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<p>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 <InlineEquation ID="IEq1"><EquationSource Format="MATHML"><math><msub><mi>R</mi><mn>0</mn></msub></math></EquationSource><EquationSource Format="TEX">$R_{0}$</EquationSource></InlineEquation> and discuss its asymptotic properties with respect to the diffusion rate <InlineEquation ID="IEq2"><EquationSource Format="MATHML"><math><msub><mi>d</mi><mi>I</mi></msub></math></EquationSource><EquationSource Format="TEX">$d_{I}$</EquationSource></InlineEquation> of the infected individuals. Then the threshold dynamics in terms of <InlineEquation ID="IEq3"><EquationSource Format="MATHML"><math><msub><mi>R</mi><mn>0</mn></msub></math></EquationSource><EquationSource Format="TEX">$R_{0}$</EquationSource></InlineEquation> is established. Notably, our results demonstrate dynamic consistency with their counterparts in the continuous-time setting.</p>

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Dynamics of a discrete-time reaction-diffusion SIS epidemic model in a time-periodic environment

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月4日

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  • Ruiqiang Zhuo,
  • Zhiming Guo,
  • Ruibin Jiang

摘要

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$R_{0}$ and discuss its asymptotic properties with respect to the diffusion rate dI$d_{I}$ of the infected individuals. Then the threshold dynamics in terms of R0$R_{0}$ is established. Notably, our results demonstrate dynamic consistency with their counterparts in the continuous-time setting.