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Stability and Numerical Simulations of a New SVIR Model with Two Delays on COVID-19 Booster Vaccination

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  • Xinyu Liu

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

  • Yuting Ding

    (Department of Mathematics, Northeast Forestry University, Harbin 150040, China)

Abstract

As COVID-19 continues to threaten public health around the world, research on specific vaccines has been underway. In this paper, we establish an SVIR model on booster vaccination with two time delays. The time delays represent the time of booster vaccination and the time of booster vaccine invalidation, respectively. Second, we investigate the impact of delay on the stability of non-negative equilibria for the model by considering the duration of the vaccine, and the system undergoes Hopf bifurcation when the duration of the vaccine passes through some critical values. We obtain the normal form of Hopf bifurcation by applying the multiple time scales method. Then, we study the model with two delays and show the conditions under which the nontrivial equilibria are locally asymptotically stable. Finally, through analysis of official data, we select two groups of parameters to simulate the actual epidemic situation of countries with low vaccination rates and countries with high vaccination rates. On this basis, we select the third group of parameters to simulate the ideal situation in which the epidemic can be well controlled. Through comparative analysis of the numerical simulations, we concluded that the most appropriate time for vaccination is to vaccinate with the booster shot 6 months after the basic vaccine. The priority for countries with low vaccination rates is to increase vaccination rates; otherwise, outbreaks will continue. Countries with high vaccination rates need to develop more effective vaccines while maintaining their coverage rates. When the vaccine lasts longer and the failure rate is lower, the epidemic can be well controlled within 20 years.

Suggested Citation

  • Xinyu Liu & Yuting Ding, 2022. "Stability and Numerical Simulations of a New SVIR Model with Two Delays on COVID-19 Booster Vaccination," Mathematics, MDPI, vol. 10(10), pages 1-27, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1772-:d:821805
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    References listed on IDEAS

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    1. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
    2. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Yang, Bo & Yu, Zhenhua & Cai, Yuanli, 2022. "The impact of vaccination on the spread of COVID-19: Studying by a mathematical model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    4. Li, Jinhui & Teng, Zhidong & Wang, Guangqing & Zhang, Long & Hu, Cheng, 2017. "Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatment," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 63-71.
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    Cited by:

    1. Leilei Han & Haokun Sui & Yuting Ding, 2022. "Mathematical Modeling and Stability Analysis of a Delayed Carbon Absorption-Emission Model Associated with China’s Adjustment of Industrial Structure," Mathematics, MDPI, vol. 10(17), pages 1-21, August.

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