Spatiotemporal dynamics in a periodic SIS epidemic model with Fokker–Planck-type diffusion

Abstract

To investigate the effects of seasonality and individual movement on disease transmission, we formulate a periodic SIS epidemic model with external supply governed by Fokker–Planck-type diffusion law in a spatially heterogeneous environment. A key feature of the model is the incorporation of Fokker–Planck-type diffusion to describe individual movement. We analyze the asymptotic profiles and uniform boundedness of the basic reproduction ratio $R_0$ with respect to the dispersal rate by addressing challenges arising from periodicity and the diffusion mechanism. Under certain conditions, explicit upper bounds for the solution are derived following the comparison principle and invariant region theory. The threshold dynamics indicate that the disease-free $\theta$-periodic solution is globally asymptotically stable as $R_0<1$ and the system becomes uniformly persistent as $R_0>1$. Numerical analysis demonstrates that increasing the dispersal of susceptible individuals can reduce the scale of infection. Furthermore, periodicity is shown to enhance disease persistence and induce greater complexity into the disease dynamics.