Global Stability in an SIRS Model with Zoonotic Transmission, Nonlinear Incidence Rate, and Temporary Immunity

Saumen Barua and Attila Dénes ()
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Saumen Barua: Gachhbaria Government College
Attila Dénes: University of Szeged, Bolyai Institute

A chapter in Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, 2025, pp 25-38 from Springer

Abstract: Abstract We establish and study an SIRS $$\mathit {SIRS}$$ epidemic model for a zoonotic disease only transmitted from animals to humans but not the opposite way, with a general nonlinear incidence rate assuming that the animal population has already reached an endemic equilibrium. Due to the zoonotic transmission, there is no disease-free equilibrium, and unlike in most epidemic models, no threshold dynamics can be observed. Using a transformation of variables, we derive a Lyapunov function for the global asymptotic stability of the unique endemic equilibrium, independently of model parameters.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-97461-8_2

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DOI: 10.1007/978-3-031-97461-8_2

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