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This study develops a mathematical model to track how infectious diseases spread across geographic areas and time, specifically accounting for asymptomatic transmission and the variable incubation period through memory effects. The authors prove that their integro-differential equation system has mathematically valid solutions using the Faedo-Galerkin method and demonstrate the model by simulating disease spread in Lebanon. The model incorporates both spatial diffusion of the disease and temporal memory of past infections through integral terms.
Why it matters
This modeling framework could improve predictions of disease outbreaks by capturing realistic features like asymptomatic carriers and variable incubation periods, potentially helping public health officials better allocate resources and plan interventions. The mathematical rigor provides a foundation for reliable computational simulations of epidemics in specific geographic regions.
arXiv:2605.31274v1 Announce Type: cross
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.
Source: Derivation, Analysis and Simulation of a Spatio-Temporal Epidemiology Model with Memory