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Mathematical Modeling of COVID-19 Dynamics under Two Vaccination Doses and Delay Effects

Author

Listed:
  • Gabriel Sepulveda

    (Departamento de Matematicas y Estadistica, Universidad de Cordoba, Monteria 230002, Colombia
    These authors contributed equally to this work.)

  • Abraham J. Arenas

    (Departamento de Matematicas y Estadistica, Universidad de Cordoba, Monteria 230002, Colombia
    These authors contributed equally to this work.)

  • Gilberto González-Parra

    (Department of Mathematics, New Mexico Tech, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA
    These authors contributed equally to this work.)

Abstract

The aim of this paper is to investigate the qualitative behavior of the COVID-19 pandemic under an initial vaccination program. We constructed a mathematical model based on a nonlinear system of delayed differential equations. The time delay represents the time that the vaccine takes to provide immune protection against SARS-CoV-2. We investigate the impact of transmission rates, vaccination, and time delay on the dynamics of the constructed system. The model was developed for the beginning of the implementation of vaccination programs to control the COVID-19 pandemic. We perform a stability analysis at the equilibrium points and show, using methods of stability analysis for delayed systems, that the system undergoes a Hopf bifurcation. The theoretical results reveal that under some conditions related to the values of the parameters and the basic reproduction number, the system approaches the disease-free equilibrium point, but if the basic reproduction number is larger than one, the system approaches endemic equilibrium and SARS-CoV-2 cannot be eradicated. Numerical examples corroborate the theoretical results and the methodology. Finally, conclusions and discussions about the results are presented.

Suggested Citation

  • Gabriel Sepulveda & Abraham J. Arenas & Gilberto González-Parra, 2023. "Mathematical Modeling of COVID-19 Dynamics under Two Vaccination Doses and Delay Effects," Mathematics, MDPI, vol. 11(2), pages 1-30, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:369-:d:1031403
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    References listed on IDEAS

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    1. Gergo Pinter & Imre Felde & Amir Mosavi & Pedram Ghamisi & Richard Gloaguen, 2020. "COVID-19 Pandemic Prediction for Hungary; A Hybrid Machine Learning Approach," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    2. Benlloch, José-María & Cortés, Juan-Carlos & Martínez-Rodríguez, David & Julián, Raul-S. & Villanueva, Rafael-J., 2020. "Effect of the early use of antivirals on the COVID-19 pandemic. A computational network modeling approach," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Hoang Pham, 2020. "On Estimating the Number of Deaths Related to Covid-19," Mathematics, MDPI, vol. 8(5), pages 1-9, April.
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    Cited by:

    1. Martin Kröger & Reinhard Schlickeiser, 2024. "On the Analytical Solution of the SIRV-Model for the Temporal Evolution of Epidemics for General Time-Dependent Recovery, Infection and Vaccination Rates," Mathematics, MDPI, vol. 12(2), pages 1-19, January.

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