Qualitative analysis on a spatial SIS epidemic model with linear source in advective environments II saturated incidence

Abstract: In this paper, we consider a reaction-diffusion-advection SIS epidemic model with saturated incidence rate and linear source. We study the uniform bounds of parabolic system and some asymptotic behavior of the basic reproduction number $\mathcal{R}_0$, according to which the threshold-type dynamics are given. Furthermore, we show the globally asymptotic stability of the endemic equilibrium in a special case with a large saturated incidence rate. Meanwhile, we investigate the effects of diffusion, advection, saturation and linear source on the asymptotic profiles of the endemic equilibrium. Our study shows that advection may induce the concentration phenomenon and the disease will be eradicated with small dispersal rate of infected individuals. Moreover, our results also reveal that the linear source can enhance persistence of infectious disease and large saturation can help speed up the elimination of disease.