Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 4

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

Pages: 311 – 343

DOI: https://dx.doi.org/10.4310/DPDE.2011.v8.n4.a2

Authors

Folashade B. Agusto (Department of Mathematics, Austin Peay State University, Clarksville, Tennessee, U.S.A.)

Rana D. Parshad (Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia)

Abstract

In this paper we study the long time dynamics of a reaction diffusion 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.

Keywords

global existence of solutions, global attractor, dengue, reaction diffusion system

2010 Mathematics Subject Classification

Primary 35B41, 35K57. Secondary 92D25.

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Published 16 December 2011