Oscillations Induced by Quiescent Adult Female in a Reaction–Diffusion Model of Wild Aedes Aegypti Mosquitoes

Abstract

This paper takes the reaction–diffusion approach to deal with the quiescent females phase, so as to describe the dynamics of invasion of aedes aegypti mosquitoes, which are divided into three subpopulations: eggs, pupae and female. We mainly investigate whether the time of quiescence (delay) in the females phase can induce Hopf bifurcation. By means of analyzing the eigenvalue spectrum, we show that the persistent positive equilibrium is asymptotically stable in the absence of time delay, but loses its stability via Hopf bifurcation when time delay crosses some critical value. Using normal form and center manifold theory, we investigate the stability of the bifurcating branches of periodic solutions and the direction of the Hopf bifurcation. Numerical simulations are carried out to support our theoretical results.