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

Christoph Walker

doi:10.48550/arXiv.2212.10137

Details

Original language	English
Article number	52
Journal	Journal of Mathematical Biology
Volume	87
Issue number	3
Publication status	Published - 31 Aug 2023

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.

Keywords

math.AP, Stability of steady states, Age-strucutre, Spatial diffusion

ASJC Scopus subject areas

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

Sustainable Development Goals

SDG 3 - Good Health and Well-being

Cite this

Well-Posedness and Stability Analysis of an Epidemic Model with Infection Age and Spatial Diffusion. / Walker, Christoph.
In: Journal of Mathematical Biology, Vol. 87, No. 3, 52, 31.08.2023.

Research output: Contribution to journal › Article › Research › peer review

Walker, C 2023, 'Well-Posedness and Stability Analysis of an Epidemic Model with Infection Age and Spatial Diffusion', Journal of Mathematical Biology, vol. 87, no. 3, 52. https://doi.org/10.48550/arXiv.2212.10137, https://doi.org/10.1007/s00285-023-01980-y

Walker, C. (2023). Well-Posedness and Stability Analysis of an Epidemic Model with Infection Age and Spatial Diffusion. Journal of Mathematical Biology, 87(3), Article 52. https://doi.org/10.48550/arXiv.2212.10137, https://doi.org/10.1007/s00285-023-01980-y

Walker C. Well-Posedness and Stability Analysis of an Epidemic Model with Infection Age and Spatial Diffusion. Journal of Mathematical Biology. 2023 Aug 31;87(3):52. doi: 10.48550/arXiv.2212.10137, 10.1007/s00285-023-01980-y

Walker, Christoph. / Well-Posedness and Stability Analysis of an Epidemic Model with Infection Age and Spatial Diffusion. In: Journal of Mathematical Biology. 2023 ; Vol. 87, No. 3.

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Research@Leibniz University