Aedes, Wolbachia and Dengue
Résumé
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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