The transmission of many infectious diseases exhibits distinct seasonal patterns, with infection and recovery rates showing periodic fluctuations over time. Therefore, incorporating temporal periodicity allows for a more accurate capture of the epidemic dynamics. In this paper, we consider a discrete-time reaction-diffusion SIS model with temporal periodicity and spatial heterogeneity. We introduce a basic reproduction number R₀ and discuss its asymptotic properties with respect to the diffusion rate d₈ of the infected individuals. Then the threshold dynamics in terms of R₀ is established. Notably, our results demonstrate dynamic consistency with their counterparts in the continuous-time setting.
Zhuo et al. (Mon,) studied this question.