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

TL;DR

This paper analyzes a spatial epidemic model incorporating infection age and diffusion, establishing well-posedness and stability properties of disease states, advancing understanding of disease dynamics with spatial and temporal factors.

Contribution

It introduces a well-posedness and stability framework for an epidemic model with infection age and spatial diffusion, including spectral analysis of steady states.

Findings

Global well-posedness of the model is proven.

Spectral properties of linearized operators are derived.

Stability conditions for disease-free and endemic states are established.

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.