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

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.

Positive solutions for diffusive Logistic equation with refuge

In this paper, we study the stationary solutions of the Logistic equation $$\begin{array}{} \displaystyle u_t=\mathcal {D}[u]+\lambda u-[b(x)+\varepsilon]u^p \text{ in }{\it\Omega} \end{array}$$ with Dirichlet boundary condition, here 𝓓 is a diffusion operator and ε > 0, p > 1. The weight function b(x) is nonnegative and vanishes in a smooth subdomain Ω0 of Ω. We investigate the asymptotic profiles of positive stationary solutions with the critical value λ when ε is sufficiently small. We find that the profiles are different between nonlocal and classical diffusion equations.