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<p>Seasonal variations not only influence the external transmission patterns of diseases but also significantly alter the duration of the incubation period. To incorporate seasonal effects on disease transmission and time-dependent latency in a theoretical framework, we propose and investigate a nonlocal reaction–diffusion epidemic model in almost periodic environments, incorporating time-dependent latency and spatial heterogeneity. Based on the characterization of the principal Lyapunov exponent <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda ^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>λ</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation> for a linear almost periodic reaction–diffusion equation with a time-dependent delay, we show that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda ^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>λ</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation> serves as a threshold determining the uniform persistence and extinction for the model. In particular, a numerical method for estimating the principal Lyapunov exponent is presented. Moreover, we illustrate our theoretical findings by employing numerical simulations and discuss the effects of parameters on the persistence and extinction of the model.</p>

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Threshold dynamics of a reaction–diffusion epidemic model with an almost periodic time-dependent delay

  • 期刊论文

  • 发表日期：

    2026年5月22日

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  • Lizhong Qiang,
  • Xiaoting Zhang

摘要

Seasonal variations not only influence the external transmission patterns of diseases but also significantly alter the duration of the incubation period. To incorporate seasonal effects on disease transmission and time-dependent latency in a theoretical framework, we propose and investigate a nonlocal reaction–diffusion epidemic model in almost periodic environments, incorporating time-dependent latency and spatial heterogeneity. Based on the characterization of the principal Lyapunov exponent \(\lambda ^*\) λ ∗ for a linear almost periodic reaction–diffusion equation with a time-dependent delay, we show that \(\lambda ^*\) λ ∗ serves as a threshold determining the uniform persistence and extinction for the model. In particular, a numerical method for estimating the principal Lyapunov exponent is presented. Moreover, we illustrate our theoretical findings by employing numerical simulations and discuss the effects of parameters on the persistence and extinction of the model.