Dynamics of a parasite-host epidemiological model in spatial heterogeneous environment

Yongli Cai; Weiming Wang

doi:10.3934/dcdsb.2015.20.989

Article Contents

2015, Volume 20, Issue 4: 989-1013. Doi: 10.3934/dcdsb.2015.20.989

This issue Previous Article An energy-consistent depth-averaged Euler system: Derivation and properties Next Article Multidimensional stability of disturbed pyramidal traveling fronts in the Allen-Cahn equation

Dynamics of a parasite-host epidemiological model in spatial heterogeneous environment

Yongli Cai^1, and
Weiming Wang^2,

1.
Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275
2.
College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035

Received: April 2014

Revised: July 2014

Published: June 2015

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Abstract

In this paper, we explore a parasite-host epidemiological model incorporating demographic and epidemiological processes in a spatially heterogeneous environment in which the individuals are subject to a random movement. We show the global stability of the extinction equilibrium in three different cases, and prove the existence, uniqueness and the global stability of the disease--free equilibrium. When the death rate in the model becomes a constant, we give the existence of the endemic equilibrium and the global stability of the endemic equilibrium in a special case. Furthermore, we perform a series of numerical simulations to display the effects of the movement of hosts and the heterogeneous environment on the disease dynamics. Our analytical and numerical results reveal that the disease extinction/outbreak can be ignited by both individual mobility and the environmental heterogeneity.

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Mathematics Subject Classification: Primary: 35K57, 35B35; Secondary: 92D25.

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