| Abstract: |
| In this talk, we consider a reaction-diffusion-advection SIS epidemic model with a saturated incidence function in a spatio-temporally heterogeneous environment. We introduce the basic reproduction number and establish the threshold dynamics of disease transmission based on this value. For the special case of equal diffusion rates, we prove the global attractivity of both the disease-free and endemic periodic solutions. Furthermore, we explore the asymptotic properties of $\mathcal{R}_0$ in relation to dispersal rates, advection, and total population size, while investigating the influence of the period parameter on the limiting profiles of $\mathcal{R}_0$. Finally, we determine the spatial distribution of the disease when the diffusion rate of the infected population is sufficiently small. Our findings suggest that restricting the movement of infected individuals remains a highly effective strategy for disease elimination. |
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