A diffusion-advection epidemic model with mass action infection mechanism and birth-death effect☆

This paper is concerned with a reaction-diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with mass action infection mechanism and linear birth-death effect. We derive a variational expression of the basic reproduction number R0 and establish its threshold role between disease extinction and persistence. More importantly, we investigate asymptotic profiles of endemic equilibrium with respect to large advection or small motility of susceptible/infected individuals. Compared with three other closely related modeling systems in previous works, it turns out that our model is not only mathematically more difficult to tackle, but also the theoretical findings reveal rather different phenomena concerning spreading and spatial distribution of infectious diseases. These results may bring some prospective applications in disease control strategies.