematicsUniversity of Venda Private Bag X5050 Thohoyandou 0950 South Africa

Correspondence should be addressed to Winston Garira winstongariraunivenacza

Received 13 October 2016 Revised 8 April 2017 Accepted 15 May 2017 Published 20 July 2017

Academic Editor Jose Siri

Copyright copy 2017 Rendani Netshikweta and Winston Garira This is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

Guinea worm disease (GWD) is both a neglected tropical disease and an environmentally driven infectious disease Environmen-tally driven infectious diseases remain one of the biggest health threats for human welfare in developing countries and the threat isincreased by the looming danger of climate change In this paper we present a multiscale model of GWD that integrates the within-host scale and the between-host scale The model is used to concurrently examine the interactions between the three organismsthat are implicated in natural cases of GWD transmission the copepod vector the human host and the protozoan worm parasite(Dracunculus medinensis) and identify their epidemiological roles The results of the study (through sensitivity analysis of 1198770)show that the most efficient elimination strategy for GWD at between-host scale is to give highest priority to copepod vectorcontrol by killing the copepods in drinking water (the intermediate host) by applying chemical treatments (eg temephos anorganophosphate) This strategy should be complemented by health education to ensure that greater numbers of individuals andcommunities adopt behavioural practices such as voluntary reporting of GWD cases prevention of GWD patients from enteringdrinking water bodies regular use of water from safe water sources and in the absence of such water sources filtering or boilingwater before drinking Taking into account the fact that there is no drug or vaccine forGWD (interventionswhich operate at within-host scale) the results of our study show that the development of a drug that kills female worms at within-host scale would havethe highest impact at this scale domain with possible population level benefits that include prevention of morbidity and preventionof transmission

1 Introduction

Guinea worm disease (GWD) sometimes known as Dra-cunculiasis or dracontiasis [1] is a nematode infection trans-mitted to humans exclusively through contaminated drink-ing water People become infected when they drink watercontaminated with copepods or cyclopoids (tiny aquaticcrustaceans) harbouring infective Dracunculus larvae alsoknown asDracunculus medinensisThe larvae ofDracunculusmedinensis are released into the stomach when the copepodsare digested by the effect of the gastric juice and get killed bythe acid environment Although the disease has lowmortalityits morbidity is considerably high causing huge economiclosses and devastating disabilities [2] There is no vaccineor drug for the disease Our ability to eliminate GWD restspartly on gaining better insights into the functioning of theimmune system especially its interaction with Guinea worm

parasite and partly on development of drugs to treat thedisease together with implementation of preventive mea-sures Currently the only therapy for GWD is to physicallyextract the worm from the human body Humans are thesole definitive host for GWD parasite Efforts to eradicate thedisease are focused on preventivemeasures which include thefollowing

(a) Parasite control in the physical water environmentThismay involve chlorination of drinking water or boilingthe water before drinking or applying a larvicide allof which have the effect of killing the parasite andthereby reduce parasite population in the physicalwater environment

(b) Parasite control within the human host This involvesphysically extracting the worm from the human body

HindawiComputational and Mathematical Methods in MedicineVolume 2017 Article ID 1473287 29 pageshttpsdoiorg10115520171473287

2 Computational and Mathematical Methods in Medicine

by rolling it over an ordinary stick or matchstick [1 3]and ensuring that the patient receives care by cleaningand bandaging the wound until all the worms areextracted from the patient This process may take upto two months to complete as the worm can grow upto a meter in length and only 1-2 centimeters can beremoved per day [4 5]

(c) Vector control This consists of killing the copepodsin water (the intermediate host) by applying a chem-ical called temephos an organophosphate to unsafedrinking water sources everymonth during the trans-mission season thus reducing vector population andreducing the chances of individuals contracting thedisease [2 6 7]The adult vectormay also be removedfrom drinking water by filtering the water using anylon cloth or by boiling the water

(d) Health educationThis is disseminated throughposterradio and television broadcast village criers andmar-kets face-to-face communication (social mobiliza-tion and house-to-house visits) by health workers andvolunteers to ensure that greater numbers of indi-viduals and communities adopt behavioural practicesaimed at preventing transmission of GWD [8] Thesebehavioural practices include voluntary reporting ofGWD cases prevention of GWD patients from enter-ing drinking water bodies regular use of water fromsafe water sources and in the absence of such watersources filtering or boiling water before drinking [6]

(e) Provision of safe water sourcesThis involves providingsafe drinkingwater supplies throughprotecting hand-dug wells and sinking deep bore wells improvingexisting surface water sources by constructing bar-riers to prevent humans from entering water andfiltering the water through sand-filters [4]

To date these preventive measures have reduced the inci-dence of GWDby over 99 [6]makingGWD themost likelyparasitic disease that will soon be eradicated without the useof any drug or vaccine Most countries including the wholeof Asia are now declared free from GWD and transmissionof the disease is now limited to African countries especiallySudan Ghana Mali Niger and Nigeria [8] GWD is one ofthe neglected tropical diseases It is also an environmentallydriven infectious diseaseTherefore its transmission dependson the parasitersquos survival in the environment and finding newhosts (humans and copepod vectors) in order to replicate andsustain parasite population Because this process is complexit has hampered eradication efforts During the parasitersquosmovement through the environment to the human andcopepod vector hosts many environmental factors influenceboth the parasitersquos population and the vector population

For infectious diseases including environmentally driveninfectious diseases such as GWD mathematical models havea long history of being used to study their transmission andalso to compare and evaluate the effectiveness and afford-ability of intervention strategies that can be used to controlor eliminate them [9 10] Currently the predominant focusof modelling of infectious diseases is centered on concepts

of epidemiological modelling and immunological modellingbeing considered as separate disease processes even for thesame infectious disease In epidemiological or between-hostmodelling of infectious diseases the focus is on studying oftransmission of infectious diseases between hosts be theyanimals or humans or even both in the case of multiple hostinfections In the immunological or within-host modelling ofinfectious diseases the focus is on studying the interaction ofpathogen and the immune system togetherwith otherwithin-host processes in order to elucidate outcomes of infectionwithin a single host [11 12] To the best of our knowledgethere has been nomathematicalmodel to study themultiscalenature of GWD transmission by integrating between-hostscale and within-host scale disease processes Such modelsare sometimes called immunoepidemiological models [13]Most of the mathematical models that have been developedso far are focused on the study ofGWDat the epidemiologicalscale [14ndash16] The purpose of this study is to develop animmunoepidemiological model of GWD Immunoepidemi-ological modelling of infectious diseases is the quantitativeapproach which assists in developing a systems approachto understanding infectious disease transmission dynamicswith regard to the interdependences between epidemiological(between-host scale) and immunological (within-host scale)processes [17 18] The immunoepidemiological model ofGWD presented in this paper is based on a modelling frame-work of the immunoepidemiology of environmentally driveninfectious diseases developed recently by the authors [13]This new and innovative immunoepidemiological modellingframework while maintaining the limits of a mathemat-ical model offers a solid platform to bring the separatemodelling efforts (immunological modelling and epidemi-ological modelling) that focus on different aspects of thedisease processes together to cover a broad range of diseaseaspects and time-scales in an integrated systems approachIt bridges host environmental and parasitic disease phe-nomena using mathematical modelling of parasite-host-environment-vector interactions and epidemiology to illu-minate the fundamental processes of disease transmission inchanging environments For GWD there are three distincttime-scales associatedwith its transmission cyclewhich are asfollows

(i) The epidemiological time-scale which is associatedwith the infection between hosts (human and cope-pod vector hosts)

(ii) The within-host time-scale which is related to thereplication and developmental stages of Guineawormparasite within an individual human host and theindividual copepod vector host

(iii) Theenvironmental time-scale which is associatedwiththe abundance and survival of Guinea worm parasitepopulation and vector population in the physicalwater environment

In order to try and integrate these different processes andthe associated time-scales of GWD the immunoepidemio-logical model of GWDpresented here incorporates the actualparasite load of the human host and copepod vector rather

Computational and Mathematical Methods in Medicine 3

than simply tracking the total number of infected humans Italso incorporates the various stages of the parasitersquos life cycleas well as the within-host effects such as the effect of gastricjuice within an infected human host and describes how thelife stages in the definitive human host environment andintermediate vector are interconnected with the parasitersquos lifecycle through contact establishment and parasite fecundityThe paper is organized as follows In Section 2 we presentbrief discussion of the life cycle of Guinea worm parasite anduse this information to develop the immunoepidemiologicalmodel of GWD in the same section In Sections 3 4and 5 we derive the analytical results associated with theimmunoepidemiological model and show that the model ismathematically and epidemiologically well-posed We alsoshow the reciprocal influence between the within-host scaleand between-host scale of GWD transmission dynamicsTheresults of the sensitivity analysis of the reproductive numberare given in Section 6while the numerical results of themodelare presented in Section 7 The paper ends with conclusionsin Section 8

2 The Mathematical Model

We develop a multiscale model of Guinea worm disease thattraces the parasitersquos life cycle of Guinea worm diseaseThe lifecycle of GWD involves three different environments physicalwater environment biological human host environment andbiological copepod host environment For more details onthe life cycle of GWD see the published works [6 19] Weonly give a brief description in this sectionThe transmissioncycle of Guinea worm disease begins when the humanindividual drinks contaminated water with copepods thatare infected with Guinea mature worm larvae (L3 larvae)After ingestion gastric juice in the human stomach killsthe infected copepods and mature worm larvae are releasedThen the released mature worm larvae penetrate the humanstomach and intestinal wall and move to abdominal tissueswhere they grow and mate After mating the male wormsdie soon and fertilized female worms migrate towards theskin surface (usually on the lower limbs or feet) After a yearof infection the fertilized female worm makes a blister onthe infected individualrsquos skin causing burning and itchingwhich forces an infected individual to immerse his or her feetinto water (which is the only source of drinking water) toseek relief from pain At that point the female worm emergesand releases thousands of worm eggs The worm eggs thenhatch Guinea worm larvae (L1 larvae stage) which are thenconsumed by copepods and take approximately two weeksto develop and become infective mature larvae (L3 larvae)within the copepodsThen ingestion of the infected copepodsby human closes the life cycle The multiscale model whichwe now present explicitly traces this life cycle of Dracunculusmedinensis in three different environments which are phys-ical water environment biological human environment andbiological copepod environment The model flow diagram isshown in Figure 1

The full multiscale model presented in this paper is basedon monitoring the dynamics of ten populations at any time119905 which are susceptible humans 119878119867(119905) and infected humans

119868119867(119905) in the behavioural human environment infectedcopepods 119868119862 in the human biological environment matureGuinea worms 119882119872(119905) and fertilized female Guinea worms119882119865(119905) in the biological human environment (within-hostparasite dynamics) Guinea worm eggs 119864119882(119905) and Guineaworm larvae 119871119882(119905) in the physical water environmentsusceptible copepods 119878119864(119905) and infected copepods 119868119864(119905) inthe physical water environment and gastric juice 119866119869(119905) inthe human biological environment We make the followingassumptions for the model

(a) There is no vertical transmission of the disease

(b) The transmission of the disease in the human popu-lation is only through drinking contaminated waterwith infected copepods 119868119864(119905) harbouring infectivefree-living pathogens (first-stage larvae)119871119882(119905) in thephysical water environment

(c) For an infected individual more than one Guineaworm can emerge simultaneously or sequentially overthe course of weeks depending on the number andintensity of infection the preceding year

(d) Humans do not develop temporary or permanentimmunity

(e) Copepods do not recover from infection

(f) The total population of humans and copepods is con-stant

(g) Except for the effects of gastric juice in the stomachthere is no immune response in the human host

(h) Copepods die in the human stomach due to the effectsof gastric juice at a rate 120572119862 before their larvae under-goes two molts in the copepod to become L3 larvaeand therefore are nonviable and noninfectious larvae

From the model flow diagram presented in Figure 1and the assumptions that we have now made we have thefollowing system of ordinary differential equations as ourmultiscale model for GWD transmission dynamics

(1) 119889119878119867 (119905)119889119905 = Λ119867 minus 120582119867 (119905) 119878119867 (119905) minus 120583119867119878119867 (119905)+ 120572119867119868119867 (119905) (2) 119889119868119867 (119905)119889119905 = 120582119867 (119905) 119878119867 (119905) minus (120583119867 + 120575119867 + 120572119867) 119868119867 (119905) (3) 119889119868119862 (119905)119889119905 = 120582ℎ (119905) 119878ℎ (119905) minus 120583119862119866119869 (119905) 119868119862 (119905)minus 120572119862119868119862 (119905) (4) 119889119882119872 (119905)119889119905 = 119873119862120583119862119866119869 (119905) 119868119862 (119905)minus (120572119872 + 120583119872)119882119872 (119905)


훼HIH

ΛH 휆HSHSH

휇HSH

휆ℎSℎ

휇JGJ

GJG0

WM WF

휇FWF

훼FWF

IH

(휇H + 훿H) IH

Iℎ훼FWF

LWNW훼WEW EW

휇LLW

IE

(휇E + 훿E) IE

휆ESE SEΛE

휇ESE

훼CIC

IC

훼JICGJ

휇MWM

NC휇CICGJ

휇WEW

(12) 훼WWM

Figure 1 A conceptual diagram of the multiscale model of Guinea worm disease transmission dynamics

(5) 119889119882119865 (119905)119889119905 = 1205721198722 119882119872 (119905) minus (120583119865 + 120572119865)119882119865 (119905) (6) 119889119866119869 (119905)119889119905 = 1198660 + 120572119869119866119869 (119905) 119868119862 (119905) minus 120583119869119866119869 (119905) (7) 119889119864119882 (119905)119889119905 = 120572119865119882119865 (119905) 119868ℎ (119905) minus (120583119882 + 120572119882) 119864119882 (119905) (8) 119889119871119882 (119905)119889119905 = 119873119882120572119882119864119882 (119905) minus 120583119871119871119882 (119905) (9) 119889119878119864 (119905)119889119905 = Λ 119864 minus 120582119864 (119905) 119878119864 (119905) minus 120583119864119878119864 (119905) (10) 119889119868119864 (119905)119889119905 = 120582119864 (119905) 119878119864 (119905) minus (120583119864 + 120575119864) 119868119864 (119905) (1)

where 120582119867 (119905) = 120573119867119868119864 (119905)1198750 + 120598119868119864 (119905) 120582119864 (119905) = 120573119864119871119882 (119905)1198710 + 120598119871119882 (119905) 119868ℎ (119905) = 119868119867 (119905) + 1

119878ℎ (119905) = 119878119867 (119905) minus 1120582ℎ (119905) = 120573119867119868119864 (119905)[1198750 + 120598119868119864 (119905)] [119868119867 (119905) + 1] (2)

Equations (1) and (2) of the model system (1) describethe evolution with time of susceptible and infected humanhosts respectively At any time 119905 new susceptible humansare recruited at a constant rate Λ119867 and we assume that therecruited humans are all susceptible Susceptible individualsleave the susceptible class either through infection at rate120582119867(119905)119878119867(119905) by drinking contaminated water with infectedcopepods to join infected group or through natural deathat a rate 120583119867 The infected group is generated throughinfection when susceptible humans acquire the disease at arate 120582119867(119905)119878119867(119905) through drinking water contaminated withcopepods infected with Dracunculus medinensis Infectedhumans leave the infected group either through recovery ata rate 120572119867 to join the susceptible group or through naturaldeath at a rate 120583119867 or through disease induced death at arate 120575119867 Equation (3) of the model system (1) represents theevolution with time of infected copepods within an infectedhuman host The infected copepods within a human hostare generated following uptake of infected copepods in thephysical water environment through drinking contaminated


water In the human population this uptake of infectedcopepods which harbour Guinea worm larvae is the trans-mission of Guinea worm parasite from the physical waterenvironment to susceptible humans who become infectedhumans Following the methodology described in [13] formodelling reinfection (superinfection) for environmentallytransmitted infectious disease systems (because GWD andschistosomiasis are bothwater-borne and vector-borne infec-tions) wemodel the average rate at which a single susceptiblehuman host uptakes the infected copepods in the physicalwater environment through drinking contaminated waterand becomes an infected human host by the expression120582ℎ (119905) 119878ℎ (119905) = 120582119867 (119905) [119878119867 (119905) minus 1][119868119867 (119905) + 1] (3)

where 120582119867(119905) 119878119867(119905) and 119868119867(119905) are as defined previously Thisis because in our case we define such a single infection by asingle transition(119878119867 (119905) 119868119867 (119905) 119868119864 (119905))997888rarr (119878119867 (119905) minus 1 119868119867 (119905) + 1 119868119864 (119905)) (4)

Therefore the average number of infected copepods119868119862(119905) within a single infected human host increases at ameanrate 120582ℎ(119905)119878ℎ(119905) and decreases through death due to digestionby human gastric acid at a rate 120583119862 after their larvae undergotwo molts in the copepod to become L3 larvae and releaseviable and infectious larvae or naturally at a rate 120572119862 beforetheir larvae undergo two molts in the copepod to become L3larvae and release nonviable and noninfectious larvae

Equations (4ndash6) of the model system (1) representchanges with time of the average population ofmature worms119882119872(119905) fertilized female worms 119882119865(119905) and the amount ofgastric acid 119866119869(119905) within a single infected human hostrespectively The average mature worm population 119882119872(119905)in a single infected human host is generated following thedigestion of infected copepods in the human stomach bygastric acid and then mature worms are released We assumethat mature worms die naturally at a rate 120583119872 and they exit thehuman stomach to the abdominal tissues at a rate 120572119872 wherethey grow and mate The population of fertilized femaleworms 119882119865(119905) within an infected human host is generatedfollowing the developmental changes undergone by maturefertilized female worms These developmental changes resultinmature worms reaching sexualmaturity andmating and allmale worms die soon after mating We assume that fertilizedfemale worms die naturally at a rate 120583119865 and emerge outthrough an infected human individualrsquos skin (usually thelower limbs) to release Guinea worm eggs into a water sourceat a rate 120572119865 when an infected human comes into contact withwater The average amount of gastric acid inside a humanstomach is generated following copepod vector inducedproliferation at a rate 120572119869119868119862(119905) which is proportional to thedensity of infected copepods within an infected human hostWe assume that the amount of gastric acid is also increasedby the spontaneous production of gastric acid by the humanbody at a rate 1198660 and diluted or degraded at a rate 120583119869Equation (7) of model system (1) describes the evolution with

time of the Guinea worm eggs 119864119882(119905) in the physical waterenvironment We note that the population of Guinea wormeggs increases when each infected human host excretes eggsat a rate120572119865119882119865(119905)Therefore the rate at which infected humanscontaminate the physical water environment by excretingGuineaworm eggs ismodelled by120572119865119882119865(119905)119868ℎ(119905)The last threeequations of the model system (1) describe the evolution withtime of Guinea worm larvae 119871119882(119905) susceptible copepods119878119864(119905) and infected copepods 119868119864(119905) in the physical waterenvironment respectively The population of Guinea wormlarvae is generated through each egg hatching an average of119873119882 worms larvae with eggs hatching at an average rate of120572119882 Therefore the total Guinea worm larvae in the physicalwater environment aremodelled by119873119882120572119882119864119882(119905)We assumethat worm larvae in the physical water environment dienaturally at a constant rate 120583119871 Similar to human populationat any time 119905 new susceptible copepods are recruited ata constant Λ 119864 Susceptible copepods leave the susceptiblegroup to join the infected copepods group through infectionat a rate 120582119864(119905)119878119864(119905) when they consume first-stage Guineaworm larvae in the physical water environment We assumethat the population of copepods die naturally at a constantrate 120583119864 and further we also assume that infected copepodshave an additional mortality rate 120575119864 due to infection Themodel state variables are summarized in Table 1

3 Invariant Region of the Model

Themodel system (1) can be analysed in a regionΩ sub R10+ ofbiological interest Now assume that all parameters and statevariables for model system (1) are positive for all 119905 gt 0 andfurther suppose that 119866119869 is bounded above by 1198660120583119869 It can beshown that all solutions for themodel system (1) with positiveinitial conditions remain bounded

Letting 119873119867 = 119878119867 + 119868119867 and adding (1) and (2) of modelsystem (1) we obtain119889119878119867119889119905 + 119889119868119867119889119905 = 119889119873119867119889119905 = Λ119867 minus 120583119867119873119867 minus 120575119867119868119867le Λ119867 minus 120583119867119873119867 (5)

This implies that

lim119905rarrinfin

sup (119873119867 (119905)) le Λ119867120583119867 (6)

Similarly letting119873119864 = 119878119864 + 119868119864 and adding (9) and (10) ofmodel system (1) we obtain119889119878119864119889119905 + 119889119868119864119889119905 = 119889119873119864119889119905 = Λ 119864 minus 120583119867119873119864 minus 120575119867119868119864le Λ 119864 minus 120583119867119873119864 (7)

This also implies that

lim119905rarrinfin

sup (119873119864 (119905)) le Λ 119864120583119864 (8)


Table 1 Description of the state variables of the model system (1)

State variable Description Initial value119878119867(119905) The susceptible human population size in the behavioural human environment 2500119868119867(119905) The infected human population size in the behavioural human environment 10119868119862(119905) The infected copepod population size in the biological human environment 0119882119872(119905) Themature worm population size in the biological human environment 0119882119865(119905) The female worm population size in the biological human environment 0119866119869(119905) Amount of gastric acid in the human stomach 15119878119864(119905) The susceptible copepod population size in the physical water environment 105119868119864(119905) The infected copepod population size in the physical water environment 0119864119882(119905) The worm egg population size in the physical water environment 0119871119882(119905) The worm larvae population size in the physical water environment 5000

Now considering the third equation of model system (1)given by119889119868119862119889119905 = 120582ℎ119878ℎ minus 120583119862119866119869119868119862 minus 120575119862119868119862= ( 120573119867119868119864 (119878119867 minus 1)(1198750 + 120598119868119864) (119868119867 + 1)) minus (120583119862119866119869 + 120572119862) 119868119862 (9)

we obtain 119889119868119862119889119905 le ( 120573119867Λ 119864 (Λ119867 minus 120583119867)(1198750120583119864 + 120598Λ 119864) (Λ119867 + 120583119867))minus 1120583119869 (1205831198621198660 + 120572119862120583119869) 119868119862 (10)

This implies that

lim119905rarrinfin

sup (119868119862 (119905))le ( 120573119867Λ 119864 (Λ119867 minus 120583119867)(1198750120583119864 + 120598Λ 119864) (Λ119867 + 120583119867))( 120583119869(1205831198621198660 + 120575119867120583119869)) (11)

Using (6) (8) and (11) similar expression can be derivedfor the remaining model variables Hence all feasible solu-tions of the model system (1) are positive and enter a regiondefined byΩ = (119878119867 119868119867 119868119862119882119872119882119865 119866119869 119864119882 119871119882 119878119864 119868119864)isin R

10+ 0 le 119878119867 + 119868119867 le 1198781 0 le 119878119864 + 119868119864 le 1198782 0 le 119868119862le 1198783 0 le 119882119872 le 1198784 0 le 119882119865 le 1198785 0 le 119866119869 le 1198786 0le 119864119882 le 1198787 0 le 119871119882 le 1198788

(12)

which is positively invariant and attracting for all 119905 gt 0 where1198781 = Λ119867120583119867 1198782 = Λ 119864120583119864

1198783 = ( 120583119869(1205831198621198660 + 120572119862120583119869)) 11987891198784 = (119873119862120572119862120583119862120572119872 + 120583119872)( 120583119869(1205831198621198660 + 120572119862120583119869)) 11987891198785 = 12 ( 120572119872120572119865 + 120583119865)(119873119862120572119862120583119862120572119872 + 120583119872)( 120583119869(1205831198621198660 + 120572119862120583119869)) 11987891198786 = 1198660120583119869 1198787 = 12 ( 120572119865120572119882 + 120583119882)( 120572119872120572119865 + 120583119865)(119873119862120572119862120583119862120572119872 + 120583119872)sdot ( 120583119869(1205831198621198660 + 120572119862120583119869)) 11987891198788 = 12 (119873119882120572119882120583119871 )( 120572119865120572119882 + 120583119882)( 120572119872120572119865 + 120583119865)sdot ( 119873119862120572119862120583119862120572119872 + 120583119872)( 120583119869(1205831198621198660 + 120572119862120583119869)) 11987891198789 = ( 120573119867Λ119862 (Λ119867 minus 120583119867)(1198750120583119862 + 120598Λ119862) (Λ119867 + 120583119867))

(13)

Therefore it is sufficient to consider solutions of themodelsystem (1) inΩ since all solutions starting inΩ remain therefor all 119905 ge 0 Hence the model system is mathematically andepidemiologically well-posed and it is sufficient to considerthe dynamics of the flow generated by model system (1) inΩ whenever Λ119867 gt 120583119867 We shall assume in all that follows(unless stated otherwise) that Λ119867 gt 1205831198674 Determination of Disease-FreeEquilibrium and Its Stability

To obtain the disease-free equilibrium point of system (1) weset the left-hand side of the equations equal to zero and


further we assume that 119868119867 = 119868119862 = 119882119867 = 119882119867 = 119864119882 = 119871119882 =119868119864 = 0 This means that all the populations are free from thedisease Thus we get1198640 = (1198780119867 1198680119867 119868011986211988201198721198820119865 1198660119869 1198640119882 1198710119882 1198780119864 1198680119864) = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (14)

as the disease-free equilibrium of the model system (1)

41 The Basic Reproduction Number of the Model System(1) The basic reproduction number of the system model (1)is calculated in this section using next generation operatorapproach described in [20] Thus the model system (1) canalso be written in the form119889119883119889119905 = 119891 (119883 119884 119885) 119889119884119889119905 = 119892 (119883 119884 119885) 119889119885119889119905 = ℎ (119883 119884 119885)

(15)

where

(i) 119883 = (119878119867 119878119864 119866119869) represents all compartments of indi-viduals who are not infected

(ii) 119884 = (119868119867 119868119862119882119872119882119865 119864119882) represents all compart-ments of infected individuals who are not capable ofinfecting others

(iii) 119885 = (119868119864 119871119882) represents all compartments of infectedindividuals who are capable of infecting others

We also let the disease-free equilibrium of the model (1)be denoted by the following expression

1198800 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (16)

Following [20] we let119892 (119883lowast 119885) = (1198921 (119883lowast 119885) 1198922 (119883lowast 119885) 1198923 (119883lowast 119885) 1198924 (119883lowast 119885) 1198925 (119883lowast 119885)) (17)

with

1198921 (119883lowast 119885) = 120573119867Λ1198671198851120583119867 (120583119867 + 120575119867 + 120572119867) (1198750 + 120598119868119864) 1198922 (119883lowast 119885) = 120573119867 (Λ119867 minus 120583119867) 120583119869 (120583119867 + 120575119867 + 120572119867) 1198851(1205831198621198660 + 120583119869120572119862)11987211 1198923 (119883lowast 119885) = 119873119862120572119862120573119867 (Λ119867 minus 120583119867) 1198660 (120583119867 + 120575119867 + 120572119867) 1198851(120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862)11987211 1198924 (119883lowast 119885) = 120572119872119873119862120572119862120573119867 (Λ119867 minus 120583119867) 1198660 (120583119867 + 120575119867 + 120572119867) 11988512 (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862)11987211 1198925 (119883lowast 119885) = 120572119865120572119872119873119862120572119862120573119867 (Λ119867 minus 120583119867) 119866011988512 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (1198750 + 120598119868119864)

(18)

where

11987211 = 120598120573119867Λ119867119868119864 + 120583119867 (120583119867 + 120575119867 + 120583119867) (1198750 + 120598119868119864) (19)

We deduce that

ℎ (119883 119884 119885) = (ℎ1 (119883 119884 119885) ℎ2 (119883 119884 119885)) (20)

with ℎ1 (119883 119884 119885) = 120582119864119878119864 minus (120583119864 + 120572119864) 119868119864= 120573119864Λ 1198641198852120583119864 (1198710 + 1205981198852) minus (120583119864 + 120572119864) 1198851ℎ2 (119883 119884 119885) = 119873119882120572119882119864119882 minus 120583119871119871119882= 1198701198851(1198750 + 1205981198851) minus 1205831198711198852(21)


where119870= 120572119865120572119872119873119882120572119882119873119862120572119862120573119867 (Λ119867 minus 120583119867) 11986602 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (22)

119860matrix

119860 = 119863119885ℎ (119883lowast 119892 (119883lowast 0) 0) = [[[[minus (120583119864 + 120572119864) 1198701198750120573119864Λ 1198641205831198641198710 minus120583119871]]]] (23)

can be written in the form 119860 = 119872 minus 119863 so that

119872 = [[[[0 1198701198750120573119864Λ 1198641205831198641198710 0 ]]]] (24)

119863 = [(120583119864 + 120572119864) 00 120583119871] (25)

The basic reproductive number is the spectral radius(dominant eigenvalue) of the matrix 119879 = 119872119863minus1 Hence thebasic reproduction number of the immumoepidemiologicalmodel (1) is expressed by the following quantity

1198770 = radic12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 sdot 120573119867 (Λ119867 minus 120583119867)1198750120583119867 sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710= radic11987701198611198770119882 (26)

with

1198770119861 = 120573119867 (Λ119867 minus 120583119867)1198750120583119867sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (27)

1198770119882 = 12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 (28)

The expression 1198770119861 in (27) represents GWDrsquos partialreproductive number associatedwith the between-host trans-mission of the disease while the expression 1198770119882 in (28)represents GWDrsquos partial reproductive number associatedwith the within-host transmission of the disease From theabove two expressions in (27) and (28) respectively wetherefore make the following deductions

(i) The epidemiological (between-host) transmission pa-rameters such as the rate at which susceptible humanscome into contact with water contaminated withinfected copepods 120573119867 (through drinking contami-nated water with infected copepods) and the rate atwhich susceptible copepods come into contact withGuinea worm larvae 120573119864 the supply rate of susceptiblehumans Λ119867 and copepods Λ 119864 (through birth) therate at which worms emerge from infected humansto contaminate the physical water environment 120572119865by laying eggs every time infected humans comeinto contact with water sources the rate at whicheggs in physical water environment hatch to produceworm larvae119873119882120572119882 all contribute to the transmission

of Guinea worm disease Therefore control mea-sures such as reducing the rate at which infectedhuman hosts visit water sources when an individualis infected reducing contact rate between susceptiblehumans with contaminated water through educatingthe public and treating water bodies with chemicalsthat kill worm eggs worm larvae and copepods mayhelp to reduce the transmission risk of GWD

(ii) The immunological (within-host) transmission pa-rameters such as the rate at which infected copepodswithin an infected human host release mature worms119873119862120583119862 after digestion by human gastric juice the rateat which mature worms become fertilized femalesworms 1205721198722 and the rate at which mature wormsand females worms die all contribute to the trans-mission of Guinea worm disease Therefore immunemechanisms that kill infected copepods and wormswithin infected human host and also treatment intendto kill bothmature worms and fertilized female wormpopulation may help to reduce the transmission riskof GWD

Therefore both the epidemiological and immunologicalfactors affect the transmission cycle of GWD in both humansand copepod population

42 Local Stability of DFE In this section we determine thelocal stability of DFE of the model system (1) We linearizeequations of the model system (1) in order to obtain aJacobian matrix Then we evaluate the Jacobian matrix of thesystem at the disease-free equilibrium (DFE)

1198640 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (29)


The Jacobian matrix of the model system (1) evaluated atthe disease-free equilibrium state (DFE) is given by

119869 (1198640) =(((((((((((((((((((((((((((

minus120583119867 120572119867 0 0 0 0 0 0 0 minus11986000 minus1199020 0 0 0 0 0 0 0 11986000 0 minus1199021 0 0 0 0 0 0 11986010 0 1198731198621205831198621198660120583119869 minus1199022 0 0 0 0 0 00 0 0 1205721198722 minus1199023 0 0 0 0 00 0 1205721198691198660120583119869 0 0 minus120583119869 0 0 0 00 0 0 0 120572119865 0 minus1199024 0 0 00 0 0 0 0 0 119873119882120572119882 minus120583119871 0 00 0 0 0 0 0 0 minus120573119864Λ 1198641205831198641198710 minus120583119864 00 0 0 0 0 0 0 120573119864Λ 1198641205831198641198710 0 minus1199025

)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)

We consider stability of DFE by calculating the eigenval-ues (120582119904) of the Jacobian matrix given by (30) The character-istic equation for the eigenvalues is given by1205820 [1205826 + 12058711205825 + 12058721205824 + 12058731205823 + 12058741205822 + 1205875120582 + 1205876]= 0 (32)

where1205820 = (minus120583119867 minus 120582) (minus120583119864 minus 120582) (minus120583119869 minus 120582) (minus1199020 minus 120582) (33)

It is clear from (32) that there are four negative eigen-values (minus120583119867 minus120583119864 minus120583119869 and minus1199020) Now in order to make

conclusions about the stability of the DFE we use the Routh-Hurwitz criteria to determine the sign of the remainingeigenvalues of the polynomial1205826 + 12058711205825 + 12058721205824 + 12058731205823 + 12058741205822 + 1205875120582 + 1205876 = 0 (34)

where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)


Using the Routh-Hurwitz stability criterion the equilib-rium state associated with themodel system (1) is stable if andonly if the determinants of all theHurwitzmatrices associatedwith the characteristic equation (34) are positive that is

Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)

The Routh-Hurwitz criterion applied to (37) requires thatthe following conditions (H1)ndash(H6) be satisfied in order toguarantee the local stability of the disease-free equilibriumpoint of the model system (1)

(H1) 1205871 gt 0(H2) 12058711205872 minus 1205873 gt 0(H3) 1205871(12058721205873 + 1205875) gt 12058711205874 + 12058723 (H4) 1205871[1205872(1205873(1205874 + 1205875) + 12058711205876) + (1205871 + 1205874)] gt 1205871[120587221205875 +12058731205876 + 120587112058724] + 120587321205874 + 12058725

(H5) 1205876[1205871(212058721205875 + 1205873(12058711205874 minus 31205875 minus 1205873)) + 120587331205876] +1205875[1205875(212058711205874+12058721205873minus12058711205872(1205872+1)+1205874(120587112058721205873minus120587211205874minus12058723))] gt 0(H6) 12058726[1205871(212058721205875 + 1205873(12058711205874 minus 31205875 minus 1205873)) + 120587331205876] +12058751205876[1205875(212058711205874 + 12058721205873 minus 12058711205872(1205872 + 1) + 1205874(120587112058721205873 minus120587211205874 minus 12058723))] gt 0From (37) we note that all the coefficients 1205871 1205872 12058731205874 1205875 and 1205876 of the polynomial 119875(120582) are greater than zero

whenever 11987720 lt 1 And we also noted that the conditionsabove are satisfied if and only if 11987720 lt 1 Hence all the roots ofthe polynomial 119875(120582) either are negative or have negative realparts The results are summarized in the following theorem

Theorem 1 The disease-free equilibrium point of the modelsystem (1) is locally asymptotically stable whenever 1198770 lt 143 Global Stability of DFE To determine the global stabilityof DFE of the model system (1) we use Theorem 2 in[21] to establish that the disease-free equilibrium is globallyasymptotically stable whenever 1198770 lt 1 and unstable when1198770 gt 1 In this section we list two conditions that if met alsoguarantee the global asymptotic stability of the disease-freestate We write the model system (1) in the form119889119883119889119905 = 119865 (119883 119885) 119889119884119889119905 = 119866 (119883 119885) (38)

where

(i) 119883 = (119878119867 119878119864 119866119869) represents all uninfected compo-nents

(ii) 119885 = (119868119867 119868119862119882119872119882119865 119864119882 119871119882 119868119864) represents all com-partments of infected and infectious components

We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)

denote the disease-free equilibrium (DFE) of the systemTo guarantee global asymptotic stability of the disease-freeequilibrium conditions (H1) and (H2) below must be met[20]

(H1) 119889119883119889119905 = 119865(119883 0) is globally asymptotically stable

(H2) 119866(119883119885) = 119860119885minus119866(119883119885) and119866(119883119885) ge 0 for (119883 119885) isinR10+ where 119860 = 119863119885119866(119883lowast 0) is an119872-matrix and R10+is the region where the model makes biological sense

In our case

119865 (119883 0) = [[[Λ119867 minus 120583119867119878119867Λ 119864 minus 1205831198641198781198641198660 minus 120583119869119866119869 ]]] (40)


Matrix 119860 is given by

119860 =[[[[[[[[[[[[[[[[[[[[[

minus1198860 0 0 0 0 0 120573119867Λ11986711987501205831198670 minus1198861 0 0 0 0 120573119867 (Λ119867 minus 120583119867)12058311986711987500 1198731198621205831198621198660120583119869 minus1198862 0 0 0 00 0 1205721198722 minus1198863 0 0 00 0 0 120572119865 minus1198864 0 00 0 0 0 119873119882120572119882 minus120583119871 00 0 0 0 0 120573119864Λ 1198641198710120583119864 minus1198865

]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[

( Λ1198671205831198671198750 minus 1198781198671198750 + 120598119868119864)120573119867119868119864((Λ119867 minus 120583119867)1205831198671198750 minus (119878119867 minus 1)1198750 + 120598119868119864 )120573119867119868119864 + 119868119862(120583119862(119866119869 minus 1198660120583119869 ) + 120572119862 (1 minus 120583119869))0000( Λ 1198641205831198641198710 minus 1198781198641198710 + 120598119871119882)120573119864119871119882

]]]]]]]]]]]]]]]]]]]

(42)

Assume that 119866119869 = 1198660120583119869 and 120583119869 isin [0 1] It is clear that119866(119883119885) ge 0 for all (119883 119885) isin R10+ since Λ1198671205831198671198750 ge 119878119867(1198750 +120598119868119864) Λ 1198641205831198641198710 ge 119878119864(1198710 + 120598119871119882) and (Λ119867 minus 120583119867)1205831198671198750 ge(119878119867 minus 1)(1198750 + 120598119868119862) provided that Λ119867 gt 120583119867 It is also clearthat 119860 is an 119872-matrix since the off diagonal elements of 119860are nonnegative We state a theorem which summarizes theabove result

Theorem 2 The disease-free equilibrium of model system (1)is globally asymptotically stable if 1198770 le 1 and the assumptions(H1) and (H2) are satisfied

5 The Endemic EquilibriumState and Its Stability

At the endemic equilibriumhumans are infected by copepodsthat have been infected by first-stage larvae (119871119882) Theendemic equilibrium point of the model system (1) given by1198641 = (119878lowast119867 119868lowast119867 119868lowast119862119882lowast119872119882lowast119865 119866lowast119869 119864lowast119882 119871lowast119882 119878lowast119864 119868lowast119864) (43)

satisfies 0 = Λ119867 minus 120582lowast119867119878lowast119867 minus 120583119867119878lowast119867 + 120572119867119868lowast1198670 = 120582lowast119867119878lowast119867 minus (120583119867 + 120575119867 + 120572119867) 119868lowast119867

12 Computational and Mathematical Methods in Medicine0 = 120582lowastℎ119878lowastℎ minus 120583119862119866lowast119869 119868lowast119862 minus 120572119862119868lowast1198620 = 119873119862120583119862119866lowast119869 119868lowast119862 minus (120572119872 + 120583119872)119882lowast1198720 = 1205721198722 119882lowast119872 minus (120583119865 + 120572119865)119882lowast119865 0 = 1198660 + 120572119869119866lowast119869 119868lowast119862 minus 120583119869119866lowast119869 0 = 120572119865119882lowast119865 119868lowastℎ minus (120583119882 + 120572119882) 119864lowast1198820 = 119873119882120572119882119864lowast119882 minus 120583119871119871lowast1198820 = Λ 119864 minus 120582lowast119864119878lowast119864 minus 120583119864119878lowast1198640 = 120582lowast119864119878lowast119864 minus (120583119864 + 120575119864) 119868lowast119864 (44)

for all 119878lowast119867 119868lowast119867 119868lowast119862119882lowast119872119882lowast119865 119866lowast119869 119864lowast119882 119871lowast119882 119878lowast119864 119868lowast119864 gt 0 We there-fore obtain the following endemic values The endemic valueof susceptible humans is given by119878lowast119867 = Λ119867 + 120572119867119868lowast119867(120582lowast119867 + 120583119867) (45)

From (45) we note that the susceptible human populationat endemic equilibrium is proportional to the average timeof stay in the susceptible class and the rate at which newsusceptible individuals are entering the susceptible classeither through birth or through infected individuals whorecover from the disease Individuals leave the susceptibleclass through either infection or death The endemic value ofinfected humans is given by119868lowast119867 = 120582lowast119867119878lowast119867(120583119867 + 120575119867 + 120572119867) (46)

Wenote from (46) that the population of infected humansat the endemic equilibrium point is proportional to theaverage time of stay in the infected class the rate at whichsusceptible individuals become infected and the densityof susceptible individuals The endemic value of infectedcopepods population within a single infected human at theequilibrium point is given by119868lowast119862 = 120582lowast119867 (119878lowast119867 minus 1)(119868lowast119867 + 1) (120583119862119866lowast119869 + 120572119862) (47)

where 119878lowast119867 gt 1 From (47) we note that the average infect-ed copepod population within a single infected human isproportional to the average life-span of infected copepodswithin a single infected human host and the rate of infectionof a single susceptible individual to become infected Wealso note that this expression provides a link between thedynamics of the infected copepods within-host and humanpopulation dynamics The endemic value of mature wormpopulation within a single infected human is given by119882lowast119872 = 119873119862120583119862119866lowast119869 119868lowast119862(120572119872 + 120583119872) (48)

We note from (48) that the population of mature wormswithin a single infected human at endemic equilibrium pointis proportional to the average life-span of mature worms andthe rate at which mature worms are released after infectedcopepods within human host have been killed by humangastric juice The endemic value of fertilized female wormpopulation within a single infected human is given by119882lowast119865 = 12 120572119872119882lowast119872(120572119865 + 120583119865) (49)

The average population of fertilized female worms withinan infected human at endemic equilibrium point is equal tothe average life-span of female worms and the rate at whichmature worms become fertilized female wormsThe endemicvalue of a single human gastric juice is given by119866lowast119869 = 1198660(120583119869 minus 120572119869119868lowast119862) (50)

where 120583119869 gt 120572119869119868lowast119862 The endemic value of Guinea worm eggspopulation in the physical water environment is given by119864lowast119882 = 120572119865119882lowast119865 (119868lowast119867 + 1)(120572119882 + 120583119882) (51)

We note from (51) that the worm egg population atequilibrium point is proportional to the average life-span ofeggs the rate at which each infected human host excretesGuinea worm eggs and the total number of infected humansThe endemic value of Guinea worm larva population in thephysical water environment is given by119871lowast119882 = 119873119882120572119882119864lowast119882120583119871 (52)

We note from (52) that the larvae population at equi-librium point is proportional to the rate at which Guineaworm eggs hatch the number of larvae generated by eachegg and the average life-span of larvae The value of sus-ceptible copepod population at equilibrium point is givenby 119878lowast119864 = Λ 119864(120582lowast119864 + 120583119864) (53)

From (53) we note that susceptible copepod populationat endemic equilibrium is proportional to the average time ofstay in susceptible copepod class and the rate at which newsusceptible copepods are entering the susceptible copepodclass through birth The endemic value of infected copepodpopulation is given by119868lowast119864 = 120582lowast119864119878lowast119864(120575119864 + 120583119864) = 120582lowast119864Λ 119864(120582lowast119864 + 120583119864) (120575119864 + 120583119864) (54)

We note from (54) that infected copepod population atthe endemic equilibrium point is proportional to the averagetime of stay in the infected copepod class the rate at whichsusceptible copepods become infected and the density of sus-ceptible copepods We also make the endemic equilibrium ofthe model system (1) given by expressions (45)ndash(54) depend


on both within-host and between-host disease parame-ters

51 Existence of the Endemic EquilibriumState In this sectionwe present some results concerning the existence of an

endemic equilibrium solution for the model system (1) Todetermine the existence and uniqueness of the endemicequilibriumpoint (EEP) of themodel system (1) we can easilyexpress 119878lowast119867 119868lowast119867 119868lowast119862119882lowast119872119882lowast119865 119864lowast119882 and 119871lowast119882 in terms of 119868lowast119864 in theform

119878lowast119867 (119868lowast119864) = [Λ119867 (1198861 + 1198862119868lowast119864) + 1205721198671198860119868lowast119864] (1198750 + 120598119868lowast119864)(1198861 + 1198862119868lowast119867) [120573119867119868lowast119864 + 120583119867 (1198750 + 120598119868lowast119864)] 119868lowast119867 (119868lowast119864) = 1198860119868lowast1198641198861 + 1198862119868lowast119864 119868lowast119862 (119868lowast119864) = 119868lowast119864 [120573119867 (Λ119867 minus 120583119867) 119885(119886)119864 + 119885(119887)119864 120573119867119868lowast119864](1198750 + 120598119868lowast119864) (120583119862119867119866lowast119869 + 120572119862) (119868lowast119867 + 1)119885(119888)119864

119882lowast119872 (119868lowast119864) = 119873119862120583119862119866lowast119869 119868lowast119864 [120573119867 (Λ119867 minus 120583119867) 119885(119886)119864 + 119885(119887)119864 120573119867119868lowast119864](120572119872 + 120583119872) (1198750 + 120598119868lowast119864) (120583119862119866lowast119869 + 120572119862) (119868lowast119867 + 1)119885(119888)119864 119882lowast119865 (119868lowast119864) = 12 120572119872119873119862120583119862119866lowast119869 119868lowast119864 [120573119867 (Λ119867 minus 120583119867) 119885(119886)119864 + 119885(119887)119864 120573119867119868lowast119864](120572119865 + 120583119865) (120572119872 + 120583119872) (1198750 + 120598119868lowast119864) (120583119862119867119866lowast119869 + 120572119862) (119868lowast119867 + 1)119885(119888)119864 119864lowast119882 (119868lowast119864) = 120572119865120572119872119873119862120583119862119866lowast119869 119868lowast119864 [120573119867 (Λ119867 minus 120583119867) 119885(119886)119864 + 119885(119887)119864 120573119867119868lowast119864]2 (120572119882 + 120583119882) (120572119865 + 120583119865) (120572119872 + 120583119872) (1198750 + 120598119868lowast119864) (120583119862119867119866lowast119869 + 120572119862)119885(119888)119864 119871lowast119882 (119868lowast119864) = 119876119864119866lowast119869(120583119862119866lowast119869 + 120572119862) sdot 120573119867 (Λ119867 minus 120583119867) 119868lowast119864119885(119886)119864 + 119885(119887)119864 120573119867119868lowast2119864(1198750 + 120598119868lowast119864) 119885(119888)119864

(55)

where

119885(119886)119864 = (1198861 + 1198862119868lowast119864) (1198750 + 120598119868lowast119864) 119885(119887)119864 = Λ1198671205721198671198860 (1198750 + 120598119868lowast119864) minus (1198861 + 1198862119868lowast2119864 ) 120573119867119885(119888)119864 = (1198861 + 1198862119868lowast119864) (120573119867119868lowast119864 + 120583119867 (1198750 + 120598119868lowast119864)) 119876119864 = 12 sdot 119873119862120583119862120583119871 sdot 119873119882120572119882(120583119882 + 120572119882) sdot 120572119865(120583119865 + 120572119865)sdot 120572119872(120583119872 + 120572119872)

1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)

Substituting the expression 120582119864 = 120573119864119871119882(1198710 + 120598119871119882)and 119871lowast119882 = 119876119864119866lowast119869 (120583119862119866lowast119869 + 120572119862) sdot ((120573119867(Λ119867 minus 120583119867)119868lowast119864119885(119886)119864 +119885(119887)119864 120573119867119868lowast2119864 )(1198750 + 120598119868lowast119864)119885(119888)119864 ) into (25) we get119868lowast119864ℎ (119868lowast119864) = 119868lowast119864 [1205743119868lowast3119864 + 1205742119868lowast2119864 + 1205741119868lowast119864 + 1205740] = 0 (57)

where

1205743 = 119866lowast119869 (1205831198621198660 + 120583119869120572119862) (120573119864 + 120598120583119864) 11987101205831198641198750120583119867120598120573119864Λ 1198641198660 (120583119862119866lowast119869 + 120572119862) 11987720 [1198862 (120573119867 minus 120583119867) + 1198862 (120573119867 + 120583119867120598) 1205831198641198710 minus 120573119867Λ1198671205721198671198860] gt 01205741 = 119866lowast119869 (1205831198621198660 + 120583119869120572119862) (120573119864 + 120598120583119864) 1198710120583119864 (120583119864 + 120575119867) 11987520120583119867 (1198861 + Λ1198671205721198671198860)120573119864Λ 1198641198660 (120583119862119866lowast119869 + 120572119862) 11987720


+ 1198861 [1 minus 120573119867 (120583119864 + 120575119864) (1205831198621198660 + 120583119869120572119862)1198660 11987720] + 119875012058311986411987101198862 (120573119867 + 120583119867120598)minus 11987101205831198641198750120583119867 (1205831198621198660 + 120583119869120572119862) 119866lowast1198691198660 (120583119862119866lowast119869 + 120572119862) [1198861120598 + 11988621198750 + Λ1198671198660120598(Λ119867 minus 120583119867)]

1205742 = 119861120573119867 (Λ119867 minus 120583119867) [1198861120598 + 11988621198750 + 11988621205831198641198710 (120573119867 + 120598120583119864)(Λ119867 minus 120583119867) ] + 119860120573119867 [120573119867 minus (Λ119867 minus 120583119867) 120598] 1205740 = 120583119864119871012058311986711988611198750 [1 minus 119866lowast119869 (1205831198621198660 + 120583119869120575119862)(120583119862119866lowast119869 + 120572119862)1198660 11987720] minus 119866lowast119869 (1205831198621198660 + 120583119869120572119862) 119871012058311986411987520120583119867120573119867(Λ119867 minus 120583119867) 1198660 (120583119862119866lowast119869 + 120572119862) [120583119867 (120583119867 + 120575119867 + 120572119867) minus Λ2119867120572119867] 11987720119860 = 119876119864119866lowast119869120573119864Λ 119864(120583119862119866lowast119869 + 120572119862) (120583119864 + 120575119864) 119861 = 119876119864119866lowast119869 (120573119864 + 120598120583119864)(120583119862119866lowast119869 + 120572119862)

(58)

We can easily note that (57) gives 119868lowast119864 = 0 whichcorresponds to the disease-free equilibrium andℎ (119868lowast119864) = 1205743119868lowast3119864 + 1205742119868lowast2119864 + 1205741119868lowast119864 + 1205740 = 0 (59)

which corresponds to the existence of endemic equilibriaSolving for 119868lowast119864 in ℎ(119868lowast119864) = 0 the roots of ℎ(119868lowast119864) = 0 aredetermined by using Descartesrsquos rule of sign The variouspossibilities are tabulated in Table 2

We summarize the results in Table 2 in the followingTheorem 3

Theorem 3 The model system (1)

(1) has a unique endemic equilibriumwhenever Cases 1 23 4 5 6 7 and 8 are satisfied and if 1198770 gt 1

(2) could have more than one endemic equilibrium ifCase 8 is satisfied and 1198770 gt 1

(3) could have two endemic equilibria if Cases 3 5 and 7are satisfied

We now employ the center manifold theory [22] to estab-lish the local asymptotic stability of the endemic equilibriumof model system (1)

52 Local Stability of the Endemic Equilibrium Wedeterminethe local asymptotic stability of the endemic steady state ofthe model system (1) by using the center manifold theorydescribed in [22] In our case we use center manifold theoryby making the following change of variables Let 119878119867 = 1199091119868119867 = 1199092 119868119862 = 1199093 119882119872 = 1199094 119882119865 = 1199095 119866119869 = 1199096 119864119882 = 1199097119864119882 = 1199098 119878119864 = 1199099 and 119868119864 = 11990910 We also use the vector

notation x = (1199091 1199092 1199093 1199094 1199095 1199096 1199097 1199098 1199099 11990910)119879 so that themodel system (1) can be written in the form119889x119889119905 = f (x 120573lowast) (60)

where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)

Therefore model system (1) can be rewritten as1 = Λ119867 minus 1205821198671199091 minus 1205831198671199091 + 12057211986711990922 = 1205821198671199091 minus (120583119867 + 120575119867 + 120572119867) 11990923 = 120582119867 (1199091 minus 1)1199092 + 1 minus (1205831198621199096 + 120572119862) 11990934 = 11987311986212058311986211990961199093 minus (120572119872 + 120583119872) 11990945 = 1205721198722 1199094 minus (120583119865 + 120572119865) 11990956 = 1198660 + 12057211986911990961199093 minus 12058311986911990967 = 1205721198651199095 (1199092 + 1) minus (120583119882 + 120572119882) 11990978 = 1198731198821205721198821199097 minus 12058311987111990989 = Λ 119864 minus 1205821198641199099 minus 120583119864119909910 = 1205821198641199099 minus (120583119864 + 120575119864) 11990910

(62)


where 120582119867 = 120573lowast119909101198750 + 12059811990910 120582119864 = 119896120573lowast11990981198710 + 1205981199098 (63)

The method involves evaluating the Jacobian matrix ofsystem (62) at the disease-free equilibrium 1198640 denoted by119869(1198640) The Jacobian matrix associated with the system of(62) evaluated at the disease-free equilibrium (1198640) is givenby

119869 (1198640) =

(((((((((((((((((((((((((((((((

minus120583119867 120572119867 0 0 0 0 0 0 0 minus120573119867Λ11986712058311986711987500 1198870 0 0 0 0 0 0 0 120573119867Λ11986711987501205831198670 0 1198871 0 0 0 0 0 0 120573119867 (Λ119867 minus 120583119867)12058311986711987500 0 1198731198621205831198621198660120583119869 1198872 0 0 0 0 0 00 0 0 1205721198722 1198873 0 0 0 0 00 0 1205721198691198660120583119869 0 0 minus120583119869 0 0 0 00 0 0 0 120572119865 0 1198874 0 0 00 0 0 0 0 0 119873119882120572119882 minus120583119871 0 00 0 0 0 0 0 0 minus120573119864Λ 1198641205831198641198710 minus120583119864 00 0 0 0 0 0 0 120573119864Λ 1198641205831198641198710 0 1198875

)))))))))))))))))))))))))))))))

(64)

where

1198870 = minus (120583119867 + 120575119867 + 120572119867) 1198871 = minus(1205831198621198660 + 120583119869120572119862)120583119869 1198872 = minus (120583119872 + 120572119872)

1198873 = minus (120583119865 + 120572119865) 1198874 = minus (120583119882 + 120572119882) 1198875 = minus (120583119864 + 120572119864) (65)

By using the similar approach from Section 41 the basicreproductive number of model system (62) is

1198770 = radic12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 sdot 120573119867 (Λ119867 minus 120583119867)1198750120583119867 sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (66)

Now let us consider 120573119864 = 119896120573119867 regardless of whether 119896 isin(0 1) or 119896 ge 1 and let 120573119867 = 120573lowast Taking 120573lowast as the bifurcation parameter and if we consider 1198770 = 1 and solve for 120573lowast in (66)we obtain

120573lowast = radic21198710 (120583119864 + 120575119864) 120583119864 (120583119882 + 120572119882) 120583119871 (120583119872 + 120572119872) (120583119865 + 120572119865) (1205831198621198660 + 120572119862120583119869) 11987501205831198671198961205721198651205721198721198731198621205831198621198660119873119882120572119882 (Λ119867 minus 120583119867) Λ 119864 (67)

Note that the linearized system of the transformedequations (62) with bifurcation point 120573lowast has a simple zero

eigenvalue Hence the center manifold theory [22] can beused to analyse the dynamics of (62) near 120573119867 = 120573lowast


Table 2 Number of possible positive roots of ℎ(119868lowast119864) = 0Cases 1205743 1205742 1205741 1205740 Number of

sign changes

Number of possiblereal roots (endemic

equilibrium)1 + + + + 0 02 + + + minus 1 13 + + minus + 2 0 24 + + minus minus 1 15 + minus minus + 2 0 26 + minus minus minus 1 17 + minus + + 2 0 28 + minus + minus 3 1 3

In particular Theorem 41 in Castillo-Chavez and Song[23] reproduced below as Theorem 4 for convenience willbe used to show the local asymptotic stability of the endemicequilibrium point of (62) (which is the same as the endemicequilibrium point of the original system (1) for 120573119867 = 120573lowast)Theorem 4 Consider the following general system of ordinarydifferential equations with parameter 120601119889119909119889119905 = 119891 (119909 120601) 119891 R119899 times R 997888rarr R 119891 C2 (R2 times R) (68)

where 0 is an equilibrium of the system that is 119891(0 120601) = 0 forall 120601 and assume that

(A1) 119860 = 119863119909119891(0 0) = ((120597119891119894120597119909119895)(0 0)) is a linearizationmatrix of themodel system (68) around the equilibrium0 with 120601 evaluated at 0 Zero is a simple eigenvalue of119860 and other eigenvalues of 119860 have negative real parts

(A2) matrix119860 has a right eigenvector 119906 and a left eigenvectorV corresponding to the zero eigenvalue

Let 119891119896 be the 119896th component of 119891 and119886 = 119899sum119896119894119895=1

119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)

The local dynamics of (68) around 0 are totally governed by119886 and 119887 and are summarized as follows

(i) 119886 gt 0 and 119887 gt 0 When 120601 lt 0 with |120601| ≪ 1 0 islocally asymptotically stable and there exists a positiveunstable equilibrium when 0 lt 120601 ≪ 1 0 is unstableand there exists a negative and locally asymptoticallystable equilibrium

(ii) 119886 lt 0 and 119887 lt 0 When 120601 lt 0 with |120601| ≪ 1 0 isunstable when 0 lt 120601 ≪ 1 0 is locally asymptoticallystable and there exists a positive unstable equilibrium

(iii) 119886 gt 0 and 119887 lt 0 When 120601 lt 0 with |120601| ≪ 1 0 isunstable and there exists a locally asymptotically stablenegative equilibrium when 0 lt 120601 ≪ 1 0 is stable anda positive unstable equilibrium appears

(iv) 119886 lt 0 and 119887 gt 0 When 120601 changes from negative topositive 0 changes its stability from stable to unsta-ble Correspondingly a negative unstable equilibriumbecomes positive and locally asymptotically stable

In order to applyTheorem 4 the following computationsare necessary (it should be noted that we are using 120573lowast as thebifurcation parameter in place of 120601 in Theorem 4)

Eigenvectors of 119869120573lowast For the case when1198770 = 1 it can be shownthat the Jacobian matrix of (62) at 120573119867 = 120573lowast (denoted by 119869120573lowast)has a right eigenvector associated with the zero eigenvaluegiven by

u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where

1199061 = 120573lowastΛ11986712058321198671198750 [ 120572119867(120583119867 + 120575119867 + 120572119867) minus 1] 1199062 = 120573lowastΛH(120583119867 + 120575119867 + 120572119867) 1198750120583119867 1199063 = 120573lowast (Λ119867 minus 120583119867)1198750120583119867 120583119869(1205831198621198660 + 120583119869120572119862) 1199064 = 1198731198621205721198621198660(1205831198621198660 + 120583119869120572119862) sdot 120573lowast (Λ119867 minus 120583119867)1198750120583119867 (120583119872 + 120572119872) 1199065 = 1205721198722 (120583119872 + 120572119872) (120583119865 + 120572119865) 1198731198621205831198621198660(1205831198621198660 + 120583119869120572119862)sdot 120573lowast (Λ119867 minus 120583119867)1198750120583119867 1199066 = 1205721198691198660120583119869 (1205831198621198660 + 120583119869120572119862) sdot 120573lowast (Λ119867 minus 120583119867)1198750120583119867 1199067 = 1205721198721205721198652 (120583119872 + 120572119872) (120583119865 + 120572119865) 1198731198621205831198621198660(1205831198621198660 + 120583119869120572119862)sdot 120573lowast (Λ119867 minus 120583119867)1198750120583119867 1(120583119882 + 120572119882) 1199068 = 1205721198721205721198652 (120583119872 + 120572119872) (120583119865 + 120572119865) 1198731198621205831198621198660(1205831198621198660 + 120583119869120572119862)sdot 120573lowast (Λ119867 minus 120583119867)1198750120583119867 119873119882120572119882120583119871 (120583119882 + 120572119882)


1199069 = minus 1205721198721205721198652 (120583119872 + 120572119872) (120583119865 + 120572119865) 1198731198621205831198621198660(1205831198621198660 + 120583119869120572119862)sdot 120573lowast2 (Λ119867 minus 120583119867)1198750120583119867 119873119882120572119882120583119871 (120583119882 + 120572119882) sdot 119896Λ 11986411987101205832119864 11990610 = 1(71)

In addition the left eigenvector of the Jacobian matrix in(64) associated with the zero eigenvalue at 120573119867 = 120573lowast is givenby

k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)

whereV1 = 0V2 = 0V3 = 1V4 = 120573lowast2 (Λ119867 minus 120583119867)1205831198671198750 sdot 1205721198651205721198722 (120583119865 + 120572119865) (120583119872 + 120572119872)sdot 119873119882120572119882120583119871 (120583119882 + 120572119882) sdot 119896Λ 119864120583119864 (120583119864 + 120575119864) 1198710 V5 = 120573lowast2 (Λ119867 minus 120583119867)1205831198671198750 sdot 120572119865(120583119865 + 120572119865) sdot 119873119882120572119882120583119871 (120583119882 + 120572119882)sdot 119896Λ 119864120583119864 (120583119864 + 120575119864) 1198710 V6 = 0V7 = 120573lowast2 (Λ119867 minus 120583119867)1205831198671198750 sdot 119873119882120572119882120583119871 (120583119882 + 120572119882)sdot 119896Λ 119864120583119864 (120583119864 + 120575119864) 1198710 V8 = 120573lowast2 (Λ119867 minus 120583119867)1205831198671198750 sdot 1120583119871 sdot 119896Λ 119864120583119864 (120583119864 + 120575119864) 1198710 V9 = 0V10 = 120573lowast (Λ119867 minus 120583119867)(120583119864 + 120575119864) 1205831198671198750

(73)

Computation of Bifurcation Parameters 119886 and 119887 We evaluatethe nonzero second-order mixed derivatives of f with respectto the variables and 120573lowast in order to determine the signsof 119886 and 119887 The sign of 119886 is associated with the followingnonvanishing partial derivatives of f 12059721198911120597119909210 = 2120598120573lowastΛ11986711987520120583119867 12059721198912120597119909210 = minus2120598120573lowastΛ11986711987520120583119867

12059721198913120597119909210 = minus2120598120573lowast (Λ119867 minus 120583119867)11987520120583119867 1205972119891912059711990928 = 2120598119896120573lowastΛ 11986411987120120583119864 12059721198911012059711990928 = minus2120598119896120573lowastΛ 11986411987120120583119864 (74)

The sign of 119887 is associated with the following nonvanish-ing partial derivatives of f 1205972119891112059711990910120597120573lowast = minus Λ1198671205831198671198750 1205972119891212059711990910120597120573lowast = Λ1198671205831198671198750 1205972119891312059711990910120597120573lowast = (Λ119867 minus 120583119867)1205831198671198750 120597211989191205971199098120597120573lowast = minus 119896Λ 1198641205831198641198710 1205972119891101205971199098120597120573lowast = 119896Λ 1198641205831198641198710

(75)

Substituting expressions (71) (73) and (74) into (69) weget

119886 = 1199061V210 12059721198911120597119909210 + 1199062V210 12059721198912120597119909210 + 1199063V210 12059721198913120597119909210 + 1199069V28 1205972119891912059711990928+ 11990610V28 12059721198911012059711990928= 1199061V210 [2120598120573lowastΛ11986711987520120583119867 ] + 1199062V210 [minus2120598120573lowastΛ11986711987520120583119867 ]+ 1199063V210 [minus2120598120573lowast (Λ119867 minus 120583119867)11987520120583119867 ]+ 1199069V28 [2120598119896120573lowastΛ 11986411987120120583119864 ] + 11990610V28 [minus2120598119896120573lowastΛ 11986411987120120583119864 ]

= 2120598120573lowastΛ11986711987520120583119867 sdot V210 [1199061 minus 1199062]minus 1199063V210 [2120598120573lowast (Λ119867 minus 120583119867)11987520120583119867 ] + 2120598119896120573lowastΛ 11986411987120120583119864sdot V28 [1199069 minus 11990610]lt 0

(76)

since (1199061 minus 1199062) lt 0 (1199069 minus 11990610) lt 0 1199063 gt 0 and V10 gt 0


Similarly substituting expressions (71) and (73) and (75)into (69) we get119887 = 1199061V10 1205972119891112059711990910120597120573lowast + 1199062V10 1205972119891212059711990910120597120573lowast + 1199063V10 120597211989131205971199098120597120573lowast+ 1199069V8 1205972119891912059711990910120597120573lowast + 11990610V8 1205972119891101205971199098120597120573lowast= V10 [ Λ1198671198750120583119867 sdot 1199062 minus Λ1198671198750120583119867 sdot 1199061 + (Λ119867 minus 120583119867)1198750120583119867 sdot 1199063]

+ 119896Λ 1198641198710120583119864 sdot V8 [11990610 minus 1199069]= Λ1198671198750120583119867 V10 [1199062 minus 1199061] + (Λ119867 minus 120583119867)1198750120583119867 V101199063+ 119896Λ 1198641198710120583119864 V8 [11990610 minus 1199069]gt 0

(77)

since (1199062 minus 1199061) gt 0 (11990610 minus 1199069) gt 0 1199063 gt 0 and V10 gt 0Thus 119886 lt 0 and 119887 gt 0 Using Theorem 4 item (iv)

we have established the following result which only holds for1198770 gt 1 but close to 1Theorem 5 The endemic equilibrium guaranteed byTheorem3 is locally asymptotically stable for 1198770 gt 1 near 16 Sensitivity Analysis

In this section we carry out sensitivity analysis to evaluatethe relative change in basic reproduction number (1198770) whenthe within-host and between-host parameters as well as theenvironmental parameters of the model system (1) changeWe used the normalized forward sensitivity index of the basicreproduction number 1198770 of the model system (1) to eachof the model parameters The normalized forward sensitivityindex of a variable to a parameter is typically defined as ldquotheratio of the relative change in the variable to the relativechange in the parameterrdquo [24] In this case if we let 1198770be a differentiable function of the parameter 119906 then thenormalized forward sensitivity index of 1198770 at 119906 is defined asΥ1198770119906 = 1205971198770120597119906 times 1199061198770 (78)

where the quotient 1199061198770 is introduced to normalize thecoefficient by removing the effect of units [25] For examplethe sensitivity index of1198770 with respect to the human infectionrate 120573119867 is given byΥ1198770

120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)

It can be easily noted that the sensitivity index of 1198770with respect to the parameter 120573119867 does not depend on anyof the parameter values The indices of worm larvae death

rate within a host and copepods death rate in the physicalenvironment are respectively given byΥ1198770120583119865 = minus12 120583119865(120583119865 + 120572119865) = minus05

Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)

Using (78)ndash(80) similar expressions can be derived forthe remaining parametersThe resulting sensitivity indices of1198770 to the different model parameters are shown in Table 3We see from (78)ndash(80) that the index of parameter 120573119867is positive and indexes of both parameters 120583119871 and 120583119864 arenegative The sign of the index value indicates whether theparameter increases the reproduction number or reduces thereproduction number Therefore increasing human infectionrate 120573119867 reduces 1198770 and also increasing 120583119871 or 120583119864 reduces 1198770Based on the results shown in Table 3 we observe that thereproduction number 1198770 is sensitive to the changes of boththe within-host and between-host parameters as well as theenvironmental parameters (parameters which can be modi-fied by environmental conditions which impact on survivaland reproduction of the parasite and vector populations)More specifically we deduce the following results for thebetween-host scale

(i) The reproductive number is most sensitive to thechanges of parameter 120583119864 and the natural death rateof copepods in the physical water environment Thisimplies that interventions focused on vector controlhave highest impact on GWD control Since Υ1198770120583119864 =minus09991 increasing 120583119864 by 10 decreases the repro-duction number by 9991 Therefore increasing thedeath rate of copepods by using chemical such asABATE or temephos will eventually reduce the trans-mission of Guinea worm disease

(ii) The reproductive number also shows significant sen-sitivity to 120573119867 and 120573119864 since Υ1198770120573119867 = Υ1198770

120573119864= 05 This

implies that reducing human infection rates 120573119867 and120573119864 by 10 reduces 1198770 by 5 for each of theseparameters Therefore health education to ensurethat greater numbers of individuals and communi-ties adopt behavioural practices such as voluntaryreporting ofGWDcases prevention ofGWDpatientsfrom entering drinking water bodies regular use ofwater from safe water sources and in the absence ofsuch water sources filtering or boiling water beforedrinking aimed at preventing transmission of GWDwould have high impact in complementing vectorcontrol in elimination of GWD

(iii) Similarly Υ1198770120572119865 = 04639 This implies that reducingthe rate at which eggs are excreted in the physicalwater environment 120572119865 by 10 reduces 1198770 by 4639Therefore educating people about GWD (ie teach-ing people not to immerse their infected feet intothe drinking water when the fertilized female wormis emerging out from their feet or to always filter


Table 3 Sensitivity indices ofmodel reproductionnumber1198770 to parameters formodel system (1) evaluated at the parameters values presentedin Tables 4ndash6

Parameter DescriptionSensitivity indexwith positive

sign

Sensitivity indexwith negative

sign120583119864 Natural decay rate of copepods in the water environment minus09991120572119862 Natural decay rate of copepods within human host minus04853120583119862 Release rate of mature worms within human host minus04853Λ119867 Human birth rate +050013120573119867 Human infection rate +05119873119882 Fecundity rate of worm larvae in the environment +05120583119871 Natural decay rate of Guinea worm larvae minus051198710 Larvae saturation constant minus05119873119862 Fecundity rate of mature worm +05Λ 119864 Copepods birth rate +05120573119864 Copepods infection rate +051198750 Copepods saturated constant minus05120572119867 Human recovery minus04998120583119865 Natural decay rate of fertilized female worms minus04639120572119865 Migration rate of fertilized female worms to surface of hostrsquos skin +04639120583119882 Natural decay rate of worm eggs in the water environment minus04545120572119882 Worm egg hatching rate +04545120583119872 Natural decay rate of mature worms within human host minus025120572119872 Migration rate of mature worms to subcutaneous tissues +025120583119869 Dilutiondegradation rate of gastric juice minus001471198660 Supply rate of gastric juice from the source of the body +00147120575119864 Induced decay rate of copepods in the water environment minus0000894Table 4 Human host parameter values used in simulations

Parameter Description Initial values Units SourceΛ119867 Human birth rate 01013 People dayminus1 [14]120573119867 Human infection rate 01055 Copepod dayminus1 Estimated120583119867 Human natural death rate 2548 times 10minus5 Dayminus1 [15 16]120572119867 Human recovery rate 003 Dayminus1 Estimated120575119867 GWD induced death rate 4 times 10minus8 Dayminus1 Estimated

Table 5 Within-host parameter values of the model system (1)

Parameter Description Initial values Units Source119873119862 Fecundity rate of mature worms 700 People Estimated120583119862 Decay rate of copepods within a human host due to gastric juice 099 Copepod dayminus1 Estimated120572119862 Natural death rate of copepods within a human host 0001 Dayminus1 Estimated120583119872 Natural decay rate of mature worms within a human host 09 Dayminus1 Estimated120572119872 Migration rate of mature worms to subcutaneous tissues 09 Dayminus1 Estimated120583119865 Natural death rate of fertilized female worms within a human host 09 Dayminus1 Estimated120572119865 Migration rate of fertilized female worms to surface of skin 007 Dayminus1 Estimated120583119869 Dilutiondegradation rate of gastric juice 005 Dayminus1 Estimated120572119869 Proliferation rate of gastric juice due to infection 04 Dayminus1 Estimated1198660 Supply rate of gastric juice from within a human body 15 Dayminus1 Estimated


Table 6 Free-living pathogens and their associated environmental parameter values used in simulations

Parameter Description Initial value Units SourceΛ 119864 Copepods birth rate 075 Copepod dayminus1 Estimated120573119864 Copepods infection rate 07 Larvae dayminus1 Estimated120583119864 Natural decay rate of copepods 0005 Dayminus1 [15 16]120575119864 Disease induced death rate of copepods 9 times 10minus6 Dayminus1 Estimated1198750 Copepods saturation constant 20 0000 Dayminus1 [15 16]120583119882 Natural decay rate of Guinea worm eggs 0333 Dayminus1 [15 16]120572119882 Hatching rate of worm eggs 0009 Dayminus1 Estimated119873119882 Number of Guinea worm larvae hatched 300 Larvae egg minus1 dayminus1 Estimated120583119871 Natural decay rate of Guinea worm larvae 00333 Dayminus1 [15 16]1198710 Larvae saturation constant 5000000 Dayminus1 [15 16]120598 Limitation growth rate 00991 Dayminus1 Estimated

contaminated water before drinking the water) willreduce the transmission of the disease

Further we also deduce the following results for thewithin-host scale

(i) The development of a drug that would kill matureworms within human host would have significantbenefits at within-host However the drugwould haveeven higher impact if it would kill fertilized femaleworms

(ii) The development of interventions that would increasethe supply rate of gastric juice would have no benefitsin the control of GWD

Therefore the lack of drugs to treat GWD has delayedprogress in eliminating GWD

7 Numerical Analysis

The behaviour of model system (1) was investigated usingnumerical simulations using a Python program version V 26on the Linux operation system (Ubuntu 1404) The programuses a package odeint function in the scipyintegrate forsolving a system of differential equations The behaviour ofthe system model (1) was simulated in order to illustrate theanalytical results we obtained in this paper We used param-eter values presented in Tables 4ndash6 Some of the parametervalues used in the numerical simulations are from publishedliterature while others were estimated as values of someparameters are generally not reported in literatureThe initialconditions used for simulations are given by 119878119867(0) = 2500119868119867(0) = 10 119868119862(0) = 0 119866119869(0) = 150119882119872(0) = 0119882119865(0) = 0119878119864(0) = 100000 119868119864(0) = 0 119864119882(0) = 0 and 119871119882(0) = 50000

Figure 2 illustrates the solution profile of the populationof (a) infected humans (b) infected copepods in the physicalwater environment (c) worm eggs in the physical waterenvironment and (d) worm larvae in the physical waterenvironment for different values of the infection rate ofhumans 120573119867 120573119867 = 01055 120573119867 = 055 and 120573119867 = 09The numerical results show that higher rates of infection atthe human population level result in increased population ofparasites (worm eggs and worm larvae) in the physical water

environment and a noticeable increase in infected copepodpopulation in the physical water environment Thereforehuman behavioural changes which reduce contact withcontaminated water bodies through drinking contaminatedwater reduce transmission of the disease at both human andcopepod population level

Figure 3 illustrates the solution profile of the populationof (a) infected humans (b) infected copepods in the physicalwater environment (c) worm eggs in the physical waterenvironment and (d) worm larvae in the physical waterenvironment for different values of natural death rate ofcopepod population in the physical water environment 120583119864120583119864 = 0005 120583119864 = 005 and 120583119864 = 05 The results show thatenvironmental conditions which increase death of copepodsaffect transmission of the disease in the human populationIncreased death of copepod population reduces transmissionrisk of the disease at humans population therefore anymech-anisms which enhance the killing of copepod population inthe physical water environment reduces transmission risk ofGWD within disease endemic communities

Figure 4 shows graphs of numerical solutions of modelsystem (1) showing propagation of (a) population of infectedhumans (119868119867) (b) population of infected copepods (119868119864)(c) population of Guinea worm eggs in the physical waterenvironment and (d) population of Guinea worm larvae inthe physical water environment for different values of naturaldeath rate of Guinea worm eggs in the physical waterenvironment 120583119882 120583119882 = 0005 120583119882 = 05 and 120583119882 = 09The results show that the environmental conditions whichenhance death of worm eggs affect transmission of GWDin the human population Increased death of worm eggpopulation reduces transmission risk of the disease at humanpopulation level Therefore any mechanisms which enhancethe killing of worm egg population in the physical waterenvironment reduce transmission risk of the disease withinGWD endemic communities

Figure 5 shows graphs of numerical solutions of modelsystem (1) showing propagation of (a) population of infectedhumans (119868119867) (b) population of infected copepods (119868119864) (c)population of Guinea worm eggs and (d) population ofGuinea worm larvae in the physical water environment fordifferent values of natural death rate ofGuineaworm larvae in


H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)

Figure 2 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of infected humans (119868119867) (b)population of infected copepods (119868119864) (c) population of Guinea worm eggs in the physical water environment and (d) population of Guineaworm larvae in the physical water environment for different values of the infection rate of humans 120573119867 120573119867 = 01055 120573119867 = 055 and 120573119867 = 09

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)

Figure 3 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of infected humans (119868119867) (b)population of infected copepods (119868119864) (c) population of Guinea worm eggs in the physical water environment and (d) population of Guineaworm larvae in the physical water environment for different values of natural death rate of copepods 120583119864 120583119864 = 0005 120583119864 = 005 and 120583119864 = 05


W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)

(d)Figure 4 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of infected humans (119868119867)(b) population of infected copepods (119868119864) (c) population of Guinea worm eggs in the physical water environment and (d) population ofGuinea worm larvae in the physical water environment for different values of natural death rate of Guinea worm eggs in the physical waterenvironment 120583119882 120583119882 = 0005 120583119882 = 05 and 120583119882 = 09

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)

(d)Figure 5 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of infected humans (119868119867) (b)population of infected copepods (119868119864) (c) population of Guinea worm eggs and (d) population of Guinea worm larvae in the physical waterenvironment for different values of natural death rate of Guinea worm larvae in the physical water environment 120583119871 120583119871 = 0005 120583119871 = 05and 120583119871 = 09


M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)

(d)Figure 6 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of infected humans (119868119867) (b)population of infected copepods (119868119864) (c) population of Guinea worm eggs in the physical water environment and (d) population of Guineaworm larvae in the physical water environment for different values of natural death rate of mature worms inside a single infected humanhost 120583119872 120583119872 = 09 120583119872 = 009 and 120583119872 = 0009the physical water environment 120583119871 120583119871 = 0005 120583119871 = 05 and120583119871 = 09 The results show that the environmental conditionswhich increase death of worm larvae reduce transmission ofGWD in the human population Increased death of wormlarvae population reduces transmission risk of the disease athuman population level Therefore any interventions whichenhance the killing of worm larvae population in the physicalwater environment reduce transmission risk of GWD withinthe human population

Figure 6 shows graphs of numerical solution of modelsystem (1) showing propagation of (a) population of infectedhumans (119868119867) (b) population of infected copepods (119868119864)(c) population of Guinea worm eggs in the physical waterenvironment and (d) population of Guinea worm larvae inthe physical water environment for different values of naturaldeath rate of mature worms inside a single infected humanhost 120583119872 120583119872 = 09 120583119872 = 009 and 120583119872 = 0009 The resultsshow that the within-host process of death of mature wormsaffects transmission of the disease in the human populationlevel Increased death of mature worm population within aninfected human host reduces transmission risk of the diseaseat humanpopulation levelTherefore any interventionswhichenhance the killing of mature worm population inside aninfected human host reduce transmission risk of the diseasewithin communities

Figure 7 shows graphs of numerical solution of modelsystem (1) showing propagation of (a) population of infectedhumans (119868119867) (b) population of infected copepods (119868119864)

(c) population of Guinea worm eggs and (d) populationof Guinea worm larvae in the physical water environmentfor different values of natural death rate of fertilized femaleworms inside a single infected human host 120583119865 120583119865 = 09 120583119865 =009 and 120583119865 = 0009 The results show that the within-hostprocesses which increase the death of fertilized female wormscan be a potent control measure for GWD Increased death offertilized female worms within infected human hosts reducestransmission risk of the disease at human population levelTherefore any interventions which enhance the killing offertilized female worm population inside an infected humanhost reduce transmission risk of GWD within a commu-nity

Figure 8 illustrates the solution profiles of the populationof (a) infected humans (119868119867) (b) infected copepods (119868119864) in thephysical water environment (c) worm eggs in the physicalwater environment and (d) worm larvae in the physicalwater environment for different values of the rate of wormlarvae fecundity 119873119882 119873119882 = 30 119873119882 = 300 and 119873119882 =30000 The results show that an increase of worm larvaeproduced per day by worm eggs increases the transmission ofthe disease Therefore any interventions which reduce wormlarvae fecundity in the physical water environment reduce thetransmission risk of the disease in the community

Figure 9 shows graphs of numerical solution of modelsystem (1) showing the propagation of the population of (a)infected humans (119868119867) (b) population of infected copepods(119868119864) (c) worm eggs in the physical water environment and


F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)

(d)Figure 7 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of infected humans (119868119867) (b)population of infected copepods (119868119864) (c) population of Guinea worm eggs and (d) population of Guinea worm larvae in the physical waterenvironment for different values of natural death rate of fertilized female worm within a single infected human host 120583119865 120583119865 = 09 120583119865 = 009and 120583119865 = 0009

NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)

(d)Figure 8 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of infected humans (119868119867)(b) population of infected copepods (119868119864) (c) population of Guinea worm eggs in the physical water environment and (d) population ofGuinea worm larvae in the physical water environment for different values of Guinea worm larvae fecundity119873119882119873119882 = 30119873119882 = 300 and119873119882 = 30000


F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)

Figure 9 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of infected humans (119868119867) (b)population of infected copepods (119868119864) (c) population of Guinea worm eggs in the physical water environment and (d) population of Guineaworm larvae in the physical water environment for different values of the rate at which an emerging fertilized female worm from a singleinfected human host excretes eggs into the physical water environment 120572119865 120572119865 = 0007 120572119865 = 007 and 120572119865 = 07(d) worm larvae in the physical water environment fordifferent values of the rate at which an emerging fertilizedfemale worm from a single infected human host excretesnumber of eggs into the physical water environment 120572119865 120572119865 =0007 120572119865 = 007 and 120572119865 = 07 The results show that higherrate of excretion of worm eggs by each infected human hostresults in increased population of parasites (worm eggs andworm larvae) in the physical water environment and a notice-able increase in infected copepods Therefore improvementsin individual sanitation (which reduce contamination ofwater source with human eggs) are good for the communitybecause they reduce the risk of the disease transmission in thecommunity

Figure 10 demonstrates numerical solutions showing thepropagation of the population of (a) mature worm withininfected human host and (b) population of fertilized femaleworm within infected human host for different values of theinfection rate of humans 120573119867 120573119867 = 01055 120573119867 = 001055120573119867 = 0001055 and 120573119867 = 055 The results show the influ-ence of between-host disease process on within-host diseaseprocess of Guinea wormdisease Here as transmission rate ofGWD in the community increases the within-host infectionintensity of the disease also increases The numerical resultsdemonstrate that the transmission of the disease at thepopulation level influences the dynamics within an infectedindividual Therefore human behavioural changes (such asfiltering water before drinking) which reduce contact with

infected copepods reduce infection intensity at individuallevel Equally good sanitation by community which reducescontamination of water bodies reduces the intensity of infec-tion of humans at individual level

Figure 11 illustrates the graphs of numerical solutionsshowing the propagation of the population of (a) matureworm within infected human host and (b) population offertilized female worm within infected human host fordifferent values of the natural death rate of copepods in thephysical water environment 120583119864 120583119864 = 0005 120583119864 = 005 and120583119864 = 05The results demonstrate the potency of public healthinterventions intended to reduce copepods population (suchas killing copepods using temephos or boiling the water) onthe infection intensity within an infected individual

Figure 12 illustrates the graphs of numerical solutionsshowing the propagation of the population of (a) matureworm within infected human host and (b) population offertilized female worm within infected human host fordifferent values of the natural death rate of worm larvaein the physical water environment 120583119871 120583119871 = 0005 120583119871 =005 and 120583119871 = 05 The results demonstrate the influenceof public health interventions intended to reduce wormlarvae population in the physical water environment (such asdestroying worm larvae using chemicals or boiling the water)on the infection intensity within an infected individualOverall the numerical results verify the following aspectsabout GWD transmission dynamics


훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)

Figure 10 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of mature worm withininfected human host and (b) population of fertilized female worm within infected human host for different values of the infection rate ofhumans 120573119867 120573119867 = 01055 120573119867 = 001055 120573119867 = 0001055 and 120573119867 = 055

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)

Figure 11 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of mature worm withininfected human host and (b) population of fertilized female worm within infected human host for different values of the natural death rateof copepods 120583119864 120583119864 = 0005 120583119864 = 005 and 120583119864 = 05


500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)

Figure 12 Graphs of numerical solutions of model system (1) showing the evolution with time of (a) population of mature worm withininfected human host and (b) population of fertilized female worm within infected human host for different values of natural death rate ofworm larvae in the physical water environment 120583119871 120583119871 = 0005 120583119871 = 005 and 120583119871 = 05

(i) Higher rates of infection at the human populationlevel result in increased population of parasites (wormeggs and worm larvae) in the physical water environ-ment and a noticeable increase in infected copepodpopulation in the physical water environment

(ii) Interventions which increase death of copepodsthrough enhanced killing of copepod population inthe physical water environment reduce transmissionrisk of GWD within a disease endemic communities

(iii) Interventions which enhance death of worm eggsthrough enhanced killing of worm egg population inthe physical water environment reduce transmissionrisk of the disease within GWD endemic communi-ties

(iv) Health interventions which increase death of wormlarvae in the physical water environment reducetransmission risk of GWD within the human popu-lation

(v) Within-host scale interventions which increase deathof mature worm population inside an infected humanhost reduce transmission risk of the disease withincommunities

(vi) Within-host scale interventions which increase thedeath of fertilized female worms can also be a potentcontrolmeasure forGWD through reduced transmis-sion risk of GWD within a community

(vii) An increase in worm fecundity with an infectedhuman host has considerable impact on the transmis-sion of GWD

(viii) Higher rate of contamination of the physical waterenvironment through excretion of worm eggs by eachinfected human host results in increased populationof parasites (worm eggs and worm larvae) in thephysical water environment and a noticeable increasein infected copepods

(ix) Transmission of the GWD shows reciprocal influenceof within-host scale interventions (medical interven-tions) and between-host scale interventions (publichealth interventions) Therefore human behaviouralchanges (such as filtering water before drinking)which reduce contact with infected copepods reduceinfection intensity at individual level Equally goodsanitation by community which reduces contamina-tion of water bodies reduces the intensity of infectionof humans at individual level

8 Conclusions

Guinea worm disease like most neglected parasitic diseasesurgently needs renewed attention and sustainable interven-tions in AfricaThe limited scientific knowledge about GWDrepresents a challenge to the successful elimination of thedisease In this paper we have sought to identify a broadrange of within-host and between-host processes that should


be better understood if GWD is to be eliminated A mul-tiscale model of GWD transmission dynamics is presentedThe multiscale model is shown to be mathematically andepidemiologically well-posed Sensitivity analyses of the basicreproduction number to the variation of model parameterswere carried out The sensitivity results of the reproductionnumber show that between-host model parameters (such asinfection rate of human host 120573119867 and supply rate of humansΛ119867) within-host model parameters (such as excretion rateof eggs 120572119865 into the physical water environment by eachinfected human host fecundity rate of mature worm 119873119862decay rate of mature worms 120583119872 migration rate of matureworms to the subcutaneous tissue 120572119872 and decay rate offertilized worms 120583119865) and environmental model parameters(such as the production rate of larvae per egg worm perday 120572119882 fecundity of larvae 119873119882 generated by eggs deathrate of egg worms 120583119882 larva worms 120583119871 in the physical waterenvironment supply rate of copepods Λ 119864 and decay rateof copepods 120583119864) all are responsible for the transmissiondynamics of Guinea worm disease within the communityTherefore reducing the infection rate of human excretion rateof eggs into physical water and the population of parasites(worm eggs and worm larvae) as well as population of vectorhost (copepods) in the physical water environment couldeventually contribute in eradicating GWD completely fromthe community

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors acknowledge financial support from SouthAfrica National Research Foundation (NRF) Grant no IPRR(UID 81235) and partial financial support from the SouthernAfrican Systems Analysis Centre

References

[1] S K Diamenu and A A Nyaku ldquoGuinea worm disease - Achance for successful eradication in the Volta region GhanardquoSocial Science and Medicine vol 47 no 3 pp 405ndash410 1998

[2] SWatts ldquoPerceptions and priorities in disease eradication dra-cunculiasis eradication in Africardquo Social Science and Medicinevol 46 no 7 pp 799ndash810 1998

[3] R Muller ldquoGuinea worm disease -The final chapterrdquo Trends inParasitology vol 21 no 11 pp 521ndash524 2005

[4] J M Hunter ldquoAn introduction to guinea worm on the eve of itsdeparture dracunculiasis transmission health effects ecologyand controlrdquo Social Science and Medicine vol 43 no 9 pp1399ndash1425 1996

[5] B J Visser ldquoDracunculiasis eradication - Finishing the jobbefore surprises ariserdquo Asian Pacific Journal of Tropical Medi-cine vol 5 no 7 pp 505ndash510 2012

[6] G Biswas D P Sankara J Agua-Agum and A Maiga ldquoDra-cunculiasis (guinea worm disease) eradication without a drugor a vaccinerdquo Philosophical transactions of the Royal Society

of London Series B Biological sciences vol 368 no 1623 p20120146 2013

[7] S Cairncross A Tayeh and A S Korkor ldquoWhy is dracunculia-sis eradication taking so longrdquo Trends in Parasitology vol 28no 6 pp 225ndash230 2012

[8] N C Iriemenam W A Oyibo and A F Fagbenro-BeyiokuldquoDracunculiasis - The saddle is virtually endedrdquo ParasitologyResearch vol 102 no 3 pp 343ndash347 2008

[9] HWHethcote ldquoThemathematics of infectious diseasesrdquo SIAMReview vol 42 no 4 pp 599ndash653 2000

[10] W Garira ldquoThe dynamical behaviours of diseases in Africardquo inIn Handbook of Systems and Complexity in Health pp 595ndash623Springer New York 2013

[11] M A Nowak and R M May Virus Dynamics MathematicsPrinciples of Immunology andVirology OxfordUniversity PressLondon UK 2000

[12] G Magombedze W Garira and E Mwenje ldquoModellingthe human immune response mechanisms to Mycobacteriumtuberculosis infection in the lungsrdquo Mathematical Biosciencesand eNgineering vol 3 no 4 pp 661ndash682 2006

[13] W Garira D Mathebula and R Netshikweta ldquoA mathematicalmodelling framework for linked within-host and between-host dynamics for infections with free-living pathogens in theenvironmentrdquo Mathematical Biosciences vol 256 pp 58ndash782014

[14] J S Robert C Patrick H James and D Alex ldquoA MathematicalModel for the eradication of Guinea worm diseaserdquo Under-standing the dynamics of emerging and re-emerging infectiousdiseases using mathematical models pgs pp 133ndash156 2012

[15] M O Adewole ldquoA Mathematical Model of Dracunculiasis Epi-demic and Eradicationrdquo IOSR Journal ofMathematics vol 8 no6 pp 48ndash56 2013

[16] L Kathryn ldquoGuinea worm disease (Dracunculiasis) Openinga mathematical can of wormsrdquo Tech Rep Bryn Mawr CollegePennsylvania 2012

[17] B Hellriegel ldquoImmunoepidemiology - Bridging the gapbetween immunology and epidemiologyrdquo Trends in Parasitol-ogy vol 17 no 2 pp 102ndash106 2001

[18] D M Vickers and N D Osgood ldquoA unified framework ofimmunological and epidemiological dynamics for the spreadof viral infections in a simple network-based populationrdquoTheoretical Biology and Medical Modelling vol 4 article no 492007

[19] C Greenaway ldquoDracunculiasis (guinea worm disease)rdquo CMAJvol 170 no 4 pp 495ndash500 2004

[20] C Castillo-Chavez Z Feng and W Huang ldquoOn the compu-tation of R0 and its role in global stability In MathematicalApproaches for Emerging and Re-emerging Infectious DiseasesPart 1 An Introduction toModels Methods andTheoryrdquo inTheIMA Volumes in Mathematics and Its Applications C Castillo-Chavez S Blower P van den Driessche and and D KirschnerEds vol 125 pp 229ndash250 Springer-Verlag Berlin 125 2002

[21] P J Van den Driessche and P J Watmough ldquoReproductionnumbers and sub-threshold endemic equilibria for compart-mental models of disease transmissionrdquo Mathematical bio-sciences vol 180 no 1 pp 29ndash48 2002

[22] J Carr Applications of Centre Manifold Theory Springer NewYork NY USA 1981

[23] C Castillo-Chavez and B Song ldquoDynamical models of tuber-culosis and their applicationsrdquo Mathematical Biosciences andEngineering (MBE) vol 1 no 2 pp 361ndash404 2004


[24] N Chitnis J M Hyman and J M Cushing ldquoDeterminingimportant parameters in the spread of malaria through thesensitivity analysis of a mathematical modelrdquo Bulletin of Math-ematical Biology vol 70 no 5 pp 1272ndash1296 2008

[25] H J B Njagavah and F Nyambaza ldquoModelling the impact ofrehabitation amelioration and relapse on the prevalence of drugepidemics Journal of Biology SystemsrdquoVol vol 21 article no 12012

Submit your manuscripts athttpswwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


by rolling it over an ordinary stick or matchstick [1 3]and ensuring that the patient receives care by cleaningand bandaging the wound until all the worms areextracted from the patient This process may take upto two months to complete as the worm can grow upto a meter in length and only 1-2 centimeters can beremoved per day [4 5]

(c) Vector control This consists of killing the copepodsin water (the intermediate host) by applying a chem-ical called temephos an organophosphate to unsafedrinking water sources everymonth during the trans-mission season thus reducing vector population andreducing the chances of individuals contracting thedisease [2 6 7]The adult vectormay also be removedfrom drinking water by filtering the water using anylon cloth or by boiling the water

(d) Health educationThis is disseminated throughposterradio and television broadcast village criers andmar-kets face-to-face communication (social mobiliza-tion and house-to-house visits) by health workers andvolunteers to ensure that greater numbers of indi-viduals and communities adopt behavioural practicesaimed at preventing transmission of GWD [8] Thesebehavioural practices include voluntary reporting ofGWD cases prevention of GWD patients from enter-ing drinking water bodies regular use of water fromsafe water sources and in the absence of such watersources filtering or boiling water before drinking [6]

(e) Provision of safe water sourcesThis involves providingsafe drinkingwater supplies throughprotecting hand-dug wells and sinking deep bore wells improvingexisting surface water sources by constructing bar-riers to prevent humans from entering water andfiltering the water through sand-filters [4]

To date these preventive measures have reduced the inci-dence of GWDby over 99 [6]makingGWD themost likelyparasitic disease that will soon be eradicated without the useof any drug or vaccine Most countries including the wholeof Asia are now declared free from GWD and transmissionof the disease is now limited to African countries especiallySudan Ghana Mali Niger and Nigeria [8] GWD is one ofthe neglected tropical diseases It is also an environmentallydriven infectious diseaseTherefore its transmission dependson the parasitersquos survival in the environment and finding newhosts (humans and copepod vectors) in order to replicate andsustain parasite population Because this process is complexit has hampered eradication efforts During the parasitersquosmovement through the environment to the human andcopepod vector hosts many environmental factors influenceboth the parasitersquos population and the vector population

For infectious diseases including environmentally driveninfectious diseases such as GWD mathematical models havea long history of being used to study their transmission andalso to compare and evaluate the effectiveness and afford-ability of intervention strategies that can be used to controlor eliminate them [9 10] Currently the predominant focusof modelling of infectious diseases is centered on concepts

of epidemiological modelling and immunological modellingbeing considered as separate disease processes even for thesame infectious disease In epidemiological or between-hostmodelling of infectious diseases the focus is on studying oftransmission of infectious diseases between hosts be theyanimals or humans or even both in the case of multiple hostinfections In the immunological or within-host modelling ofinfectious diseases the focus is on studying the interaction ofpathogen and the immune system togetherwith otherwithin-host processes in order to elucidate outcomes of infectionwithin a single host [11 12] To the best of our knowledgethere has been nomathematicalmodel to study themultiscalenature of GWD transmission by integrating between-hostscale and within-host scale disease processes Such modelsare sometimes called immunoepidemiological models [13]Most of the mathematical models that have been developedso far are focused on the study ofGWDat the epidemiologicalscale [14ndash16] The purpose of this study is to develop animmunoepidemiological model of GWD Immunoepidemi-ological modelling of infectious diseases is the quantitativeapproach which assists in developing a systems approachto understanding infectious disease transmission dynamicswith regard to the interdependences between epidemiological(between-host scale) and immunological (within-host scale)processes [17 18] The immunoepidemiological model ofGWD presented in this paper is based on a modelling frame-work of the immunoepidemiology of environmentally driveninfectious diseases developed recently by the authors [13]This new and innovative immunoepidemiological modellingframework while maintaining the limits of a mathemat-ical model offers a solid platform to bring the separatemodelling efforts (immunological modelling and epidemi-ological modelling) that focus on different aspects of thedisease processes together to cover a broad range of diseaseaspects and time-scales in an integrated systems approachIt bridges host environmental and parasitic disease phe-nomena using mathematical modelling of parasite-host-environment-vector interactions and epidemiology to illu-minate the fundamental processes of disease transmission inchanging environments For GWD there are three distincttime-scales associatedwith its transmission cyclewhich are asfollows

(i) The epidemiological time-scale which is associatedwith the infection between hosts (human and cope-pod vector hosts)

(ii) The within-host time-scale which is related to thereplication and developmental stages of Guineawormparasite within an individual human host and theindividual copepod vector host

(iii) Theenvironmental time-scale which is associatedwiththe abundance and survival of Guinea worm parasitepopulation and vector population in the physicalwater environment

In order to try and integrate these different processes andthe associated time-scales of GWD the immunoepidemio-logical model of GWDpresented here incorporates the actualparasite load of the human host and copepod vector rather


















훼HIH

ΛH 휆HSHSH

휇HSH

휆ℎSℎ

휇JGJ

GJG0

WM WF

휇FWF

훼FWF

IH

(휇H + 훿H) IH

Iℎ훼FWF

LWNW훼WEW EW

휇LLW

IE

(휇E + 훿E) IE

휆ESE SEΛE

휇ESE

훼CIC

IC

훼JICGJ

휇MWM

NC휇CICGJ

휇WEW

(12) 훼WWM



where 120582119867 (119905) = 120573119867119868119864 (119905)1198750 + 120598119868119864 (119905) 120582119864 (119905) = 120573119864119871119882 (119905)1198710 + 120598119871119882 (119905) 119868ℎ (119905) = 119868119867 (119905) + 1

119878ℎ (119905) = 119878119867 (119905) minus 1120582ℎ (119905) = 120573119867119868119864 (119905)[1198750 + 120598119868119864 (119905)] [119868119867 (119905) + 1] (2)











This implies that

lim119905rarrinfin

sup (119873119867 (119905)) le Λ119867120583119867 (6)



lim119905rarrinfin

sup (119873119864 (119905)) le Λ 119864120583119864 (8)






This implies that

lim119905rarrinfin

sup (119868119862 (119905))le ( 120573119867Λ 119864 (Λ119867 minus 120583119867)(1198750120583119864 + 120598Λ 119864) (Λ119867 + 120583119867))( 120583119869(1205831198621198660 + 120575119867120583119869)) (11)



(12)



(13)







(15)

where





1198800 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (16)


with


(18)

where

11987211 = 120598120573119867Λ119867119868119864 + 120583119867 (120583119867 + 120575119867 + 120583119867) (1198750 + 120598119868119864) (19)

We deduce that

ℎ (119883 119884 119885) = (ℎ1 (119883 119884 119885) ℎ2 (119883 119884 119885)) (20)



where119870= 120572119865120572119872119873119882120572119882119873119862120572119862120573119867 (Λ119867 minus 120583119867) 11986602 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (22)

119860matrix



119872 = [[[[0 1198701198750120573119864Λ 1198641205831198641198710 0 ]]]] (24)

119863 = [(120583119864 + 120572119864) 00 120583119871] (25)



with

1198770119861 = 120573119867 (Λ119867 minus 120583119867)1198750120583119867sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (27)

1198770119882 = 12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 (28)







1198640 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (29)



119869 (1198640) =(((((((((((((((((((((((((((


)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)





where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)



Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

































훼HIH

ΛH 휆HSHSH

휇HSH

휆ℎSℎ

휇JGJ

GJG0

WM WF

휇FWF

훼FWF

IH

(휇H + 훿H) IH

Iℎ훼FWF

LWNW훼WEW EW

휇LLW

IE

(휇E + 훿E) IE

휆ESE SEΛE

휇ESE

훼CIC

IC

훼JICGJ

휇MWM

NC휇CICGJ

휇WEW

(12) 훼WWM



where 120582119867 (119905) = 120573119867119868119864 (119905)1198750 + 120598119868119864 (119905) 120582119864 (119905) = 120573119864119871119882 (119905)1198710 + 120598119871119882 (119905) 119868ℎ (119905) = 119868119867 (119905) + 1

119878ℎ (119905) = 119878119867 (119905) minus 1120582ℎ (119905) = 120573119867119868119864 (119905)[1198750 + 120598119868119864 (119905)] [119868119867 (119905) + 1] (2)











This implies that

lim119905rarrinfin

sup (119873119867 (119905)) le Λ119867120583119867 (6)



lim119905rarrinfin

sup (119873119864 (119905)) le Λ 119864120583119864 (8)






This implies that

lim119905rarrinfin

sup (119868119862 (119905))le ( 120573119867Λ 119864 (Λ119867 minus 120583119867)(1198750120583119864 + 120598Λ 119864) (Λ119867 + 120583119867))( 120583119869(1205831198621198660 + 120575119867120583119869)) (11)



(12)



(13)







(15)

where





1198800 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (16)


with


(18)

where

11987211 = 120598120573119867Λ119867119868119864 + 120583119867 (120583119867 + 120575119867 + 120583119867) (1198750 + 120598119868119864) (19)

We deduce that

ℎ (119883 119884 119885) = (ℎ1 (119883 119884 119885) ℎ2 (119883 119884 119885)) (20)



where119870= 120572119865120572119872119873119882120572119882119873119862120572119862120573119867 (Λ119867 minus 120583119867) 11986602 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (22)

119860matrix



119872 = [[[[0 1198701198750120573119864Λ 1198641205831198641198710 0 ]]]] (24)

119863 = [(120583119864 + 120572119864) 00 120583119871] (25)



with

1198770119861 = 120573119867 (Λ119867 minus 120583119867)1198750120583119867sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (27)

1198770119882 = 12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 (28)







1198640 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (29)



119869 (1198640) =(((((((((((((((((((((((((((


)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)





where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)



Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















훼HIH

ΛH 휆HSHSH

휇HSH

휆ℎSℎ

휇JGJ

GJG0

WM WF

휇FWF

훼FWF

IH

(휇H + 훿H) IH

Iℎ훼FWF

LWNW훼WEW EW

휇LLW

IE

(휇E + 훿E) IE

휆ESE SEΛE

휇ESE

훼CIC

IC

훼JICGJ

휇MWM

NC휇CICGJ

휇WEW

(12) 훼WWM



where 120582119867 (119905) = 120573119867119868119864 (119905)1198750 + 120598119868119864 (119905) 120582119864 (119905) = 120573119864119871119882 (119905)1198710 + 120598119871119882 (119905) 119868ℎ (119905) = 119868119867 (119905) + 1

119878ℎ (119905) = 119878119867 (119905) minus 1120582ℎ (119905) = 120573119867119868119864 (119905)[1198750 + 120598119868119864 (119905)] [119868119867 (119905) + 1] (2)











This implies that

lim119905rarrinfin

sup (119873119867 (119905)) le Λ119867120583119867 (6)



lim119905rarrinfin

sup (119873119864 (119905)) le Λ 119864120583119864 (8)






This implies that

lim119905rarrinfin

sup (119868119862 (119905))le ( 120573119867Λ 119864 (Λ119867 minus 120583119867)(1198750120583119864 + 120598Λ 119864) (Λ119867 + 120583119867))( 120583119869(1205831198621198660 + 120575119867120583119869)) (11)



(12)



(13)







(15)

where





1198800 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (16)


with


(18)

where

11987211 = 120598120573119867Λ119867119868119864 + 120583119867 (120583119867 + 120575119867 + 120583119867) (1198750 + 120598119868119864) (19)

We deduce that

ℎ (119883 119884 119885) = (ℎ1 (119883 119884 119885) ℎ2 (119883 119884 119885)) (20)



where119870= 120572119865120572119872119873119882120572119882119873119862120572119862120573119867 (Λ119867 minus 120583119867) 11986602 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (22)

119860matrix



119872 = [[[[0 1198701198750120573119864Λ 1198641205831198641198710 0 ]]]] (24)

119863 = [(120583119864 + 120572119864) 00 120583119871] (25)



with

1198770119861 = 120573119867 (Λ119867 minus 120583119867)1198750120583119867sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (27)

1198770119882 = 12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 (28)







1198640 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (29)



119869 (1198640) =(((((((((((((((((((((((((((


)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)





where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)



Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

























This implies that

lim119905rarrinfin

sup (119873119867 (119905)) le Λ119867120583119867 (6)



lim119905rarrinfin

sup (119873119864 (119905)) le Λ 119864120583119864 (8)






This implies that

lim119905rarrinfin

sup (119868119862 (119905))le ( 120573119867Λ 119864 (Λ119867 minus 120583119867)(1198750120583119864 + 120598Λ 119864) (Λ119867 + 120583119867))( 120583119869(1205831198621198660 + 120575119867120583119869)) (11)



(12)



(13)







(15)

where





1198800 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (16)


with


(18)

where

11987211 = 120598120573119867Λ119867119868119864 + 120583119867 (120583119867 + 120575119867 + 120583119867) (1198750 + 120598119868119864) (19)

We deduce that

ℎ (119883 119884 119885) = (ℎ1 (119883 119884 119885) ℎ2 (119883 119884 119885)) (20)



where119870= 120572119865120572119872119873119882120572119882119873119862120572119862120573119867 (Λ119867 minus 120583119867) 11986602 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (22)

119860matrix



119872 = [[[[0 1198701198750120573119864Λ 1198641205831198641198710 0 ]]]] (24)

119863 = [(120583119864 + 120572119864) 00 120583119871] (25)



with

1198770119861 = 120573119867 (Λ119867 minus 120583119867)1198750120583119867sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (27)

1198770119882 = 12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 (28)







1198640 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (29)



119869 (1198640) =(((((((((((((((((((((((((((


)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)





where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)



Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















This implies that

lim119905rarrinfin

sup (119868119862 (119905))le ( 120573119867Λ 119864 (Λ119867 minus 120583119867)(1198750120583119864 + 120598Λ 119864) (Λ119867 + 120583119867))( 120583119869(1205831198621198660 + 120575119867120583119869)) (11)



(12)



(13)







(15)

where





1198800 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (16)


with


(18)

where

11987211 = 120598120573119867Λ119867119868119864 + 120583119867 (120583119867 + 120575119867 + 120583119867) (1198750 + 120598119868119864) (19)

We deduce that

ℎ (119883 119884 119885) = (ℎ1 (119883 119884 119885) ℎ2 (119883 119884 119885)) (20)



where119870= 120572119865120572119872119873119882120572119882119873119862120572119862120573119867 (Λ119867 minus 120583119867) 11986602 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (22)

119860matrix



119872 = [[[[0 1198701198750120573119864Λ 1198641205831198641198710 0 ]]]] (24)

119863 = [(120583119864 + 120572119864) 00 120583119871] (25)



with

1198770119861 = 120573119867 (Λ119867 minus 120583119867)1198750120583119867sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (27)

1198770119882 = 12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 (28)







1198640 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (29)



119869 (1198640) =(((((((((((((((((((((((((((


)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)





where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)



Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




















(15)

where





1198800 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (16)


with


(18)

where

11987211 = 120598120573119867Λ119867119868119864 + 120583119867 (120583119867 + 120575119867 + 120583119867) (1198750 + 120598119868119864) (19)

We deduce that

ℎ (119883 119884 119885) = (ℎ1 (119883 119884 119885) ℎ2 (119883 119884 119885)) (20)



where119870= 120572119865120572119872119873119882120572119882119873119862120572119862120573119867 (Λ119867 minus 120583119867) 11986602 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (22)

119860matrix



119872 = [[[[0 1198701198750120573119864Λ 1198641205831198641198710 0 ]]]] (24)

119863 = [(120583119864 + 120572119864) 00 120583119871] (25)



with

1198770119861 = 120573119867 (Λ119867 minus 120583119867)1198750120583119867sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (27)

1198770119882 = 12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 (28)







1198640 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (29)



119869 (1198640) =(((((((((((((((((((((((((((


)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)





where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)



Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















where119870= 120572119865120572119872119873119882120572119882119873119862120572119862120573119867 (Λ119867 minus 120583119867) 11986602 (120583119882 + 120572119882) (120583119865 + 120572119865) (120583119872 + 120572119872) (1205831198621198660 + 120583119869120572119862) 120583119867 (22)

119860matrix



119872 = [[[[0 1198701198750120573119864Λ 1198641205831198641198710 0 ]]]] (24)

119863 = [(120583119864 + 120572119864) 00 120583119871] (25)



with

1198770119861 = 120573119867 (Λ119867 minus 120583119867)1198750120583119867sdot 119873119882120572119882(120572119882 + 120583119882) 120583119871 120573119864Λ 119864120583119864 (120583119864 + 120575119864) 1198710 (27)

1198770119882 = 12 sdot 120572119872120572119872 + 120583119872 sdot 120572119865120572119865 + 120583119865 sdot 11987311986212058311986211986601205831198621198660 + 120583119869120572119862 (28)







1198640 = (Λ119867120583119867 0 0 0 0 1198660120583119869 0 0 Λ 119864120583119864 0) (29)



119869 (1198640) =(((((((((((((((((((((((((((


)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)





where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)



Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















119869 (1198640) =(((((((((((((((((((((((((((


)))))))))))))))))))))))))))

(30)

where 1199020 = (120583119867 + 120575119867 + 120572119867) 1199021 = (1205831198621198660 + 120583119869120572119862)120583119869 1199022 = (120583119872 + 120572119872) 1199023 = (120583119865 + 120572119865) 1199024 = (120583119882 + 120572119882) 1199025 = (120583119864 + 120572119864) 1198600 = 120573119867Λ1198671198750120583119867 1198601 = 120573119867 (Λ119867 minus 120583119867)1205831198671198750

(31)





where1205871 = 1199021 + 1199022 + 1199023 + 1199024 + 1199025 + 1205831198711205872 = 11990211199022 + 11990231199024 + (1199021 + 1199022 + 1199023 + 1199024) (1199025 + 120583119871)+ 1199025120583119871 + (1199021 + 1199022) (1199023 + 1199024) 1205873 = 11990211199022 (1199023 + 1199024) + 11990231199024 (1199021 + 1199022)+ (1199021 + 1199022) (1199023 + 1199024) (1199025 + 120583119871)+ 11990211199022 (1199025 + 120583119871) + 11990231199024 (1199025 + 120583119871)+ 1199025120583119871 (1199021 + 1199022 + 1199023 + 1199024) 1205874 = 1199021119902211990231199024 + 11990231199024 (1199021 + 1199022) (1199025 + 120583119871)+ 11990211199022 (1199023 + 1199024) (1199025 + 120583119871)+ (1199021 + 1199022) (1199023 + 1199024) 1199021120583119871 + 119902511990241199023120583119871+ 1199021119902211990251205831198711205875 = 1199021119902211990231199024 (1199025 + 120583119871) + 11990231199024 (1199021 + 1199022) 1199025120583119871+ 11990211199022 (1199023 + 1199024) 11990251205831198711205876 = 11990211199022119902311990241199025120583119871 (1 minus 11987720)

(35)



Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















Det (119867119895) gt 0 119895 = 1 2 6 (36)

where 1198671 = (1205871) 1198672 = (1205871 11205873 1205872) 1198673 = (1205871 1 01205873 1205872 12058711205875 1205874 1205873)1198674 = (1205871 1 0 01205873 1205872 1205871 11205875 1205874 1205873 12058720 1205876 1205875 1205874)

1198675 = ((((

1205871 1 0 0 01205873 1205872 1205871 1 01205875 1205874 1205873 1205872 12058710 1205876 1205875 1205874 12058730 0 0 1205876 1205875))))

1198676 = (((((((

1205871 1 0 0 0 01205873 1205872 1205871 1 0 01205875 1205874 1205873 1205872 1205871 10 1205876 1205875 1205874 1205873 12058720 0 0 1205876 1205875 12058740 0 0 0 0 1205876)))))))

(37)






where



We let 1198800 = (119883lowast 0) = (Λ119867120583119867 0 0 Λ119862120583119862 0 0 0) (39)




In our case




119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















119860 =[[[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]]] (41)

where

1198860 = (120583119867 + 120575119867 + 120572119867) 1198861 = 1120583119869 (120583119862 + 120572119862120583119869) 1198862 = (120583119872 + 120572119872) 1198863 = (120583119865 + 120572119865) 1198864 = (120583119882 + 120572119882) 1198865 = (120583119864 + 120572119864)

119866 (119883 119885) =[[[[[[[[[[[[[[[[[[[


]]]]]]]]]]]]]]]]]]]

(42)
























(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


































(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















(55)

where


1198860 = 120573119867Λ1198671198861 = 1205831198671198750 (120583119867 + 120575119867 + 120572119867) 1198862 = 120573119867 (120583119867 + 120575119867) 120583119867120598 (120583119867 + 120575119867 + 120572119867) (56)


where





(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















(58)











where

f = (1198911 1198912 1198913 1198914 1198915 1198916 1198917 1198918 1198919 11989110) (61)


(62)




119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















119869 (1198640) =

(((((((((((((((((((((((((((((((


)))))))))))))))))))))))))))))))

(64)

where











sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















sign changes








119906119896V119894V119895 1205972119891119896120597119909119894120597119909119895 (0 0) 119887 = 119899sum119896119894=1

119906119896V119894 1205972119891119896120597119909119894120597120601 (0 0) (69)








u = [1199061 1199062 1199063 1199064 1199065 1199066 1199067 1199068 1199069 11990610 11990611 11990612]119879 (70)

where





k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















k = [V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12]119879 (72)


(73)




(75)




(76)





(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















(77)





120573119867= 1205971198770120597120573119867 times 1205731198671198770 = 05 (79)



Υ1198770120583119864 = minus12 (2120583119864 + 120575119864)(120583119864 + 120575119864) = minus09991 (80)




120573119864= 05 This






sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



















sign






















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
































H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

0

500

1000

1500

2000

2500

Infe

cted

hum

ans(

I H)

(a)

H = 001055

H = 01055

H = 055

010000200003000040000500006000070000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

H = 001055

H = 01055

H = 055

500 1000 1500 20000Time (days)

02000400060008000

10000120001400016000

Eggs

in w

ater

(EW)

(c)

H = 001055

H = 01055

H = 055

20001000 15005000Time (days)

0200000400000600000800000

10000001200000

Larv

ae in

wat

er(L

W)

(d)


E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus200

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus10000

01000020000300004000050000

Infe

cted

cope

pods

(IE)

(b)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus500

50100150200250300350400

Eggs

in w

ater

(EW)

(c)

E = 0005

E = 005

E = 05

500 1000 1500 20000Time (days)

minus50000

050000

100000150000200000250000300000

Larv

ae in

wat

er(L

W)

(d)



W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0

5000

10000

15000

20000

25000

Eggs

in w

ater

(EW)

(c)

W = 0005

W = 05

W = 09

500 1000 1500 20000Time (days)

0200000400000600000800000

10000001200000140000016000001800000

Larv

ae in

wat

er(L

W)


L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

L = 0005

L = 05

L = 09

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

L = 0005

L = 05

L = 09

0

1000

2000

3000

4000

5000

Eggs

in w

ater

(EW)

500 1000 1500 20000Time (days)

(c)

L = 0005

L = 05

L = 09

1e7

500 1000 1500 20000Time (days)

00

02

04

06

08

10

Larv

ae in

wat

er(L

W)



M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Infe

cted

hum

ans(

I H)

(a)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0100002000030000400005000060000

Infe

cted

cope

pods

(IE)

(b)

M = 09

M = 009

M = 0009

500 1000 1500 20000Time (days)

0200400600800

10001200

Eggs

in w

ater

(EW)

(c)

M = 09

M = 009

M = 0009

0100000200000300000400000500000600000700000

Larv

ae in

wat

er(L

W)

500 1000 1500 20000Time (days)








F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 09

F = 009

F = 0009

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

500 1000 1500 20000Time (days)

(b)

F = 09

F = 009

F = 0009

500 1000 1500 20000Time (days)

02000400060008000

1000012000140001600018000

Eggs

in w

ater

(EW)

(c)

F = 09

F = 009

F = 0009

500 1500 20000 1000Time (days)

010000002000000300000040000005000000600000070000008000000

Larv

ae in

wat

er(L

W)


NW = 30

NW = 300

NW = 30000

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

500 1000 1500 20000Time (days)

(a)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0

20000

40000

60000

80000

100000

Infe

cted

cope

pods

(IE)

(b)

NW = 30

NW = 300

NW = 30000

500 1000 1500 20000Time (days)

0200400600800

1000120014001600

Eggs

in w

ater

(EW)

(c)

NW = 30

NW = 300

NW = 30000

1e7

500 1000 1500 20000Time (days)

00051015202530354045

Larv

ae in

wat

er(L

W)



F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0200400600800

100012001400

Infe

cted

hum

ans(

I H)

(a)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

01000020000300004000050000600007000080000

Infe

cted

cope

pods

(IE)

(b)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0500

10001500200025003000350040004500

Eggs

in w

ater

(EW)

(c)

F = 0007

F = 007

F = 07

500 1000 1500 20000Time (days)

0

500000

1000000

1500000

2000000

2500000

Larv

ae in

wat

er(L

W)

(d)







훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

20

40

60

80

100

120

140

160M

atur

e wor

ms(

WM)

(a)

훽H = 055

훽H = 01055

훽H = 001055

훽H = 0001055

500 1000 1500 20000Time (days)

0

5

10

15

20

25

30

35

40

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)


휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus10

0

10

20

30

40

50

60

70

Mat

ure w

orm

s(W

M)

(a)

휇E = 0005

휇E = 005

휇E = 05

500 1000 1500 20000Time (days)

minus5

0

5

10

15

20

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)



500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















500 1000 1500 20000Time (days)

휇L = 0005

휇L = 05

휇L = 09

0

10

20

30

40

50

60

70

80M

atur

e wor

ms(

WM)

(a)

휇L = 0005

휇L = 05

휇L = 09

500 1000 1500 20000Time (days)

0

5

10

15

20

25

Fert

ilize

d fe

mal

e wor

ms(

WF)

(b)











8 Conclusions






Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




















Acknowledgments


References

































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
























of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















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