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Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID‐19 Pandemic with Optimal Control

Author

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  • Alemzewde Ayalew
  • Yezbalem Molla
  • Tenaw Tilahun
  • Tadele Tesfa

Abstract

In this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID‐19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the model system including existence and uniqueness, positivity, and invariant region of solutions are proved under a certain meaningful set. The model exhibits two equilibrium points: disease‐free and endemic equilibrium points under certain conditions. The basic reproduction number, R0, is derived via the next‐generation matrix approach, and the dynamical behavior of the model is explored in detail. The analytical analysis reveals that the disease‐free equilibrium solution is locally as well as globally asymptotically stable when the associated basic reproduction number is less than unity which indicates that COVID‐19 dies out in the population. Also, the endemic equilibrium point is globally asymptotically stable whenever the associated basic reproduction number exceeds a unity which implies that COVID‐19 establishes itself in the population. The sensitivity analysis of the basic reproduction number is computed to identify the most dominant parameters for the spreading out as well as control of infection and should be targeted by intervention strategies. Furthermore, we extended the considered model to optimal control problem system by introducing two time‐dependent variables that represent the educational campaign to susceptibles and continuous treatment for quarantined individuals. Finally, some numerical results are illustrated to supplement the analytical results of the model using MATLAB ode45.

Suggested Citation

  • Alemzewde Ayalew & Yezbalem Molla & Tenaw Tilahun & Tadele Tesfa, 2023. "Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID‐19 Pandemic with Optimal Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnljam:v:2023:y:2023:i:1:n:8570311
    DOI: 10.1155/2023/8570311
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong, 2018. "Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 310-325.
    2. Kaushik Dehingia & Ahmed A. Mohsen & Sana Abdulkream Alharbi & Reima Daher Alsemiry & Shahram Rezapour, 2022. "Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2," Mathematics, MDPI, vol. 10(13), pages 1-15, July.
    3. repec:plo:pone00:0172465 is not listed on IDEAS
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    1. Alemzewde Ayalew & Yezbalem Molla & Amsalu Woldegbreal, 2024. "Modeling and Stability Analysis of the Dynamics of Malaria Disease Transmission with Some Control Strategies," Abstract and Applied Analysis, John Wiley & Sons, vol. 2024(1).

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