# American Institute of Mathematical Sciences

May  2017, 16(3): 781-798. doi: 10.3934/cpaa.2017037

## Dynamics of a nonlocal dispersal SIS epidemic model

 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China

wtli@lzu.edu.cn (W.-T. Li)(Corresponding author)

Received  March 2016 Revised  January 2017 Published  February 2017

This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We introduce a basic reproduction number $R_0$ and establish threshold-type results on the global dynamic in terms of R0. More specifically, we show that if the basic reproduction number is less than one, then the disease will be extinct, and if the basic reproduction number is larger than one, then the disease will persist. Particularly, our results imply that the nonlocal dispersal of the infected individuals may suppress the spread of the disease even though in a high-risk domain.

Citation: Fei-Ying Yang, Wan-Tong Li. Dynamics of a nonlocal dispersal SIS epidemic model. Communications on Pure & Applied Analysis, 2017, 16 (3) : 781-798. doi: 10.3934/cpaa.2017037
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