The asymptotic behavior of an SIR epidemic model: collective Reed-Frost process

Abdelhak Eseghir, Abdelghani Kissami, Mohamed Latifi, Khalid Hattaf

Abstract


The aim of this research is to provide a historical overview of the mathematical theory of epidemics and to study the asymptotic behavior of the final size of a collective Reed-Frost epidemic process with different types of infected people. This model was introduced by Picard and Lefevre [25] provides an extension of the model of Pettigrew and Weiss [24]. Under certain conditions, we show that when the number of the initial susceptible individuals is large and the number of the initial infected people is finite, the infection process is equivalent to a multitype Galton-Watson process. Our method is simple and based on Bernstein polynomials.

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Published: 2022-02-16

How to Cite this Article:

Abdelhak Eseghir, Abdelghani Kissami, Mohamed Latifi, Khalid Hattaf, The asymptotic behavior of an SIR epidemic model: collective Reed-Frost process, Commun. Math. Biol. Neurosci., 2022 (2022), Article ID 18

Copyright © 2022 Abdelhak Eseghir, Abdelghani Kissami, Mohamed Latifi, Khalid Hattaf. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

ISSN 2052-2541

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