Dynamics of a Nonlocal Dispersal SIS Epidemic Model

TL;DR

This paper analyzes a nonlocal dispersal SIS epidemic model with spatially heterogeneous transmission and recovery rates, establishing threshold conditions for disease extinction or persistence based on a basic reproduction number.

Contribution

It introduces a basic reproduction number for the nonlocal dispersal model and proves threshold results for disease dynamics, including the potential suppression of disease spread by nonlocal dispersal.

Findings

Disease extinction when R0<1

Disease persistence when R0>1

Nonlocal dispersal can suppress disease spread

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 $R_0$. 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.