Wan-Tong Li — Page 2

arXiv2016

Dynamics of a Nonlocal Dispersal SIS Epidemic Model

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 $R_0$. 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.

math.AP↗

arXiv2016

A Nonlocal Dispersal SIS Epidemic Model in Heterogeneous Environment

This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and the total population number is constant. We first introduce the basic reproduction number $R_0$ and then discuss the existence, uniqueness and stability of steady states of the nonlocal dispersal SIS epidemic model in terms of $R_0$. In particular, we also consider the impacts of the large diffusion rates of the susceptible and infected population on the persistence and extinction of the disease, and these results imply that the nonlocal movement of the susceptible or infected individuals will enhance the persistence of the disease. Additionally, our analytical results also suggest that the spatial heterogeneity tends to boost the spread of the disease. We have to emphasize that the main difficulty is that a lack of regularizing effect occurs.

math.AP↗