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The impact of vaccination on the spread of COVID-19: Studying by a mathematical model

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  • Yang, Bo
  • Yu, Zhenhua
  • Cai, Yuanli

Abstract

The global spread of COVID-19 has not been effectively controlled, posing a huge threat to public health and the development of the global economy. Currently, a number of vaccines have been approved for use and vaccination campaigns have already started in several countries. This paper designs a mathematical model considering the impact of vaccination to study the spread dynamics of COVID-19. Some basic properties of the model are analyzed. The basic reproductive number ℜ1 of the model is obtained, and the conditions for the existence of endemic equilibria are provided. There exist two endemic equilibria when ℜ1<1 under certain conditions, which will lead to backward bifurcation. The stability of equilibria are analyzed, and the condition for the backward bifurcation is given. Due to the existence of backward bifurcation, even if ℜ1<1, COVID-19 may remain prevalent. Sensitivity analysis and simulations show that improving vaccine efficacy can control the spread of COVID-19 faster, while increasing the vaccination rate can reduce and postpone the peak of infection to a greater extent. However, in reality, the improvement of vaccine efficacy cannot be realized in a short time, and relying only on increasing the vaccination rate cannot quickly achieve the control of COVID-19. Therefore, relying only on vaccination may not completely and quickly control COVID-19. Some non-pharmaceutical interventions should continue to be enforced to combat the virus. According to the sensitivity analysis, we improve the model by including some non-pharmaceutical interventions. Combining the sensitivity analysis with the simulation of the improved model, we conclude that together with vaccination, reducing the contact rate of people and increasing the isolation rate of infected individuals will greatly reduce the number of infections and shorten the time of COVID-19 spread. The analysis and simulations in this paper can provide some useful suggestions for the prevention and control of COVID-19.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:590:y:2022:i:c:s0378437121009304
    DOI: 10.1016/j.physa.2021.126717
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    References listed on IDEAS

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    1. dos Santos, I.F.F. & Almeida, G.M.A. & de Moura, F.A.B.F., 2021. "Adaptive SIR model for propagation of SARS-CoV-2 in Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    2. Alkahtani, Badr Saad T. & Alzaid, Sara Salem, 2020. "A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Bustamante-Castañeda, F. & Caputo, J.-G. & Cruz-Pacheco, G. & Knippel, A. & Mouatamide, F., 2021. "Epidemic model on a network: Analysis and applications to COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
    4. Nadim, Sk Shahid & Ghosh, Indrajit & Chattopadhyay, Joydev, 2021. "Short-term predictions and prevention strategies for COVID-19: A model-based study," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    5. Mello, Isys F. & Squillante, Lucas & Gomes, Gabriel O. & Seridonio, Antonio C. & de Souza, Mariano, 2021. "Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    6. Yu, Zhenhua & Arif, Robia & Fahmy, Mohamed Abdelsabour & Sohail, Ayesha, 2021. "Self organizing maps for the parametric analysis of COVID-19 SEIRS delayed model," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    7. Odagaki, Takashi, 2021. "Exact properties of SIQR model for COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
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    Cited by:

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    2. Almulhim, Tarifa & Barahona, Igor, 2023. "An extended picture fuzzy multicriteria group decision analysis with different weights: A case study of COVID-19 vaccine allocation," Socio-Economic Planning Sciences, Elsevier, vol. 85(C).

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