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

Florin Avram, Rim Adenane, Gianluca Bianchin and Andrei Halanay
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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

Mathematics, 2022, vol. 10, issue 3, 1-25

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.

Keywords: epidemic models; varying population models; stability; next-generation matrix approach; basic reproduction number; vaccination; loss of immunity; endemic equilibria; isoclines (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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