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arXiv · 2605.31274

Derivation, Analysis and Simulation of a Spatio-Temporal Epidemiology Model with Memory

Hassan El Bouz·Karim Faraj·Anthony Khairallah·Fatima Mroue
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Abstract

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.

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Hassan El Bouz, Karim Faraj, Anthony Khairallah, Fatima Mroue. 2026-05-29. Derivation, Analysis and Simulation of a Spatio-Temporal Epidemiology Model with Memory. https://arxiv.org/abs/2605.31274

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