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<p>In this paper, we propose an integro-differential model for the spatio-temporal evolution of infectious diseases with asymptomatic transmission. The model consists of a&#xa0;reaction-diffusion system with an integral memory term accounting for the distribution of the incubation period. We first analyze the asymptotic behavior and the properties of the integro-differential model. Then, we prove the local existence of a&#xa0;weak solution of the system by means of the Faedo-Galerkin method and a&#xa0;compactness argument. The model is applied to simulate the geographical evolution of a&#xa0;disease in Lebanon.</p>

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Derivation, analysis and simulation of a spatio-Temporal epidemiology model with memory

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • H. El Bouz,
  • K. Faraj,
  • A. Khairallah,
  • F. Mroué

摘要

In this paper, we propose an integro-differential model for the spatio-temporal evolution of infectious diseases with asymptomatic transmission. The model consists of a reaction-diffusion system with an integral memory term accounting for the distribution of the incubation period. We first analyze the asymptotic behavior and the properties of the integro-differential model. Then, we prove the local existence of a weak solution of the system by means of the Faedo-Galerkin method and a compactness argument. The model is applied to simulate the geographical evolution of a disease in Lebanon.