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Mathematical Modeling and Short-Term Forecasting of the COVID-19 Epidemic in Bulgaria: SEIRS Model with Vaccination

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)

  • Iva Ugrinova

    (Institute of Molecular Biology, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria)

  • Tsvetan Hristov

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

Abstract

Data from the World Health Organization indicate that Bulgaria has the second-highest COVID-19 mortality rate in the world and the lowest vaccination rate in the European Union. In this context, to find the crucial epidemiological parameters that characterize the ongoing pandemic in Bulgaria, we introduce an extended SEIRS model with time-dependent coefficients. In addition to this, vaccination and vital dynamics are included in the model. We construct an appropriate Cauchy problem for a system of nonlinear ordinary differential equations and prove that its unique solution possesses some biologically reasonable features. Furthermore, we propose a numerical scheme and give an algorithm for the parameters identification in the obtained discrete problem. We show that the found values are close to the parameters values in the original differential problem. Based on the presented analysis, we develop a strategy for short-term prediction of the spread of the pandemic among the host population. The proposed model, as well as the methods and algorithms for parameters identification and forecasting, could be applied to COVID-19 data in every single country in the world.

Suggested Citation

  • Svetozar Margenov & Nedyu Popivanov & Iva Ugrinova & Tsvetan Hristov, 2022. "Mathematical Modeling and Short-Term Forecasting of the COVID-19 Epidemic in Bulgaria: SEIRS Model with Vaccination," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2570-:d:870225
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    References listed on IDEAS

    as
    1. Ming Liu & Jie Cao & Jing Liang & MingJun Chen, 2020. "Epidemic-logistics Modeling: A New Perspective on Operations Research," Springer Books, Springer, number 978-981-13-9353-2, October.
    2. Marek B. Trawicki, 2017. "Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity," Mathematics, MDPI, vol. 5(1), pages 1-19, January.
    3. Olivares, Alberto & Staffetti, Ernesto, 2021. "Uncertainty quantification of a mathematical model of COVID-19 transmission dynamics with mass vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Rabih Ghostine & Mohamad Gharamti & Sally Hassrouny & Ibrahim Hoteit, 2021. "An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter," Mathematics, MDPI, vol. 9(6), pages 1-16, March.
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    Citations

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    Cited by:

    1. Svetozar Margenov & Nedyu Popivanov & Iva Ugrinova & Tsvetan Hristov, 2023. "Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data," Mathematics, MDPI, vol. 11(10), pages 1-26, May.

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