Vaccination by delayed treatment of infection.pdf

Vaccine 29 (2011) 96249631

Contents lists available at SciVerse ScienceDirect

Vaccine

journa l homepage: www.e lsev ier .com

Vaccin

Sean P. SDepartment of

a r t i c l

Article history:Received 31 MReceived in reAccepted 18 OAvailable onlin

Keywords:ModelingBiologyTreatmentVaccine

combmicrow hoorm oobialn, andeofftreatn ofbat t

l heal

1. Introdu

The control of infectious diseases is performed with preventionand treatment. Prevention can come in two forms, immunizationsand antimicrobial chemoprophylaxis. Vaccination, though whenavailable can be administered well in advance of exposure, alsorequires leais not alwaproductionlike the recis more rapbe controlleof antimicr[1]. Under cconcomitanan extent th

While indrug use foimmunemebial treatmwould be fexposing prattention tothe develop

CorresponE-mail add

re armedication such as side-effects, scarcity, and the evolution of drugresistant strains [9]. As chemoprophylaxis and treatment combinedwith exposure do not necessarily induce immunity, the abatementof disease during prolonged epidemics would require frequent re-administration. Thiswill compound consumption, side-effects, and

0264-410X/$ doi:10.1016/j.d-time for development and production, and that timeys available. For inuenza the lead-time for vaccinecan exceed six months [1]. In the case of epidemicsent H1N1 outbreak, where the spread of the diseaseid than the rate of vaccine production, the disease mustd by other measures. These measures include the useobial drugs both prophylactically and therapeuticallyertain conditions administration of antimicrobial drugstly with infection can stimulate the immune system toat it provides long-term immunity [25].fections can lead to longterm immunity, antimicrobialllowing exposure often interrupts the development ofmory [6]. There are exceptional caseswhere antimicro-ent enhances the generation of immunity above whatound through an untreated infection (e.g., treatmenteviously hidden antigens [7,8]) howeverwe restrict ourthe more common cases where drug treatment limitsment of immunity.

ding author. Tel.: +1 404 727 1015.ress: [email protected] (R. Antia).

selection of drug resistant strains, making this type of control lessthan optimal [6,9].

To understand the conference of immunity through pathogenexposure combined with antimicrobial drug use we examinethe tradeoff between the two primary effects of antimicrobialtreatment: the reduction in pathology, and the reduction in themagnitude of the immune response [10,11]. To one extreme thereis a natural, untreated infection, which generates long term immu-nity at the high cost of the pathology of the infection. The otherextreme is pre-exposure chemoprophylaxis, which can eliminateany pathology but also offers little or no immunological protec-tion against future infections [6]. Treatment at intermediate timescan offer both immunological protection and reduced pathology[12,13]. In this paper we examine how the tradeoff between gen-eration of immunity and reduction in pathology can be exploitedsuch that infection followed by treatment can act as a vac-cine.

The subject of this paper is motivated by experimental obser-vations in parasitic protozoa infection [25], bacterial infection[12], and viral infection [13]. These studies present evidence thatlive-unattenuated pathogen can be used in combination withantimicrobial drug use as a vaccine. This provides a reduction inthe pathology of the natural infection and long-term immunity.

see front matter 2011 Elsevier Ltd. All rights reserved.vaccine.2011.10.047ation by delayed treatment of infection

tromberg, Rustom Antia

Biology, Emory University, Atlanta, GA 30322, United States

e i n f o

ay 2011vised form 7 October 2011ctober 2011e 30 October 2011

a b s t r a c t

Twomedical interventions allowus towell in advance of exposure, and antiwith exposure. In this paper we sholowed by treatment being used as a fappropriately administered antimicrthe pathology caused by the infectiopathogen. The models explore the tration. This tradeoff suggests a limitedstarted and provide both amelioratiomay be particularly well suited to comularly for individuals such as medicainitial stages of a pandemic.

ction The/ locate /vacc ine

at infectiousdiseases: vaccinationwhich canbeadministeredbials which are most often administered contemporaneouslyw they can, in principle, be combined with infection fol-f vaccination. We use mathematical models to examine howtreatment following natural infection can be used to reduced also generate long-lasting immunological memory to thebetween reduction in pathology and strength of immuniza-ment window during which antimicrobial treatment can bedisease symptoms and long-term immunity. This approachhe emergence of novel pandemic inuenza infections partic-thcare professionals at greatest risk for exposure during the

2011 Elsevier Ltd. All rights reserved.

e many other drawbacks associated with antimicrobial

S.P. Stromberg, R. Antia / Vaccine 29 (2011) 96249631 9625

In protozoa infection, both Theileria and Plasmodium in com-bination with antimicrobial drug use have been shown to act asvaccines. Vaccination against Theileria is commonly performed incattle by inoculation with live-unattenuated parasite and simulta-neous admi[2,3]. Similawith eithermalaria.

A studyshowed thawhile havinresulting inexperimentof mice infThis treatmerwise certre-challeng

These exment can unot howeveand long-tenique.

In this pdynamics oto explore trobustnessoff and thetiming of athegeneratdiffer by incand stimula

Our resucan lead to bOur resultsdivision orstrategies b

2. Materia

We begiantimicrobidynamicswincludesnadifferentiat

This baspare with madditional bcyte stimulaThe programtheoreticalCD8Tcellswproliferatioterms for thmodels for

2.1. Basic m

In the bexponentiathis to logisconclusionscompared wimmune reof antimicropathogen. B

dependent on pathogen density and either antimicrobial concen-tration or lymphocyte density. When the killing rate exceeds thegrowth rate the pathogen will decay. Antimicrobial concentrationis modeled as zero until time 1 when treatment is started and is a

nt vaed, tphoeffecen als whue toen isile aitelymod

en :

crob

ells :

r cell

ry ce

phopat

ationencoden. ToefciogenIn thhogeathohaveimmls we-speso bememnowivateto cohethails oor sim, caveendix

lled p

of tpathoherectionof l

ntial

P(Nnistration of tetracycline giving long lasting immunityrly, inoculation with Plasmodium in mice being treatedantibiotic [4] or chloroquine [5] gives immunity to

of a bacterial infection with delayed treatment [12]t delayed treatment could reduce bacterial densityg little effect on lymphocyte numbers presumablyimmunity. Ruprecht et al. [13] performed a similarwith a viral infection where they delayed treatment

ected with Rauscher murine leukemia virus by 96h.ent delay was able to both rescue the mice from oth-ain death and provided them with immunity againste.perimental studies establish that antimicrobial treat-nder certain conditions be used as a vaccine. They dor explore the tradeoff between abatement of diseaserm immunity, or the robustnessof this vaccination tech-

aper we use mathematical models of the within-hostf infection and immune responses. Themodels are usedhe tradeoff between treatment and immunity, and theof this vaccination technique. The specics of this trade-robustness of the technique are studied through bothntimicrobial administration and by differing forms ofionof immune responses. The immune responsemodelslusion or omission of two factors: programmeddivisiontion by killed pathogen.lts suggest that with proper timing, delayed treatmentoth adequate reduction in pathology and to immunity.also show that in disease systems with programmedstimulation by killed antigen, successful treatmentecome less sensitive to timing.

ls and methods

n with a basic model for the dynamics of pathogen,al drugs, and the immune response. For lymphocytee focus on a typical CD8T cell response. Thebasicmodelive, effector andmemory lymphocyteswithdivisionandion in the continued presence of live pathogen.ic model is presented as a null model in order to com-odels in the following subsections that include twoiological effects. These additional effects are lympho-tion by killed pathogen, and programmed responses.med response models are based on experimental and

studies, which have shown that a short stimulation ofithantigen results in subsequent antigen-independent

n, anddifferentiation intomemory cells [12,1416]. Theeexpansionof immuneresponsesarebasedonpreviousthe dynamics of CD8 T cell responses [1620].

odel

asic model, for simplicity, we let the pathogen growlly in the absence of an immune response. Changingtic growth does not qualitatively alter our results and(provided, of course, that the carrying capacity is highith the pathogen density required to stimulate the

sponse). Pathogen death in the model can be a resultbial killing or of killing by lymphocytes specic for theoth types of killing aremodeledwithmass-action terms

constais clear

Lymnaive,pathogtor celcontinpathogsis whinden

The

pathog

antimi

naive c

effecto

memo

Lymby livestimuldependbasicmfunctioHill coof pathtiate).on patuntil p

Weby thetor celantigenWe dotor andis not king actabilityas to w

Dettions fvaluesin App

2.2. Ki

Twokilledone wconjunulationdiffere

dR

dt= hlue Am after that. At time 2 after the primary infectionreatment is stopped and A(t) returns to zero.cytes in the model are divided into three categories,tor and memory cells. Naive cells in the model killnd are stimulated to divide and differentiate into effec-en pathogen density is high. Those effector cells thenkill andwill divide as long as pathogen is present. Oncecleared the majority of effector cells die by apopto-

fraction f differentiate into memory cells which remain.el equations for the basic model are:

dP

dt= rP hP(N + E + M) aPA(t), (1)

ial : A(t) =

0 if t < 1Am if 1 t 2,0 if t > 2

(2)

dN

dt= N P

k + P , (3)

s :dE

dt= (2N + E) P

k + P dE(1 P

k + P)

, (4)

lls :dM

dt= f dE

(1 P

k + P)

. (5)

cyte division in this basic model requires stimulationhogen (this restriction is relaxed below to includewith killed pathogen and programmed division). The

e of lymphocyte stimulation on pathogen density in thel is assumed tobe amonotonically increasing, saturatingsatisfy these assumptions we use a Hill function with

ent 1 and stimulation coefcient k (roughly the densitythat stimulates lymphocytes to divide and differen-

is model lymphocyte death has a similar dependencen density, such that effector cells do not begin to decaygen has been removed from the system.a mass action term for the clearance of the pathogenune response. In previous papers typically only effec-re capable of killing pathogen. In our model we let allcic cells (naive, effector and memory) kill pathogen.cause recent experiments have shown that both effec-ory cells have similar rates of killing [21]. At present it

n whether naive cells can kill pathogen before becom-d.However, because there are very fewnaive cells, theirntrol pathogen is very limited and the model is robuster naive cells are capable of killing pathogen.n implementation of the model such as initial condi-ulating primary and secondary exposures, parameterats formodel usage and numerical routine are includedA.

athogen

he models studied in this paper contain stimulation bygen (or equivalently continued antigen presentation),it is added alone to the basic model and one added inwith programmed response. To incorporate the stim-

ymphocytes by killed pathogen we add an additionalequation for killed pathogen density to the system:

+ E + M) + aPA(t) R. (6)

9626 S.P. Stromberg, R. Antia / Vaccine 29 (2011) 96249631

The killing terms from the pathogen equation (Eq. (1)) feeddirectly into this equation which also includes a decay of killedpathogen from the system with rate . The lymphocyte equationsare also modied by replacing P with P+R which simulates stim-ulation byLymphocytdensity of bcoefcientlation givinin memory

2.3. Progra

To incormodel aboveffector celwe replace

dE1dt

= 2N

dE2dt

= 2E1

......

dEidt

= 2Ei

......

dEndt

= 2Enand E= Eiis presented

A stimution of 2n efafter the stidivisions.

The numtions presen(Table A.1).

2.4. Correla

As a medensity (marelate of mtransmissiothreshold fo(accumulatis presentedensity. Forlated memosecondary i

3. Results

The resuilar and wepathogen mcurve) and sdifferent trement (B), anare the sumdose of path

In the 1grows expo

rimarathogement in the primary exposure (B), and delayed treatment in the primarye (C). In the untreated 1 infection (A) we reach a large pathogen density.ulates adequate memory production (right hand asymptote of blue curve)t in the 2 exposure the pathogen is controlled. Under prophylaxis (B) thent during the 1 exposure prevents pathogen growth but this results in nolationofmemory cells. The2 exposure is thenunprotected resulting inpeakn density equal to an untreated 1 infection (A). For delayed treatment in aure (C) the treatment reduces the max-pathogen density and a moderateof memory cells accumulate. This provides limited protection against 2

es. (For interpretation of the references to color in this gure legend, thereferred to the web version of the article.)

. After pathogen clearance the lymphocytes decay into a sta-pulation of memory cells. The number of memory cells cann from the asymptotic value of the lymphocytes curve. Thery cells are abundant and provide excellent protection uponosure.ig. 1Bwe see that prophylactic treatment prevents pathogenand no immunity is generated. Consequently there is no

tion to a subsequent infection.ile exposure during prophylactic treatment gives negligibleity, Fig. 1C shows the effect of delaying treatment for four

fter exposure. On the left we see the effect of the treatmentinitial exposure. Once treatment begins the pathogen imme-declines. The max-pathogen density is reduced by nearly af one thousand fromanatural infection (Fig. 1A left).Wealsooderate accumulation of memory cells after the pathogence.secondary exposure in Fig. 1C shows the likely outcome iftem is later re-exposed to the pathogen without treatment.case themax-pathogendensity is again reducedbya factor ofousand from the max-pathogen of an untreated 1 exposure). Thus the infection with delayed treatment has providedrotection against a possible future exposure.next performeda set of simulations similar to the one shown1C, varying the delay in the start of treatment. From thesetions we examined the amount of memory produced afterxposure is cleared as a function of the start of treatment, andboth pathogen and killed pathogen (see Appendix A).es in these models are adequately stimulated when theoth live and killed pathogen exceeds the stimulation

(P+R k). This mechanism provides additional stimu-g amore rapid and prolonged response, and an increasecells and conferred protection.

mmed lymphocyte divisions

porate programmed cell division we modify the basice so that once stimulated, naive cells differentiate tols and proceed through n divisions. To implement thisEq. (4) with n equations:

P

k + P E1, (7)

E2, (8)

(8)

1 Ei, (9)

(9)

1 dEn, (10)

equals the total number of effector cells. The full modelin Appendix A.

lated naive cell in this model expands into a popula-fector cells regardless of the dynamics of the pathogenmulation has occurred. In our simulations we use n=18

erical values of model parameters used in the simula-ted in the following sections are found in Appendix A

tes of disease and protection

asure of pathology we look at the maximum pathogenx-pathogen density). Max-pathogen density is a cor-ore complex quantities such as disease pathology andn. Other correlates of pathology such as time abover pathogen or integral of the pathogen curve over timeed pathogen), yield qualitatively similar results to whatd in this paper and correlate well with max-pathogencorrelates of protection [22] we look at both accumu-ry cells and the projected max-pathogen density for anfection.

lts of the four models considered are qualitatively sim-illustrate the features of the output with the killedodel in Fig. 1. This gure shows primary (1 solid redecondary (2 dashed red curve) infectionsunder threeatment strategies: no treatment (A), prophylactic treat-d delayed treatment (C). The lymphocytes (blue curve)of the naive, memory and effector cells. The infectiveogen is identical in all six infections.

exposure without treatment (Fig. 1A), the pathogennentially, stimulates lymphocyte expansion, and is then

Fig. 1. Pkilled ptic treatexposurThis stimsuch thatreatmeaccumupathoge1 exposnumberexposurreader is

clearedble pobe takememo2 exp

In Fgrowthprotec

Whimmundays aon thediatelyfactor osee a mclearan

Thethe sysIn thisone th(Fig. 1Asome p

Wein Fig.simulathe 1 ey (1 , left) and secondary (2 , right) infections simulated using then model for: natural infection without treatment (A), prophylac-


the max-pathogen densities for the 1 and 2 exposures. This wasdone for four differentmodels, the basicmodel, a model with stim-ulation by killed pathogen, a model with programmed lymphocytedivision, and a model with both programmed lymphocyte divisionand stimula

Killedpagenically acThis prolonof memorysystems witreatment idecay moremore releva

Programics [12,14through sevis removedels in this pthrough 18stimulatedand CD4 T can effect.

Fig. 2 shin the startcally increaall models,long delaysout treatmegeneratingwe wait to

Stimulatduction parincreased a

In the ptinues aftermemory crgrammed rstimulate mment.

Fig. 3 shand a 2 exsimulationssities takena function o

Early tresity for the 1exposure, wThe valuesues for no trhas clearedtradeoff dep

We canbetween 1

witha signidensity ofpathogen d(two-log revalue of the(blue dotted

The winthe 1 and 2tion, is shamodels shotant, treatmalso see thawindow is

104

106

105

107

104

106

105

107

104

106

105

107

104

106

105

107

0 1 2 3 4 5 6 7 8

D. Both Effects

Delay in Start of Treatment (days)

emory accumulation for four models. A set of simulations like Fig. 1C wereed using each model while varying the delay in the start of treatment. Theof memory cells following the primary infection is plotted as a function ofment delay. As the delay is increased the density of memory increases. Thetic value corresponds to the density ofmemory cells following an untreated. When killed pathogen can stimulate lymphocytes more memory is gen-nder programmed division lymphocytes continue to divide after pathogened giving more memory for early treatment times.

onds to treatment strategies beingmore robust when thesecontribute to memory generation.immune system can also cause pathology. This is a resulttoxic T cells killing infected target cells and secreting toxices. In Appendix A we show that reduction in accumulatedopathologyhasavery similar timedependence to the reduc-max-pathogen density. Treating to reduce max-pathogenwith a two log reduction also yields at least a two-log

ion in immunopathology.2 max-pathogen density for the killed pathogen model) has a small increase around day 5. This is an effect of theimations of the model and is discussed in Appendix A.

cussion

dical management of the symptoms of pathogenic infectionsly takes two forms: immunizations and antimicrobial treat-hese are typically viewedasmutually exclusive, vaccinationn pre-exposure to prevent infection and treatment is givenxposure to ameliorate the symptoms of infection. Occasion-wever, vaccination can be used as amechanism of treatmenttion by killed pathogen.thogencan stimulate the immunesystemuntil the anti-tive molecules decay or are removed from the system.gs lymphocyte stimulation, generating greater numberscells and can function as a vaccine [23]. Not all diseasell have appreciable amounts of killed pathogen whens started and the antigens in some disease systemsmayrapidly. The persistence of killed pathogen is typicallynt for bacterial infections.meddivision is an important factor inCD8Tcell dynam-16]. When a CD8 T cell is stimulated it will proceederal rounds of division even if the stimulating antigenfrom the system. The programmed cell division mod-aper (Eqs. (7)(10)) have a stimulated lymphocyte gorounds of division yielding 218 effector cells for everynaive cell. For other lymphocyte cells, such as B cellsells, programmed division may not be as important of

ows the memory generation as a function of the delayof treatment. The memory production is a monotoni-sing function of the delay in the start of treatment forwith an asymptotic value of memory production forequal to the memory produced for an infection with-nt. The simulations show that all models are capable ofmemory under delayed treatment but that the longerbegin treatment, the more memory will be produced.ionbykilledpathogengives an increase inmemorypro-ticularly for later treatment. This effect is due to themount of killed pathogen when its density is high.rogrammed division model memory production con-the pathogen is cleared with treatment. The optimal

eation strategy in disease systems with a strong pro-esponse is to provide enough pathogen and time toany naive cells, then remove the pathogen with treat-

ows the tradeoff between pathology for a 1 exposureposure. This result was obtained from the same set ofused in Fig. 2. The gure shows themax-pathogen den-from those simulations for the 1 and 2 exposures asf the delay.atment (prophylaxis) gives a low max-pathogen den- exposure but a largemax-pathogen density for the 2

hereas late treatment gives the opposite relationship.for late treatment are in correspondence with the val-eatment, as treatment begun after the immune systemthe pathogen is ineffectual. For intermediate delays theends more heavily on the details of the model.see from Fig. 3 that all four models have tradeoffsand 2 max-pathogen density that allow for treatmentcant reduction inboth. In relation to themax-pathogenan untreated 1 infection, both the 1 and 2 max-ensities can be reduced by more than a factor of 100duction). To guide the eye we plotted the numericaltwo-log reduction from an untreated primary infectionline).

dow for when treatment can be started to reduce both max-pathogendensitieswith at least a two-log reduc-ded in blue in Fig. 3 for each of the four models. Thewus thatwhen stimulation by killed pathogen is impor-ent can be started earlier and the window is wider. Wet when there is a programmed response the treatmentmuch wider and earlier than for the basic model. This

Den

sity

of A

ccum

ulat

ed M

emor

y C

ells

Fig. 2. Mperformdensitythe treatasymptoinfectionerated. Uis remov

correspfactors

Theof cytocytokinimmuntion indensityreduct

The(Fig. 3Bapprox

4. Dis

Metypicalment. Tis givepost-eally hoC. Programmed Division

B. Killed Pathogen

A. Basic Model


Fig. 3. Maximent models. Awhile varyingmax-pathogenpathogen. Theexposures havsity. When kilearlier becausgrammed lymas stimulatedinterpretationto the web ver

and treatmenation isuseanimal [24]immunity pthe bite tocan also beexposure [2parva pathoused as a fo

The simtreatment cing patholoreduction oicant reductreatmentreduction in

The addibykilledpa

generation of memory. This increases the window of time wheredelayed treatment can reduce both the 1 and 2 max pathogendensities adequately. These mechanisms make treatment strate-gies more robust, going from a 24-h treatment window without

actoent. Ttrateech

en dindardposupe oemicts aon. Ixposle, ins meor anvemll th

lowsthese fprevalto illusthese mbetwe

Stapre-exThis tyan epidment aattentifully eavailab

Thiwork fadaptiment. Athat alum pathogen densities for 1 and 2 infections from four differ-set of simulations like Fig. 1C were performed using each modelthe delay in the start of treatment. Early treatment reduces 1

, but late treatment generates memory (Fig. 2) and reduces 2 max-blue regions indicate treatment windows where both the 1 and 2

e at least a two-log reduction (blue dotted line) inmax-pathogen den-led pathogen is included in the model the treatment window startse of the additional memory generated during early treatment. Pro-phocyte division gives an earlier and much wider treatment windowlymphocytes will continue to divide after antigen is removed. (Forof the references to color in this gure legend, the reader is referredsion of the article.)

nt can play a role for vaccination. Post-exposure vacci-d to treat rabies infection rapidlyafter thebiteof a rabid it works because the vaccination induces protectiverior to the natural infection migrating from the site ofthe central nervous system. Post-exposure vaccinationused to treat smallpox if taken within a few days of5]. Infectionwith otherwise lethal doses of live Theileriagen followed by tetracycline antimicrobial treatment isrm of vaccination against Theileriosis [3].ulations of the previous section showed that delayedould act as a vaccine, providing immunity and reduc-gy. For all models studied there was a tradeoff betweenf 1 and 2 max pathogen densities that allows signif-tion in both. The four models each predict adequatewindows where delayed treatment gives a two-logboth 1 and 2 pathogen density.

tional factors incorporated into themodels, stimulationthogenandprogrammed lymphocytedivision, aid in the

This vacity in emerThe conditian emerginby the authlikelihood o

Those pehave thegreinstance, wthroughoutside effectsby delayed

It is likedelay provthis dynambe performinfection anMedical pedelayed trebeing able tare also lespathology o

This stuthis techniqcurrent expinfection T[26]. The eing chronicas they neeconsider thimmunity ihave a comhowever thdevelopme

The simpwe have atues, the prethe parameforenotmesuch as persimple modtreatment asimple andtype of vacrs, to a nearly four day window when both factors arehese predictions are not meant to be precise but ratherthe importance of these factors. The extent to whichanisms are utilized in generating immunity may varyfferent infectious diseases.antimicrobial treatment regimens are typically either

re prophylaxis or as soon as possible post-exposure [6].f treatment is not likely to confer immunity and duringc would require constant re-treatment. Delaying treat-s a vaccine and would presumably not require futuret may even prove advantageous for people to purpose-e themselves, when a highly effective antimicrobial isorder to safely immunize in the absence of a vaccine.

thod of vaccination also has generality where it couldy micro-parasite (bacteria and viruses) that stimulatesemory and to which there exists an antimicrobial treat-at is required is a tradeoff between1 and2 pathologiesadequate reduction of both.cination technique would likely have the greatest util-ging epidemics where a vaccine is not yet available.ons and epidemiology of this type of scenario, such asg inuenza pandemic, are presently being researchedors. A key factor in the utility of the technique is thef re-exposure.ople with the highest likelihood of re-exposure wouldatest benet fromthis technique.Medical personnel forho would be in frequent contact with infected personsa pandemic, might be better protected and avoid theof prolongedprophylactic treatment,with a vaccinationtreatment.ly that much treatment already does come with someiding sufcient immunity. A better understanding ofic will prevent unnecessary re-treatment. Testing caned to ascertain where a person is in the course of and better predict when treatment should be performed.rsonnel, who have the highest potential benet fromatment, alsohave thegreatest access to frequent testing,o utilize this personalized approach. Medical personnels likely to miss the treatment window and suffer thef the untreated infection.dy looks at treatment of acute infections. The use ofue in a chronic virus infection is the subject of mucherimental and modeling research. During chronic viruscells become dysfunctional and their population can fallquations for the dynamics of immune responses dur-infections aremore complex than those presented hered to include immune exhaustion [27]. We also do note tradeoffs between treatment and the generation ofn complex helminth infections where the parasite mayplex life cycle with several stages. It is worth notingat treatment of helminth infections can accelerate thent of immune responses [7,8].lemodels used in this paper are illustrative [28].While

tempted to use biologically reasonable parameter val-cise pathology-immunity tradeoff can be sensitive toters. The predictions on treatment window are there-ant tobeprecisebut illustrate thedependenceon factorssistent antigen and programmed division. The use ofels presents a rst step in the development of usings a vaccine. While many of the results of this paper areintuitive, the models show us the robustness of thiscination. The models also illustrate the importance of


characterizing the tradeoff betweenprimary and secondarypathol-ogy to establish the robustness.

We now require measurements to determine the pathology-immunity tradeoff for delayed treatment. While this method couldbe used broeasewouldwe have usease symptknown. Masibility fromwith this tyneeds to bein maximusymptoms o

The coneralizationway of thinprovide immthis by beinuated live vcause pathopathology b

Acknowled

The authfor generouGM070749

Appendix A

Immunopat

The immthe cytotoxresponse.Waccumulateamount ofintegral of t

20

hP(t) [N

Fig. A.1immunopatwe have peing the starstarting treamary and semaximumlines.

The dotttwo-log redinfection. Thment windincluded ththat indicatpathogen dfor minimizilar to thosbe seen in tdow for maimmunopat

Accumulated immunopathology for1 and2 infections fromthe fourmod-of simulations like Fig. 1Cwere performed using eachmodel while varyingy in the start of treatment. The diagonally hashed regions indicate treat-ndowswhere both the 1 and 2 exposures have at least a two-log reductiontted line) in immunopathology. The reduction of immunopathology in thedels has very similar properties to the reduction of max-pathogen densityn Fig. 3. We have included the treatment window for two-log reduction inand 2 max-pathogen density from Fig. 3 to show that treating to reducehogen also treats to reduce immunopathology. (For interpretation of thees to color in this gure legend, the reader is referred to the web version ofle.)

equations

equations for the basic model are given in the text. (1)(5). The model equations for the model with killeden are:

en :dP

dt= rP hP(N + E + M) aPA(t), (A.2)

athogen :dR

dt= hP(N + E + M) + aPA R, (A.3)

crobial : A(t) =

0 if t < 1Am if 1 t 2,0 if t > 2

(A.4)

ells :dN

dt= N P + R

k + P + R (A.5)

cells :dE

dt= (2N + E) P + R

k + P + R dE(

1 P + Rk + P + R

)(A.6)adly to treat a range of infectious diseases, each dis-likely require a different set of parameters. Additionallyed maximum pathogen density as a correlate of dis-oms, but the exact relationship between the two is notximum pathogen is likely a good measure of transmis-one individual to another and limiting max-pathogenpe of vaccination should limit transmission. Testingperformed not only to establish the actual reduction

m pathogen density, but also how that relates to thef disease.

cept of using delayed treatment as a vaccine is a gen-of the normal vaccine concept. It provides a differentking about vaccination. More broadly a vaccine mustunity with minimal pathology. Killed pathogen does

g low in quantity to limit immuno-pathology. Atten-accine is unlikely to grow large enough in number tology. With vaccination by delayed treatment we limity externally controlling the pathogen.

gements

orswould like to thank theNational Institutes ofHealths support. S.P. Stromberg was funded by grant U01and R. Antia was funded by grant R01 AI049334.

. Model details

hology

une system itself can be a source of pathology asic T cells kill infected target cells during an immunee havemodeled accumulated immunopathology as thed loss of target cells (proportional to the accumulatedcytokine secreted) [27]. This quantity is given by thehe lymphocyte killing:

(t) + E(t) + M(t)] dt. (A.1)

shows the results of simulations for accumulatedhology for the fourmodelsused in this paper. As in Fig. 3rformed a set of simulations like the one in Fig. 1C vary-t of treatment from day 0 to day 7. The set of times fortmentandreducing immunopathology forboth thepri-condary exposures, with a two-log reduction from the

immunopathology, are shown with the diagonal hash

ed lines in each plot show the numerical value of auction in immunopathology from that of an untreatedese are provided to guide the eye in our choice in treat-ow for minimizing immunopathology. We have alsoe treatment windows from Fig. 3 (blue) for comparisone the treatmentwindows forminimizing themaximumensity. The gure shows that the treatment windowsing immunopathology by two-log reduction are sim-e for minimizing maximum pathogen density. As canhe gure, treatment within the two-log reduction win-x-pathogen results in at least a two-log reduction inhology.

Fig.A.1.els. A setthe delamentwi(blue dofour moshown iboth 1

max patreferencthe artic

Model

Theas Eqspathog

pathog

killedp

antimi

naive c

effector


memory cells :dM

dt= fdE

(1 P + R

k + P + R)

. (A.7)

Here thekilling terms fromthepathogenequation feeddirectly intothe killed pathogen equation which also includes a decay of killedpathogen from the system. The stimulation of lymphocytes is nowa function of both the live and killed pathogen P+R, where theconstant is added to account for stimulatory differences betweenlive and killed pathogen.

Setting =0 gives a model where killed pathogen has no stim-ulative effeadditional aand prolonincrease inthe infectio

Neitherment termsecondaryesures.

The prog

pathogen :

killedpatho

antimicrobi

naive cells :

gen.1Effect

gen.2Effect

gen.i Effecto

gen.nEffect

memory cel

where E=Themodel wpathogen ca

In this m2 rst-genecell divisionpathogen clcells (N+E+

Model param

The paravided in Tab

Table A.1Numerical valuesofmodelparameters. Thereare fourmodels studieddeterminedbythe incorporation of two factors: stimulation by killed pathogen, and programmedlymphocyte division. Models that have stimulation by killed pathogen have theparameter =

Parameter

Pathogen grLymphocyteAntimicrobiAntimicrobiKilled patho

cell relationpathor decry conmmepath.naive

tions

y expimulry ced thical ihe o

ary eoughin thted dory

. Thisunetionse. Toryd ad.1.

s schromthatse),to, t

caveaontiny wilntinntlyhen pathogen density is reduced below a given thresholdt to zero to reect the discrete nature of the pathogen. Inper all pathogen densities that descend to less than 101 areted to zero.basic and killed pathogen models (Eqs. (1)(5) and Eqs.A.7)) will have oscillations around a xed point value foren and lymphocyte densities. This is shown in Fig. A.2. Inse the oscillations occur around the xed point of lym-e numbers r/h=3.3105, P(t)dk/ =1.75104. For theeters used in this paper the pathogen density during pri-nfections peaks much higher than this stable point and thend below the threshold for extinction of the pathogen in theruncation of the pathogen density in the model).secondary infections with the basic model the number ofnd memory cells can give a max-pathogen density near thect on the immune system. A non-zero value for yieldsntigenic stimulation, generating amore rapid responseged proliferation of lymphocytes. This gives rise to anmemory cell production and conferred protection aftern is cleared.Eqs. (1)(5) nor Eqs. (A.3)(A.7) have amemory recruit-needed for activation of memory cells during a

xposure. This isdiscussedbelowunder secondaryexpo-

rammed division model equations are:

dP

dt= rP hP(N + E + M) aPA(t), (A.8)

gen :dR

dt= hP(N + E + M) + aPA R, (A.9)

al : A(t) =

0 if t < 1Am if 1 t 2,0 if t > 2

(A.10)

dN

dt= N P + R

k + P + R, (A.11)

ors :dE1dt

= 2N P + Rk + P + R E1, (A.12)

ors :dE2dt

= 2E1 E2, (A.13)

...... (A.14)

rs :dEidt

= 2Ei1 Ei, (A.15)

...... (A.16)

ors :dEndt

= 2En1 dEn, (A.17)

ls :dM

dt= fdEn, (A.18)

Ei. Here we have included the killed pathogen term.ith programmed division but not stimulation by killedn be obtained from these equations by setting =0.odel, once a naive cell is stimulated to divide into

ration effector cells it is committed to another n1s giving 2n cells for every stimulated naive cell. Theearance rate is proportional to the total density of CD8M).

eters

meters used in the simulations of this paper are pro-le A.1.

NaiveStimuKilledEffectoMemoPrograInitialInitial

Simula

PrimarIn s

memocells annumerusing t

SecondThr

ascertageneraa memEq. (3)an immmaturaresponof memtion anTable A

Thiment fterm (respontiate in

ModelIn c

densitthat cofrequethat wit is sethis patrunca

The(A.3)(pathogthis caphocytparammary idescenhost (t

Fornaive a1, and models where killed pathogen is inert have =0.

Symbol Value Units

owth r 3.3 day1

killing h 1105 l/cell/dayal killing a 1 kg/mg/dayal conc. Am 5 mg/kggen decay 7 day1

cruitment 2 day1

coefcient k 1105 cell/lgen coeff. 0 or 1 ay rate d 0.35 day1

version f 0.1 d divisions n 18 dens. P(0) 10 cell/lcells N(0) 200 cell/l

osuresating a primary exposure we set the initial number oflls and effector cells to zero. The initial values for naivee infective dose of pathogen are found in Table A.1. Thentegration of these equations was performed in Matlabde45 routine.

xposuresout this paper we simulate secondary infections toe degree of protection provided by the memory cellsuring the primary response. Eqs. (1)(5) do not includerecruitment term like the naive recruitment term inprevents the re-recruitment of memory cells duringresponse, which is known to not occur. Biologically theof memory takes longer than the time of an immuneo simulate a secondary infection we take the numbercells at the end of the simulation of the primary infec-d that number to the initial naive cell number found in

eme gives equivalent results to a model with recruit-memory, a source of naive cells and a naive cell decayreplenishes the naive population after the immuneand an additional cell type that effector cells differen-hat slowly differentiate into memory.

tsuous ODE models of immune responses the pathogenl never reach identically zero. This is due to the natureuous models allow fractions of a single pathogen. It isnecessary in such models to truncate the results such


Fig. A.2. Examapproximately

quasi-equilpathogendeIn these caslations are nprogramme

This effesity Fig. 3B

References

[1] Boltz Din devdoi:10.21

[2] UilenbergTropical M10540307

[3] Brown CGImmunizinfectioncycline. T

[4] Friesen J,ral immuTranslatioPMID: 20

[5] Belnoue Etective Tlive spor2004;172

[6] Fiore AE,the treatmadvisorytions andand Repohttp://ww

[7] Mutapi FChemothto schisteases 19pubmed/

[8] Klimpel Get al. Levlent francantibody.PMID: 18

[9] Regoes RR, Bonhoeffer S. Emergence of drug-resistant inuenza virus:population dynamical considerations. Science 2006;312(5772):38991,doi:10.1126/science.1122947. http://www.sciencemag.org/content/312/5772/389.abstract.

[10] Hayden FG, Treanor JJ, Fritz RS, Lobo M, Betts RF, Miller M, et al.Use of the oral neuraminidase inhibitor Oseltamivir in experimentalhuman inuenza. JAMA: The Journal of the American Medical Associa-tion 1999;282(13):12406, doi:10.1001/jama.282.13.1240. http://jama.ama-assn.org/content/282/13/1240.abstract.

[11] Fritz RS, Hayden FG, Calfee DP, Cass LMR, Peng AW, Alvord WG, et al.Nasal cytokine and chemokine responses in experimental inuenza A virusinfection: results of a placebo-controlled trial of intravenous Zanamivir treat-ment. Journal of InfectiousDiseases 1999;180(3):58693, doi:10.1086/314938.http://jid.oxfordjournals.org/content/180/3/586.abstract.

rcadomminImmup://wwrechtation wceedinp://ww

Stipen DRure Imp://wwch Sencounol

p://wwia R,8+respm. Joup://wwmrljmic sHIV inp://dxdarz Dtrol?p://wwharovventio

199p://wwia R,8+T-ce:10.10med/ber Dmemp://jimntomoRapp

khaus346-0gner EckwelwWLies. 4tple of oscillations in basic model when lymphocyte numbers areequal to r/h.

ibriumvalue. In this caseweget oscillations because thensitydoesnot fall tobelowthe threshold for extinction.es we limit our analysis to the rst peak. These oscil-ot observed experimentally or with the more realisticd division models.ct produces the slight increase in 2 max-pathogenden-on day 5.

A, Aldridge JR, Webster RG, Govorkova EA. Drugselopment for inuenza. Drugs 2010;70(11):134962,65/11537960-000000000-00000.G. Immunization against diseases causedby Theileria parva: a review.edicine & International Health: TM & IH 1999;4(9):A1220. PMID:; http://www.ncbi.nlm.nih.gov/pubmed/10540307., Radley DE, Cunningham MP, Kirimi IM, Morzaria SP, Musoke AJ.

ation against east coast fever (Theileria parva infection of cattle) byand treatment: chemoprophylaxis with n-pyrrolidinomethyl tetra-ropenmedizin Und Parasitologie 1977;28(3):3428. PMID: 910283.Silvie O, Putrianti ED, Hafalla JCR,Matuschewski K, Borrmann S. Natu-nization against malaria: causal prophylaxis with antibiotics. Sciencenal Medicine 2010;2(40):409, doi:10.1126/scitranslmed.3001058.630856; http://www.ncbi.nlm.nih.gov/pubmed/20630856., Costa FTM, Frankenberg T, Vigrio AM, Voza T, Leroy N, et al. Pro-cell immunity against malaria liver stage after vaccination with

ozoites under chloroquine treatment. The Journal of Immunology(4):248795. http://jimmunol.org/content/172/4/2487.abstract.Fry A, Shay D, Gubareva L, Bresee JS, Uyeki TM. Antiviral agents for

[12] Megraofhtt

[13] RupcinProhtt

[14] vanGreNathtt

[15] KaegenImmhtt

[16] AntCDgrahtt

[17] Kosthyofhtt

[18] Woconhtt

[19] Bocconogyhtt

[20] AntCDdoipub

[21] Barbyhtt

[22] MoIn:Bir3-0

[23] WaBla

[24] Drerabent and chemoprophylaxis of inuenza recommendations of thecommittee on immunization practices (ACIP). MMWR Recommenda-Reports: Morbidity and Mortality Weekly Report Recommendationsrts /Centers for Disease Control 2011;60(1):124. PMID: 21248682;w.ncbi.nlm.nih.gov/pubmed/21248682., Ndhlovu PD, Hagan P, Spicer JT, Mduluza T, Turner CM, et al.erapy accelerates the development of acquired immune responsesosoma haematobium infection. The Journal of Infectious Dis-98;178(1):28993. PMID: 9652458; http://www.ncbi.nlm.nih.gov/9652458.R, Eaves-Pyles T, Moen ST, Taormina J, Peterson JW, Chopra AK,

ooxacin rescues mice from lethal intra-nasal infections with viru-isella tularensis and induces immunity and production of protectiveVaccine 2008;26(52):687482, doi:10.1016/j.vaccine.2008.09.077.

930100; http://www.ncbi.nlm.nih.gov/pubmed/18930100.

[25] Hendersotion again10.1086/

[26] Moskophacutely ineffector T8469287

[27] JohnsonR, et anity, exhVirologyhttp://ww

[28] May RM2004;303sciencemR, Vijh S, Allen SE, Kerksiek K, Pilip IM, Pamer EG. Early pro-g of T cell populations responding to bacterial infection. Journalnology (Baltimore, MD) 2000;165(12):68339. PMID: 11120806;w.ncbi.nlm.nih.gov/pubmed/11120806.RM, Mullaney S, Bernard LD, Sosa MAG, Hom RC, Finberg RW. Vac-ith a live retrovirus: the nature of the protective immune response.gs of the National Academy of Sciences 1990;87(14):555862.w.pnas.org/content/87/14/5558.abstract.

donk MJB, Hardenberg G, Bijker MS, Lemmens EE, Droin NM,, et al. Dynamic programming of CD8+T lymphocyte responses.munology 2003;4(4):3615, doi:10.1038/ni912. PMID: 12640451;w.ncbi.nlm.nih.gov/pubmed/12640451.

M, Ahmed R. Memory CD8+T cell differentiation: initial anti-unter triggers a developmental program in naive cells. Natureogy 2001;2(5):41522, doi:10.1038/87720. PMID: 11323695;w.ncbi.nlm.nih.gov/pubmed/11323695.Bergstrom CT, Pilyugin SS, Kaech SM, Ahmed R. Models ofonses. 1. What is the antigen-independent proliferation pro-rnal of Theoretical Biology 2003;221(4):58598. PMID: 12713942;w.ncbi.nlm.nih.gov/pubmed/12713942.

A, Read EL, Qi Y, Allen TM, Altfeld M, Deeks SG, et al. Effects ofelection of the T-cell repertoire on HLA class I-associated controlfection. Nature 2010;465(7296):3504, doi:10.1038/nature08997..doi.org/10.1038/nature08997., Thomsen AR. Does programmed CTL proliferation optimize virus

Trends in Immunology 2005;26(6):30510, doi:16/j.it.2005.04.007.w.sciencedirect.com/science/article/pii/S1471490605001067.GA. Modelling the dynamics of LCMV infection in mice:

nal and exhaustive CTL responses. Journal of Theoretical Biol-8;192(3):283308, doi:10.1006/jtbi.1997.0612. PMID: 9650288;w.ncbi.nlm.nih.gov/pubmed/9650288.Ganusov VV, Ahmed R. The role of models in understandingll memory. Nature Reviews Immunology 2005;5(2):10111,38/nri1550. PMID: 15662368; http://www.ncbi.nlm.nih.gov/15662368.L, Wherry EJ, Ahmed R. Cutting edge: rapid in vivo killing

ory CD8 T cells. The Journal of Immunology 2003;171(1):2731.munol.org/content/171/1/27.abstract.li E, Capecchi B,HoschlerK. Correlates of protection against inuenza.uoli R, Del Giudice G, editors. Inuenza vaccines for the future.er advances in infectious diseases. Springer Basel; 2011. ISBN 978-279-2; p. 199222.K, Hewlett MJ, Bloom DC, Camerini D. Basic virology. 3rd ed. Wiley-l; 2007. ISBN 9781405147156.. Sherrismedicalmicrobiology: an introduction to infectious diseases:h ed.McGraw-Hill Medical; 2003. ISBN 9780838585290 (Chapter 40).n DA, Inglesby TV, OToole T,Mortimer PP. Can postexposure vaccina-st smallpox succeed? Clinical Infectious Diseases 2003;36(5):6229,

374054.idis D, Lechner F, Pircher H, Zinkernagel RM. Virus persistence infected immunocompetent mice by exhaustion of antiviral cytotoxiccells. Nature 1993;362(6422):75861, doi:10.1038/362758a0. PMID:; http://www.ncbi.nlm.nih.gov/pubmed/8469287.PLF, Kochin BF, McAfee MS, Stromnes IM, Regoes RR, Ahmedl. Vaccination alters the balance between protective immu-austion, escape, and death in chronic infections. Journal of2011;85(11):556570, doi:10.1128/JVI.00166-11. PMID: 21411537;w.ncbi.nlm.nih.gov/pubmed/21411537.. Uses and abuses of mathematics in biology. Science(5659):7903, doi:10.1126/science.1094442. http://www.ag.org/content/303/5659/790.abstract.

Vaccination by delayed treatment of infection1 Introduction2 Materials and methods2.1 Basic model2.2 Killed pathogen2.3 Programmed lymphocyte divisions2.4 Correlates of disease and protection

3 Results4 DiscussionAcknowledgementsAppendix A Model detailsImmunopathologyModel equationsModel parametersSimulationsPrimary exposuresSecondary exposuresModel caveats

References

Documents

Vaccination by delayed treatment of infection.pdf