Dynamics of a nonlocal dispersal SIS epidemic model

Fei-Ying Yang; Wan-Tong Li

doi:10.3934/cpaa.2017037

Article Contents

2017, Volume 16, Issue 3: 781-798. Doi: 10.3934/cpaa.2017037

This issue Previous Article On the decay and stability of global solutions to the 3D inhomogeneous MHD system Next Article W^{1, p}-estimates for elliptic equations with lower order terms

Dynamics of a nonlocal dispersal SIS epidemic model

Fei-Ying Yang and
Wan-Tong Li^,

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

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

Received: February 29, 2016

Revised: December 31, 2016

Published: January 2018

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Abstract

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.

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Mathematics Subject Classification: 35B40, 45A05, 45F05, 47G20.

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