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Dynamics of Persistent Epidemic and Optimal Control of Vaccination

Author

Listed:
  • Masoud Saade

    (S.M. Nikolsky Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

  • Sebastian Aniţa

    (Faculty of Mathematics, University Alexandru Ioan Cuza, Bd. Carol I nr. 11, 700506 Iasi, Romania)

  • Vitaly Volpert

    (S.M. Nikolsky Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia
    Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France)

Abstract

This paper is devoted to a model of epidemic progression, taking into account vaccination and immunity waning. The model consists of a system of delay differential equations with time delays determined by the disease duration and immunity loss. Periodic epidemic outbreaks emerge as a result of the instability of a positive stationary solution if the basic reproduction number exceeds some critical value. Vaccination can change epidemic dynamics, resulting in more complex aperiodic oscillations confirmed by some data on Influenza A in Norway. Furthermore, the measures of social distancing during the COVID-19 pandemic weakened seasonal influenza in 2021, but increased it during the next year. Optimal control allows for the minimization of epidemic cost by vaccination.

Suggested Citation

  • Masoud Saade & Sebastian Aniţa & Vitaly Volpert, 2023. "Dynamics of Persistent Epidemic and Optimal Control of Vaccination," Mathematics, MDPI, vol. 11(17), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3770-:d:1231758
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    References listed on IDEAS

    as
    1. Samiran Ghosh & Vitaly Volpert & Malay Banerjee, 2022. "An Epidemic Model with Time Delay Determined by the Disease Duration," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    2. Abbasi, Zohreh & Zamani, Iman & Mehra, Amir Hossein Amiri & Shafieirad, Mohsen & Ibeas, Asier, 2020. "Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Jang, Junyoung & Kwon, Hee-Dae & Lee, Jeehyun, 2020. "Optimal control problem of an SIR reaction–diffusion model with inequality constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 136-151.
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