Effect of diffusion in a spatial SIS epidemic model with spontaneous infection

Abstract

<p style='text-indent:20px;'>This paper is concerned with an SIS epidemic reaction-diffusion model with mass-action incidence incorporating spontaneous infection in a spatially heterogeneous environment. The main goal of this article is to study the influence of spontaneous infection on the endemic equilibrium (EE) of the model. To achieve this, first the existence of EE is investigated. Furthermore, we discuss the asymptotic behavior of endemic equilibrium if the migration rate of the susceptible or infected population is sufficiently small. Compared to the case without spontaneous infection, our theoretical results show that spontaneous infection can enhance persistence of infectious disease.