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

Jumpei Inoue and Kousuke Kuto
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Jumpei Inoue: Department of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
Kousuke Kuto: Department of Applied Mathematics, Waseda Univerisity, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

Mathematics, 2021, vol. 9, issue 8, 1-11

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; the sub-super solution method; radial solutions; bessel functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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