Global dynamics of a PDE model for aedes aegypti mosquitoe incorporating female sexual preference

Abstract

In this paper we study the long time dynamics of a reaction diffu-sion system, describing the spread of Aedes aegypti mosquitoes, which are the primary cause of dengue infection. The system incorporates a control attempt via the sterile insect technique. The model incorporates female mosquitoes sexual preference for wild males over sterile males. We show global existence of strong solution for the system. We then derive uniform estimates to prove the existence of a global attractor in L2(Ω), for the system. The attractor is shown to be L∞(Ω) regular and posess state of extinction, if the injection of sterile males is large enough. We also provide upper bounds on the Hausdorff and fractal dimensions of the attractor. © 2011 International Press.