# American Institute of Mathematical Sciences

June  2015, 20(4): 989-1013. doi: 10.3934/dcdsb.2015.20.989

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

 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  February 2015

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.
Citation: Yongli Cai, Weiming Wang. Dynamics of a parasite-host epidemiological model in spatial heterogeneous environment. Discrete & Continuous Dynamical Systems - B, 2015, 20 (4) : 989-1013. doi: 10.3934/dcdsb.2015.20.989
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