Bifurcation analysis of an age-structured SIRI epidemic model

Xiaohong Tian; Rui Xu; Ning Bai; Jiazhe Lin; Xiaohong Tian; Rui Xu; Ning Bai; Jiazhe Lin

doi:10.3934/mbe.2020366

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7130-7150. doi: 10.3934/mbe.2020366

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Bifurcation analysis of an age-structured SIRI epidemic model

1.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
2.
Institute of Applied Mathematics, Army Engineering University, Shijiazhuang 050003, Hebei, China

Received: 03 July 2020 Accepted: 15 September 2020 Published: 21 October 2020

In this paper, an SIRI epidemic model with age of infection and the proliferation of susceptible individuals with logistic growth is investigated. By using the theory of integral semigroup and Hopf bifurcation theory for semilinear equations with non-dense domain, it is shown that if the threshold parameter is greater than unity, sufficient condition is derived for the occurrence of the Hopf bifurcation. Numerical simulations are carried out to illustrate the theoretical results.
- an SIRI epidemic model,
- logistic growth,
- age structure,
- hopf bifurcation
Citation: Xiaohong Tian, Rui Xu, Ning Bai, Jiazhe Lin. Bifurcation analysis of an age-structured SIRI epidemic model[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7130-7150. doi: 10.3934/mbe.2020366

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Abstract

In this paper, an SIRI epidemic model with age of infection and the proliferation of susceptible individuals with logistic growth is investigated. By using the theory of integral semigroup and Hopf bifurcation theory for semilinear equations with non-dense domain, it is shown that if the threshold parameter is greater than unity, sufficient condition is derived for the occurrence of the Hopf bifurcation. Numerical simulations are carried out to illustrate the theoretical results.

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