Well-posedness and stability analysis of an epidemic model with infection age and spatial diffusion
1Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany. walker@ifam.uni-hannover.de.
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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