On Equilibria Stability in an Epidemiological SIR Model with Recovery-dependent Infection Rate

A. D. Baez Sanchez, N. Bobko

Abstract


We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also the stability of the disease-free equilibrium. We show that, in contrast with classical SIR models, a system with a recovery-dependent infection rate can have multiple endemic stable equilibria (multistability) and multiple stable and unstable saddle points of equilibria. We establish conditions for the occurrence of these phenomena and illustrate the results with some examples.


Keywords


SIR epidemiological model; Recovery-dependent infection rate; Endemic equilibria; Multistability

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DOI: https://doi.org/10.5540/tema.2020.021.03.409

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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