Global stability properties of a class of renewal epidemic models with variable susceptibility

2020/07/23 by Michael T. Meehan, Meehan, Michael T., Daniel Cocks +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #COVID-19 epidemiological studies #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE)

paper · pdf · doi:10.48550/arxiv.2007.11796

openalex publication_date 2020/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the global dynamics of a renewal-type epidemic model with variable susceptibility. We show that in this extended model there exists a unique endemic equilibrium and prove that it is globally asymptotically stable when R₀ > 1, i.e. when it exists. We also show that the infection-free equilibrium, which exists always, is globally asymptotically stable for R₀ ≤ 1.

Citations

• Global stability for the SEIR model in epidemiology
• On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations
• Global properties of basic virus dynamics models

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