Gauthier Sallet ; A.H.B. Silva Moacyr - Monotone Dynamical Systems and Some Models of Wolbachia in Aedes aegypti Populations

arima:1992 - Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, November 29, 2015, Volume 20 - 2015 - Special issue - Colloquium in Honor of Éric Benoît - https://doi.org/10.46298/arima.1992
Monotone Dynamical Systems and Some Models of Wolbachia in Aedes aegypti Populations

Authors: Gauthier Sallet ; A.H.B. Silva Moacyr

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.


Volume: Volume 20 - 2015 - Special issue - Colloquium in Honor of Éric Benoît
Published on: November 29, 2015
Submitted on: May 28, 2015
Keywords: Mathematical epidemiology, dynamical systems, stability, ODE.,Epidémiologie mathématique, Wolbachia, Aedes, systèmes dynamiques, stabilité, EDO.,[INFO] Computer Science [cs],[MATH] Mathematics [math]


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