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Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization

Author

Listed:
  • Svetozar Margenov

    (Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria)

  • Nedyu Popivanov

    (Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
    Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 1164 Sofia, Bulgaria)

  • Tsvetan Hristov

    (Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 1164 Sofia, Bulgaria)

  • Veneta Koleva

    (Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, 1164 Sofia, Bulgaria)

Abstract

A novel time-dependent deterministic SEIRS model, extended with vaccination, hospitalization, and vital dynamics, is introduced. Time-varying basic and effective reproduction numbers associated with this model are defined, which are crucial metrics in understanding epidemic dynamics. Furthermore, a parameter identification approach has been used to develop a numerical method to compute these numbers for long-term epidemics. We analyze the actual COVID-19 data from the USA, Italy, and Bulgaria to solve appropriate inverse problems and gain an understanding of the time evolution behavior of the basic and effective reproduction numbers. Moreover, an insightful comparison of key coronavirus data and epidemiological parameters across these countries has been conducted. For this purpose, while the basic and effective reproduction numbers provide insights into the virus transmission potential, we propose data-driven criteria for assessing the actual realization of the transmission potential of the SARS-CoV-2 virus and the effectiveness of the applied restrictive measures. To obtain these results, we conduct a mathematical analysis to demonstrate various biological properties of the new differential model, including non-negativity, boundedness, existence, and uniqueness of the solution. The new model and the associated numerical simulation tools proposed herein could be applied to COVID-19 data in any country worldwide and hold a promising potential for the transmission capacity and impact of the virus.

Suggested Citation

  • Svetozar Margenov & Nedyu Popivanov & Tsvetan Hristov & Veneta Koleva, 2024. "Computing the COVID-19 Basic and Effective Reproduction Numbers Using Actual Data: SEIRS Model with Vaccination and Hospitalization," Mathematics, MDPI, vol. 12(24), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3998-:d:1547848
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    References listed on IDEAS

    as
    1. Lan Meng & Wei Zhu & Binxiang Dai, 2021. "Generalized SEIR Epidemic Model for COVID-19 in a Multipatch Environment," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-12, December.
    2. Mohammadi Begum Jeelani & Rahim Ud Din & Ghaliah Alhamzi & Manel Hleili & Hussam Alrabaiah, 2024. "Deterministic and Stochastic Nonlinear Model for Transmission Dynamics of COVID-19 with Vaccinations Following Bayesian-Type Procedure," Mathematics, MDPI, vol. 12(11), pages 1-28, May.
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