Well-Posedness and Stability Analysis of an Epidemic Model with Infection Age and Spatial Diffusion

2022/12/20 by Walker, Christoph · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2212.10137

Abstract

A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the susceptibles. Global well-posedness of the equations within the class of nonnegative smooth solutions is shown. Moreover, spectral properties of the linearization around a steady state are derived. This yields the notion of linear stability which is used to determine stability properties of the disease-free and the endemic steady state.

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• A Wave-type Model for Age- and Space-structured Epidemics
• Spatio-temporal dynamics of an age-structured reaction-diffusion system of epidemic type subjected by Neumann boundary condition

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