IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i10p1772-d821805.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/10/1772/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/10/1772/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    2. Yas Al-Hadeethi & Intesar F. El Ramley & Hiba Mohammed & Nada M. Bedaiwi & Abeer Z. Barasheed, 2024. "A Novel Computational Instrument Based on a Universal Mixture Density Network with a Gaussian Mixture Model as a Backbone for Predicting COVID-19 Variants’ Distributions," Mathematics, MDPI, vol. 12(8), pages 1-24, April.
    3. Liu, Yang & Sugishita, Kashin & Hanaoka, Shinya, 2024. "Vaccination and transportation intervention strategies for effective pandemic control," Transport Policy, Elsevier, vol. 156(C), pages 126-137.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:hin:complx:9876013 is not listed on IDEAS
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    3. Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    4. Zhang, Baoxiang & Cai, Yongli & Wang, Bingxian & Wang, Weiming, 2019. "Pattern formation in a reaction–diffusion parasite–host model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 732-740.
    5. Ullah, Mohammad Sharif & Higazy, M. & Kabir, K.M. Ariful, 2022. "Dynamic analysis of mean-field and fractional-order epidemic vaccination strategies by evolutionary game approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    6. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    7. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.
    8. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. Bobryk, R.V., 2021. "Stability analysis of a SIR epidemic model with random parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    10. Cen Song & Sijia Zhou & Kyle Hunt & Jun Zhuang, 2022. "Comprehensive Evolution Analysis of Public Perceptions Related to Pediatric Care: A Sina Weibo Case Study (2013–2020)," SAGE Open, , vol. 12(1), pages 21582440221, March.
    11. Jin, Manli, 2019. "Classification of asymptotic behavior in a stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 661-666.
    12. Sabbar, Yassine, 2024. "Exploring threshold dynamics of a behavioral epidemic model featuring two susceptible classes and second-order jump–diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    13. Alzahrani, Faris & Razzaq, Oyoon Abdul & Rehman, Daniyal Ur & Khan, Najeeb Alam & Alshomrani, Ali Saleh & Ullah, Malik Zaka, 2022. "Repercussions of unreported populace on disease dynamics and its optimal control through system of fractional order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    14. Acuña-Zegarra, Manuel Adrian & Díaz-Infante, Saúl, 2018. "Stochastic asymptotic analysis of a multi-host model with vector transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 243-260.
    15. Wang, Yan & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2018. "Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 276-292.
    16. Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    17. Zain-Aldeen S. A. Rahman & Basil H. Jasim & Yasir I. A. Al-Yasir & Yim-Fun Hu & Raed A. Abd-Alhameed & Bilal Naji Alhasnawi, 2021. "A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications," Mathematics, MDPI, vol. 9(20), pages 1-25, October.
    18. Ali, Ishtiaq & Ullah Khan, Sami, 2020. "Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    19. Das, Tanuja & Srivastava, Prashant K., 2023. "Effect of a novel generalized incidence rate function in SIR model: Stability switches and bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    20. Hu, Limi & Qiu, Xiaoling, 2022. "Stability analysis of game models with fixed and stochastic delays," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    21. Liu, Qun & Jiang, Daqing, 2020. "Threshold behavior in a stochastic SIR epidemic model with Logistic birth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1772-:d:821805. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.