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

In: Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells

Author

Listed:
  • Saumen Barua

    (Gachhbaria Government College)

  • Attila Dénes

    (University of Szeged, Bolyai Institute
    National Laboratory for Health Security)

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.

Suggested Citation

  • Saumen Barua & Attila Dénes, 2025. "Global Stability in an SIRS Model with Zoonotic Transmission, Nonlinear Incidence Rate, and Temporary Immunity," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, pages 25-38, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-97461-8_2
    DOI: 10.1007/978-3-031-97461-8_2
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