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Monotone dynamical systems and some models of Wolbachia in Aedes Aegypti populations

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 experimental data obtained in the 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 R0 for Wolbachia. We observe a bistability phenomenon. Two equilibria are asymptotically stable : an equilibrium where all the population is uninfected and an equilibrium where all the population is infected. A third unstable equilibrium exists. We provide an lower bound for the basin of attraction of the desired infected equilibrium. We are in a backward bifurcation situation. The bistable situations occurs with natural biological values for the parameters.
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Submitted on : Tuesday, May 24, 2016 - 11:01:04 AM
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Gauthier Sallet, A.H.B. Silva Moacyr. Monotone dynamical systems and some models of Wolbachia in Aedes Aegypti populations. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2015, 20, pp.145-176. ⟨hal-01320616⟩

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