Well-Posedness and Stability Analysis of an Epidemic Model with Infection Age and Spatial Diffusion
- Resource Type
- Working Paper
- Authors
- Walker, Christoph
- Source
- Subject
- Mathematics - Analysis of PDEs
- Language
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.
Comment: 32 pages