Global dynamics and optimal control of SEIQR epidemic model on heterogeneous complex networks

doi:10.1088/1674-1056/adc082

Abstract This paper investigates a new SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with quarantine mechanism on heterogeneous complex networks. Firstly, the nonlinear SEIQR epidemic spreading dynamic differential coupling model is proposed. Then, by using mean-field theory and the next-generation matrix method, the equilibriums and basic reproduction number are derived. Theoretical results indicate that the basic reproduction number significantly relies on model parameters and topology of the underlying networks. In addition, the globally asymptotic stability of equilibrium and the permanence of the disease are proved in detail by the Routh-Hurwitz criterion, Lyapunov method and LaSalle's invariance principle. Furthermore, we find that the quarantine mechanism, that is the quarantine rate ($\gamma_{1},\gamma_{2}$), has a significant effect on epidemic spreading through sensitivity analysis of basic reproduction number and model parameters. Meanwhile, the optimal control model of quarantined rate and analysis method are proposed, which can optimize the government control strategies and reduce the number of infected individual. Finally, numerical simulations are given to verify the correctness of theoretical results and a practice application is proposed to predict and control the spreading of COVID-19.

Keywords: epidemic spreading SEIQR model stability and sensitivity analysis heterogeneous complex networks optimal control

Received: 30 October 2024
Revised: 08 February 2025
Accepted manuscript online: 14 March 2025

PACS:	02.50.Fz	(Stochastic analysis)
	02.40.Vh	(Global analysis and analysis on manifolds)
	02.30.-f	(Function theory, analysis)

Fund: Project supported the Natural Science Foundation of Zhejiang Province, China (Grant No. LQN25F030011), the Fundamental Research Project of Hangzhou Dianzi University (Grant No. KYS065624391), the National Natural Science Foundation of China (Grant No. 61573148), and the Science and Technology Planning Project of Guangdong Province, China (Grant No. 2019A050520001).

Corresponding Authors: Xiaodan Zhao
E-mail: xdzhao@hdu.edu.cn

Cite this article:

Xiongding Liu(柳雄顶), Xiaodan Zhao(赵晓丹), Xiaojing Zhong(钟晓静), and Wu Wei(魏武) Global dynamics and optimal control of SEIQR epidemic model on heterogeneous complex networks 2025 Chin. Phys. B 34 060203

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Global dynamics and optimal control of SEIQR epidemic model on heterogeneous complex networks

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