A Nonlocal Dispersal SIS Epidemic Model in Heterogeneous Environment

TL;DR

This paper analyzes a nonlocal dispersal SIS epidemic model in heterogeneous environments, revealing how spatial heterogeneity and movement rates influence disease persistence and extinction.

Contribution

It introduces a new nonlocal dispersal SIS model with spatial heterogeneity and studies the effects of movement rates and heterogeneity on disease dynamics.

Findings

Higher diffusion rates promote disease persistence.

Spatial heterogeneity tends to facilitate disease spread.

Nonlocal movement enhances disease persistence.

Abstract

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.