Global dynamics of an endemic disease model with vaccination: Analysis of the asymptomatic and symptomatic groups in complex networks

Erhui Li; Qingshan Zhang; Erhui Li; Qingshan Zhang

doi:10.3934/era.2023328

Electronic Research Archive

2023, Volume 31, Issue 10: 6481-6504. doi: 10.3934/era.2023328

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Research article

Global dynamics of an endemic disease model with vaccination: Analysis of the asymptomatic and symptomatic groups in complex networks

Erhui Li ¹,
Qingshan Zhang ^{1,2
,
,}

1.
School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China
2.
Postdoctoral Research Base, Henan Institute of Science and Technology, Xinxiang 453003, China

Received: 29 July 2023 Revised: 08 September 2023 Accepted: 17 September 2023 Published: 28 September 2023

In this paper, we analyze the global dynamics of an endemic mathematical model that incorporates direct immunity by vaccination, as well as the shift from the asymptomatic to the symptomatic group in complex networks. By analyzing the Jacobian matrix and constructing suitable Lyapunov functionals, the stability of the disease-free equilibrium and the endemic equilibrium is determined with respect to the basic reproduction number $ R_0 $. Numerical simulations in scale-free and Poisson network environments are presented. The results validate the correctness of our theoretical analyses.
- complex networks,
- equilibrium,
- stability,
- vaccination
Citation: Erhui Li, Qingshan Zhang. Global dynamics of an endemic disease model with vaccination: Analysis of the asymptomatic and symptomatic groups in complex networks[J]. Electronic Research Archive, 2023, 31(10): 6481-6504. doi: 10.3934/era.2023328

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Abstract

In this paper, we analyze the global dynamics of an endemic mathematical model that incorporates direct immunity by vaccination, as well as the shift from the asymptomatic to the symptomatic group in complex networks. By analyzing the Jacobian matrix and constructing suitable Lyapunov functionals, the stability of the disease-free equilibrium and the endemic equilibrium is determined with respect to the basic reproduction number $ R_0 $. Numerical simulations in scale-free and Poisson network environments are presented. The results validate the correctness of our theoretical analyses.

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