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.
Highlights
Because of the spread of COVID-19, the role of mathematical models in infectious disease epidemiology is becoming more important
We introduce the known results on the SIS model (1) and the associated stationary problem (3)
Br2 will be denoted by Br for simplicity. This setting (13) assumes a situation where the rate of disease transmission is uniform, but the recovery rate is poor within the centered area Bε
Summary
Because of the spread of COVID-19, the role of mathematical models in infectious disease epidemiology is becoming more important. This paper is aim to assert that, by mathematical analysis for a diffusive SIS model, a regional difference of recovery rates of infectious disease can make the total population of infected become large. In the field of reaction–diffusion equations, the following SIS model has been studied since thre paper by. Bolker, Lou, and Nevai [1]: ∂S SI = dS ∆S − β( x ) + γ( x ) I, ( x ∈ Ω, t > 0), ∂t S +I.
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