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Dynamics of an SIS Epidemic Model with No Vertical Transmission

In: Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics

Author

Listed:
  • Sándor Kovács

    (Eötvös Loránd University, Department of Numerical Analysis)

  • Szilvia György

    (Eötvös Loránd University, Department of Numerical Analysis)

  • Noémi Gyúró

    (Eötvös Loránd University)

Abstract

We study a population model for an infectious disease that spreads in the host population through standard incidence and no vertical transmission. We show that the global dynamics are completely determined by the basic reproduction number ℛ0. If ℛ0 1, a new (endemic) equilibrium emerges. Sensitivity analysis is performed on this epidemic threshold value, and it is then used to show that at its critical value bifurcation takes place. This bifurcation is forward: a super-threshold endemic equilibrium exists, the global asymptotic stability of which is also shown. Improving discretization (nonstandard finite difference scheme), our results are corresponding to those in the original continuous model.

Suggested Citation

  • Sándor Kovács & Szilvia György & Noémi Gyúró, 2023. "Dynamics of an SIS Epidemic Model with No Vertical Transmission," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics, pages 1-15, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-33050-6_1
    DOI: 10.1007/978-3-031-33050-6_1
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