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 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 L-2(Omega), for the system. The attractor is shown to be L-infinity(Omega) 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.

Citation
Agusto, F. B., & Parshad, R. D. (2011). Global dynamics of a PDE model for Aedes aegypti mosquitoe incorporating female sexual preference. Dynamics of Partial Differential Equations, 8(4), 311–343. doi:10.4310/dpde.2011.v8.n4.a2

Acknowledgements
The authors acknowledge the useful discussions with Dr Suzanne Lenhart and Dr. Sharon Bewick. RDP was assisted by attendance as a Short-term Visitor at NIMBioS, while FBA conducted the work as a Postdoctoral Fellow at NIMBioS. National Institute for Mathematical and Biological Synthesis (NIMBioS) is an Institute sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville. We would also like to acknowledge the comments and suggestions of the referee which helped us improve the overall quality of the manuscript.

Publisher
International Press of Boston

Journal
Dynamics of Partial Differential Equations

DOI
10.4310/dpde.2011.v8.n4.a2

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