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

Hui Cao; Mengmeng Han; Yunxiao Bai; Suxia Zhang; Hui Cao; Mengmeng Han; Yunxiao Bai; Suxia Zhang

doi:10.3934/era.2022194

Electronic Research Archive

2022, Volume 30, Issue 10: 3811-3824. doi: 10.3934/era.2022194

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

1.
School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi'an 710021, China
2.
School of Science, Xi'an University of Technology, Xi'an 710054, China

Academic Editor: Fengqi Yi

Received: 03 July 2022 Revised: 07 August 2022 Accepted: 11 August 2022 Published: 23 August 2022

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.
- SIRS epidemic model,
- the varying population sizes,
- age-structured,
- stability switch,
- Hopf bifurcation
Citation: Hui Cao, Mengmeng Han, Yunxiao Bai, Suxia Zhang. Hopf bifurcation of the age-structured SIRS model with the varying population sizes[J]. Electronic Research Archive, 2022, 30(10): 3811-3824. doi: 10.3934/era.2022194

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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.

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