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

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 {langlais_large_1988}, combined with the technique developed in recent works of Zhao et al. {zhao_spatiotemporal_2023} and Ducrot et al. {ducrot_age-structured_2024}. 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 {ducrot_age-structured_2024} to study the long time dynamics.