中国物理B ›› 2025, Vol. 34 ›› Issue (6): 60203-060203.doi: 10.1088/1674-1056/adc082

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

Xiongding Liu(柳雄顶)1, Xiaodan Zhao(赵晓丹)1,†, Xiaojing Zhong(钟晓静)2, and Wu Wei(魏武)3   

  1. 1 School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China;
    2 School of Mechanical and Electronic Information Engineering, Guangzhou University, Guangzhou 510006, China;
    3 School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2024-10-30 修回日期:2025-02-08 接受日期:2025-03-14 出版日期:2025-05-16 发布日期:2025-05-27
  • 通讯作者: Xiaodan Zhao E-mail:xdzhao@hdu.edu.cn
  • 基金资助:
    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).

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

Xiongding Liu(柳雄顶)1, Xiaodan Zhao(赵晓丹)1,†, Xiaojing Zhong(钟晓静)2, and Wu Wei(魏武)3   

  1. 1 School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China;
    2 School of Mechanical and Electronic Information Engineering, Guangzhou University, Guangzhou 510006, China;
    3 School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China
  • Received:2024-10-30 Revised:2025-02-08 Accepted:2025-03-14 Online:2025-05-16 Published:2025-05-27
  • Contact: Xiaodan Zhao E-mail:xdzhao@hdu.edu.cn
  • Supported by:
    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).

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摘要： 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.

关键词: epidemic spreading, SEIQR model, stability and sensitivity analysis, heterogeneous complex networks, optimal control

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.

Key words: epidemic spreading, SEIQR model, stability and sensitivity analysis, heterogeneous complex networks, optimal control

中图分类号:  (Stochastic analysis)

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