An SIS epidemic reaction–diffusion model with spontaneous infection in a spatially heterogeneous environment

Abstract

This paper concerns an SIS epidemic reaction–diffusion model, which includes the possibility for spontaneous infection, in addition to disease transmission. We prove the global asymptotic stability of the unique endemic equilibrium when the spatial environment is homogeneous. When the spatial environment is heterogeneous, we show the existence of endemic equilibria and then analyze their asymptotic profile if the movement (migration) rate of the susceptible or infected population is small or large. Compared to the case that spontaneous infection is ignored, our theoretical study here suggests that spontaneous infection can enhance persistence of infectious disease and therefore gives new insight into disease control and prediction.