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Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Author

Listed:
  • Yanli Ma

    (Department of General Education, Anhui Xinhua University, Hefei 230088, China)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Haixia Li

    (Department of General Education, Anhui Xinhua University, Hefei 230088, China)

Abstract

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

Suggested Citation

  • Yanli Ma & Jia-Bao Liu & Haixia Li, 2018. "Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies," Mathematics, MDPI, vol. 6(12), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:12:p:328-:d:190585
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    References listed on IDEAS

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    1. Wang, Jinyan & Xiao, Yanni & Peng, Zhihang, 2016. "Modelling seasonal HFMD infections with the effects of contaminated environments in mainland China," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 615-627.
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    Cited by:

    1. Chaeyoung Lee & Soobin Kwak & Junseok Kim, 2021. "Controlling COVID-19 Outbreaks with Financial Incentives," IJERPH, MDPI, vol. 18(2), pages 1-13, January.
    2. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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