2016/01/20 by Fei-Ying Yang, Yang, Fei-Ying, Wan-Tong Li +1
Mathematics · #35B40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40
paper · pdf · doi:10.48550/arxiv.1601.05188
21 pages
arxiv created 2016/01/20 · arxiv updated 2016/01/21
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 R0 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.