Analysis on a diffusive SIS epidemic model with saturated incidence rate and linear source in a heterogeneous environment

In this paper, we are concerned with a reaction-diffusion SIS epidemic model with saturated incidence rate and linear source in spatially heterogeneous environments. We derive the uniform bounds of parabolic system and study the extinction and persistence of the infectious disease in terms of the basic reproduction number. The existence of the endemic equilibrium (EE) is established when the basic reproduction number is greater than one. We further investigate the effects of diffusion and saturation on asymptotic profiles of the endemic equilibrium. Our study shows that the linear source can enhance persistence of infectious disease and large saturation can help speed up the elimination of disease. (C) 2020 Elsevier Inc. All rights reserved.