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# Aedes, Wolbachia and Dengue

* Corresponding author
1 EMAP
EMAP
2 Mathematics Department
FGV/EMAp - Fundação Getulio Vargas - Escola de Matemática Aplicada [Rio de Janeiro]
3 Mathematics Department
Mathematics Department [Fluminense]
4 Program for Scientific Computing
PROCC - Program for Scientific Computing / Programa de Computação Científica [Rio de Janeiro]
5 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : We present a model of infection by Wolbachia of an Aedes aegypti population. This model is designed to take into account both the biology of this infection and any available field. The objective is to use this model for predicting the sustainable introduction of this bacteria. We provide a complete mathematical analysis of the model proposed and give the basic reproduction ratio l R0 for Wolbachia. We observe a bistability phenomenon. Two equilibria are asymptotically stable : an equilibrium where all the population is uninfected and an equilibria where all the population is infected. A third unstable equilibrium exists. We are in a backward bifurcation situation. The bistable situations occurs with natural biological values for the parameters. Our model is an example of an epidemiological model with only vertical transmission. This infection model is then coupled with a classical dengue model. We prove that for the complete model the equilibrium with Wolbachia for the mosquitoes and without dengue for the human is asymptotically stable for sensible values of the parameters. We prove that, if a sufficiently large population of Wolbachia-infected mosquitoes is introduced, dengue will disappear. We use the data of a real trial of releases of infected mosquitoes in Cairns (Australia) to calibrate our model. The calibrated model behaves remarkably well vis á vis the observed field. Then we use then the calibrated model to simulate different scenarios of appearance of dengue. We assume a worst case scenarios of dengue epidemics development and take the large R0 estimation available in the literature which seems to be 24. The simulations confirm our findings, that a dengue epidemics will not occur if Wolbachia infections is sufficiently prevalent in the Aedes populations. This suggests that the introduction of Wolbachia} can become an effective control tool for dengue.
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Cited literature [75 references]

https://hal.inria.fr/hal-00939411
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Submitted on : Thursday, January 30, 2014 - 4:37:42 PM
Last modification on : Thursday, January 20, 2022 - 5:28:47 PM
Long-term archiving on: : Sunday, April 9, 2017 - 3:42:00 AM

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RR-8462.pdf
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• HAL Id : hal-00939411, version 1

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Jair Koiller, Moacyr da Silva, Max Souza, Claudia Codeço, Abderrahman Iggidr, et al.. Aedes, Wolbachia and Dengue. [Research Report] RR-8462, Inria Nancy - Grand Est (Villers-lès-Nancy, France). 2014, pp.47. ⟨hal-00939411⟩

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