Impact of Regional Difference in Recovery Rate on the Total Population of Infected for a Diffusive SIS Model

Abstract

This paper is concerned with an SIS epidemic reaction-diffusion model. The purpose of this paper is to derive some effects of the spatial heterogeneity of the recovery rate on the total population of infected and the reproduction number. The proof is based on an application of our previous result on the unboundedness of the ratio of the species to the resource for a diffusive logistic equation. Our pure mathematical result can be epidemically interpreted as that a regional difference in the recovery rate can make the infected population grow in the case when the reproduction number is slightly larger than one.

Keywords

• reaction–diffusion systems
• SIS models
• endemic equilibrium
• the reproduction number
• diffusive logistic equation
• spatial heterogeneity