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Research Article | Open Access

Hopf bifurcation of the age-structured SIRS model with the varying population sizes

Hui Cao1, Mengmeng Han1, Yunxiao Bai1, Suxia Zhang2( )
School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi'an 710021, China
School of Science, Xi'an University of Technology, Xi'an 710054, China
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Abstract

The purpose of this paper is to investigate the impact of the varying population sizes on the dynamic behavior of the age-structured epidemic model. A age-structured SIRS epidemic model with the varying population sizes is established and investigated to take into account time delay. The non-negativity of the solution, the existence and stability of the steady states, and the existence of the Hopf bifurcation are discussed. The numerical simulations show that the varying population sizes can cause the age-structured SIRS model to produce multiple stability switches.

Keywords

SIRS epidemic modelthe varying population sizesage-structuredstability switchHopf bifurcation

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Electronic Research Archive
Volume 30 Issue 10,
October 2022
Pages 3811-3824
DOI: 10.3934/era.2022194

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Cite this article:
Cao H, Han M, Bai Y, et al. Hopf bifurcation of the age-structured SIRS model with the varying population sizes. Electronic Research Archive, 2022, 30(10): 3811-3824. https://doi.org/10.3934/era.2022194

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Received: 03 July 2022
Revised: 07 August 2022
Accepted: 11 August 2022
Published: 15 October 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)