Randomized trial examines epidemic dynamics incorporating seasonal patterns in a periodic environment, suggesting improved accuracy.
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 dI 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.
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Zhuo et al. (2026) studied this question.
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