### Mathematical Biosciences and Engineering

2020, Issue 6: 7130-7150. doi: 10.3934/mbe.2020366
Research article

# Bifurcation analysis of an age-structured SIRI epidemic model

• 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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