  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.
