A periodic reaction-diffusion-advection SIS epidemic model with a saturated incidence function

This paper is concerned with a reaction-diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with a saturated incidence function in a spatio-temporally heterogeneous environment. We introduce the basic reproduction number $ \mathcal{R}_0 $ and establish the threshold dynamics for the disease transmission in terms of $ \mathcal{R}_0 $. The global attractivity of both the disease-free and endemic periodic solution are shown in the special case of equal diffusion rates. More precisely, we explore the asymptotic properties of $ \mathcal{R}_0 $ with respect to the dispersal rates, the advection rate and the total population number. We further study the monotonicity and limiting profiles of $ \mathcal{R}_0 $ with respect to the period parameter. Moreover, we determine the spatial distribution of the disease when the diffusion rate of the infected population is sufficiently small. Our findings suggest that lowering the movement rate of infected individuals is an effective strategy to eliminate the infectious disease.