Dynamics of a nonlocal dispersal SIS epidemic model with Neumann boundary conditions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Yang, Fei-Ying¹  Li, Wan-Tong¹  Ruan, Shigui² 

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

[2] Univ Miami, Dept Math, Coral Gables, FL 33146 USA

关键词: Nonlocal dispersal;    Basic reproduction number;    Disease-free equilibrium;    Endemic equilibrium;    Stability;   

DOI  :  10.1016/j.jde.2019.03.001

来源: Elsevier

【 摘 要 】

In this paper we study a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the spatial movement of individuals is described by a nonlocal (convolution) diffusion operator, the transmission rate and recovery rate are spatially heterogeneous, and the total population number is constant. We first define the basic reproduction number R-0 and discuss the existence, uniqueness and stability of steady states of the nonlocal dispersal SIS epidemic model in terms of R-0. Then we consider the impacts of the large diffusion rates of the susceptible and infectious populations on the persistence and extinction of the disease. The obtained results indicate that the nonlocal movement of the susceptible or infectious individuals will enhance the persistence of the infectious disease. In particular, our analytical results suggest that the spatial heterogeneity tends to boost the spread of the infectious disease. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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