The Effect of Delay and Diffusion on the Dynamics of Wild Aedes Aegypti Mosquitoes

Abstract

In this chapter, we give a study on the effect of time delay and diffusion on the dynamics of aedes aegypti mosquitoes invasion with quiescent females phase. The proposed model is given by a system of three delay differential equations and its corresponding reaction diffusion system, which describes the interaction between three sub-populations: Eggs, pupae and female. We focus our study on the effect of quiescent females phase represented by time delay. The existence of periodic oscillations around the persistent positive equilibrium (non-trivial equilibrium) when time delay crosses some critical value, no occurrence of Turing bifurcation and the sensitivity analysis of parameters are proved. The stability of the bifurcating branch of periodic oscillations is established by using normal form and center manifold theory. Some numerical simulations are performed to support our theoretical results and complete this work.