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

authored by

Christoph Walker

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 in a special case of the model.

Organisation(s)

Institute of Applied Mathematics

Type

Article

Journal

Journal of Mathematical Biology

Volume

87

ISSN

0303-6812

Publication date

31.08.2023

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Applied Mathematics, Agricultural and Biological Sciences (miscellaneous), Modelling and Simulation

Sustainable Development Goals

SDG 3 - Good Health and Well-being

Electronic version(s)

https://doi.org/10.48550/arXiv.2212.10137 (Access: Open)
https://doi.org/10.1007/s00285-023-01980-y (Access: Open)