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Stability Analysis of an Eight Parameter SIR-Type Model Including Loss of Immunity, and Disease and Vaccination Fatalities

Author

Listed:
  • Florin Avram

    (Laboratoire de Mathématiques Appliquées, Université de Pau, 64000 Pau, France)

  • Rim Adenane

    (Département des Mathématiques, Université Ibn-Tofail, Kenitra 14000, Morocco)

  • Gianluca Bianchin

    (Department of Electrical, Computer, and Energy Engineering, University of Colorado Boulder, Boulder, CO 80309, USA)

  • Andrei Halanay

    (Department of Mathematics and Informatics, Polytechnic University of Bucharest, 062203 Bucharest, Romania)

Abstract

We revisit here a landmark five-parameter SIR-type model, which is maybe the simplest example where a complete picture of all cases, including non-trivial bistability behavior, may be obtained using simple tools. We also generalize it by adding essential vaccination and vaccination-induced death parameters, with the aim of revealing the role of vaccination and its possible failure. The main result is Theorem 1, which describes the stability behavior of our model in all possible cases.

Suggested Citation

  • Florin Avram & Rim Adenane & Gianluca Bianchin & Andrei Halanay, 2022. "Stability Analysis of an Eight Parameter SIR-Type Model Including Loss of Immunity, and Disease and Vaccination Fatalities," Mathematics, MDPI, vol. 10(3), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:402-:d:735810
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    Cited by:

    1. Sanubari Tansah Tresna & Subiyanto & Sudradjat Supian, 2022. "Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review," Mathematics, MDPI, vol. 10(14), pages 1-12, July.

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