Development of a mathematical model for tsetse with a main objective to eradicate tsetse ... R. Lancelot1, J. Bouyer1;2, ... to produce larva is function of the temperature

Context Objectives The Data Tsetse Model Perspectives

Development of a mathematical model for tsetsepopulation dynamic to optimize the control in the

Niayes (Senegal)

A. A. FALL1,2, R. Lancelot1, J. Bouyer1,2, A. Dicko2,3 & M. T.Seck2

1 UMR Controle des Maladies Animales Exotiques et Emergentes (CMAEE)Centre de cooperation internationale en recherche agronomique pour le

developpement (CIRAD)2 Institut Senegalais de Recherches Agricoles (ISRA) (LNERV)

3 Ecole Nationale de la Statistique et de l’Analyse Economique (ENSAE-Senegal)

5 octobre 2011

A. A. FALL1,2, R. Lancelot1, J. Bouyer1,2, A. Dicko2,3 & M. T. Seck2Tsetse population dynamic


Plan

1 Context

2 Objectives

3 The Data

4 Tsetse Model

5 Perspectives



Context

The Senegalese government aims to control trypanosomosisfrom the Niayes region by eradicating the tsetse vector,Glossina palpalis gambiensis

In 2005, the Senegalese government initiated a controlcampaign called �Projet de lutte contre les glossines dans lesNiayes� with a main objective to eradicate tsetse fly in theNiayes area.



Study area

Figure: Distribution of tsetse flies in the Niayes areaA. A. FALL1,2, R. Lancelot1, J. Bouyer1,2, A. Dicko2,3 & M. T. Seck2Tsetse population dynamic


Objectives

Determination of temperatures ”feeled” by tsetse

Establish a mathematical model to optimize the controlmeasures

Estimation of the model parameters by fitting the model tofield data (densities , age structure)

Establish the map of distribution

Establish the metapopulation model using the tsetse map ofdistribution

Optimize the control processes measures for tsetse eradicationin the Niayes



The data

According to the Tsetse biology and ecology, the tsetse life cycle isdependent on the environmental and climatic conditions.We focused on the influence of average daily temperature (θt) ontsetse population dynamics.Field meteorological data are available in the study area and will bemodeled using Modis data.



Temperature / Modis

date

tem

péra

ture

15202530354045

15202530354045

15202530354045

cadda

févr.-09 août-09 févr.-10 août-10

ean

juil.-09 janv.-10 juil.-10 janv.-11

ka

2007 2008 2008 2009 2009 2010 2010

carmel

févr.-09 août-09 févr.-10 août-10

haddad

2007 2008 2008 2009 2009 2010

sall

juil.-09 janv.-10 juil.-10 janv.-11

temp_air lstnight lstday

Figure: correlation between air temperature and soil temperature



Temperature soil/air

air temperature (°C)

soil

tem

pera

ture

(°C

)

23

24

25

26

27

22 24 26 28

date

tem

pera

ture

(°C

)

22°

24°

26°

28°

air soil

juin-08 sept.-08 déc.-08 mars-09 juin-09 sept.-09 déc.-09 mars-10

Figure: correlation between air temperature and soil temperature(Haddad)



Tsetse Life Cycle

less than 5 days 1/4 hour

14 -24 days 20-80 days

Reproduction cycle of a Tsetse Fly1/2 to 2 hours

Figure: elimination des glossines dans la zone des Niayes et La PetiteCote



effect of the temperature on the tsetse development

The daily contribution of the temperature (θt) on tsetsepopulation dynamics is obtained by using Hargrove equation :

daily contribution of temperature on the pupal stagepp = (θt − 24) ∗ a1 + b1;

daily contribution of temperature on the teneral stageflp = (θt − 24) ∗ a2 + b2;

daily contribution of temperature on the adult stage.lp = (θt − 24) ∗ a3 + b3;



Conceptual Model

P1α1

αiαi-1αn-1

ci=1

clcl+1

ci+1=1

cj=1

PiP2 Pi+1 Pn

T1β1

βjβj-1βm-1TjT2 Tj+1 Tm

A1γ1

γiγl-1γm-1AlA2 Al+1 Ak

cn=1

cj=1

cm=1

Figure: Conceptual Model



Conceptual Model

P1 =∑

ci (θt)FiAi

P2 = c2(θt)α1P1...

Pn = cn(θt)αn−1Pn−1

T1 =∑

(1 − ci (θt))αiPi

T2 = c2(θt)βn+1T1...

Tm = cm(θt)βm−1Tm−1

A1 =∑

(1 − ci (θt))βiTi

A2 = c2(θt)γ2A...

Ak = ck(θt)γk−1Ak−1

(1)

En posant :Xt =

P1

P2...

Pn

T1

T2...

Tm

A1

A2...

Ak

(2)



Conceptual Model

X(t+1) = Aθt .Xt where Aθt is equal to

0 . . . 0 cj (θt )Fj 0 . . . ck (θt )Fk

c1(θt )α1 0

.

.

. 0 . . . . . . 00 c2(θt )α2 0 0 . . . . . . 0

0 0 ci (θt )αi 0 . . . . . . 0

.

.

.. . .

.

.

.. . . . . . 0 0

0 0

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.(1 − c1(θt ))α1 . . . (1 − ci (θt ))αi 0 . . . 0

0 0 0 cj (θt )β1 0 . . . 0

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.0 0 0 (1 − cj (θt ))β1 . . . (1 − cj+1(θt ))βj 0 . . . 00 0 . . . 0 ck−1(θt )γk−1 0 00 0 0 . . . 0 ck (θt )γk 0

(3)



Aθt is temperature dependent.

as the mortality is temperature-dependent

the fecundity is temperature-dependent because the time takento produce larva is function of the temperature .



0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 1 2 3 4

Figure: histogram of the frequencies of flies by parity group produce bythe model



Figure: histogram of the frequencies of flies by parity group on the fielddata



0

5

10

15

20

25

30

35

0 100 200 300 400 500 600 700 800

number of pupa or adult f lies per day

number of days

nu

mb

er o

f p

up

a/fl

ies

pupaflies

Figure: tsetse population dynamic with a temperature around 30° C(λ < 1)



0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800

number of pupa or adult f lies per day

number of days

nu

mb

er o

f p

up

a/fl

ies

pupaflies

Figure: tsetse population dynamic with a temperature around 25° C(λ > 1)



Perspectives

parameters estimation (in progress...)

sensivity analysis and uncertainty analysis

Tsetse distribution map of suitable habitat



FIN

Thanks for your attention ! ! !...


Documents

Development of a mathematical model for tsetse with a main objective to eradicate tsetse ... R. Lancelot1, J. Bouyer1;2, ... to produce larva is function of the temperature