Spatio-temporal dynamics of an age-structured reaction-diffusion system of epidemic type subjected by Neumann boundary condition

2025/07/12 by Trang, Cong-Bang, Vo, Hoang-Hung
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.09159

Abstract

This paper is concerned with the spatio-temporal dynamics of an age-structured reaction-diffusion system of KPP-epidemic type (SIS), subject to Neumann boundary conditions and incorporating L¹ blow-up type death rate. We first establish the existence of time dependent solutions using age-structured semigroup theory. Afterward, the basic reproduction number R₀ is derived by linearizing the system around the disease-free equilibrium state. In the case R₀<1, the existence, uniqueness and stability of disease-free equilibrium are shown by using ω-limit set approach of Langlais \citelanglais_large₁988, combined with the technique developed in recent works of Zhao et al. \citezhao_spatiotemporal₂023 and Ducrot et al. \citeducrot_age-structured₂024. We highlight that the absence of a general comparison principle for the age-structured SIS-model and non-separable variable mortality rate prevent the direct application of the semi-flow technique developed in \citeducrot_age-structured₂024 to study the long time dynamics.

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• The Principle of Linearized Stability in Age-Structured Diffusive Populations