A vector-bias malaria model with incubation period and diffusion

Zhiting Xu; Xiao-Qiang Zhao

doi:10.3934/dcdsb.2012.17.2615

Article Contents

2012, Volume 17, Issue 7: 2615-2634. Doi: 10.3934/dcdsb.2012.17.2615

This issue Previous Article Stability of boundary layers for the inflow compressible Navier-Stokes equations Next Article Pullback attractors for non-autonomous quasi-linear parabolic equations with dynamical boundary conditions

A vector-bias malaria model with incubation period and diffusion

Zhiting Xu^1, and
Xiao-Qiang Zhao^2,

1.
School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7

Received: May 31, 2011

Revised: February 29, 2012

Published: September 2012

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Abstract

This paper is devoted to the study of the global dynamics of a vector-bias malaria model with incubation period and diffusion. The global attractivity of the disease-free or endemic equilibrium is first proved for the spatially homogeneous system. Then the threshold dynamics is established for the spatially heterogeneous system in terms of the basic reproduction ratio. A set of sufficient conditions is further obtained for the global attractivity of the positive steady state.

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Mathematics Subject Classification: Primary: 35K57, 37N25; Secondary: 92D30.

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