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Differential and Time-Discrete SEIRS Models with Vaccination: Local Stability, Validation and Sensitivity Analysis Using Bulgarian COVID-19 Data

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

Bulgaria has the lowest COVID-19 vaccination rate in the European Union and the second-highest COVID-19 mortality rate in the world. That is why we think it is important better to understand the reason for this situation and to analyse the development of the disease over time. In this paper, an extended time-dependent SEIRS model SEIRS-VB is used to investigate the long-term behaviour of the COVID-19 epidemic. This model includes vaccination and vital dynamics. To apply the SEIRS-VB model some numerical simulation tools have been developed and for this reason a family of time-discrete variants are introduced. Suitable inverse problems for the identification of parameters in discrete models are solved. A methodology is proposed for selecting a discrete model from the constructed family, which has the closest parameter values to these in the differential SEIRS-VB model. To validate the studied models, Bulgarian COVID-19 data are used. To obtain all these results for the discrete models a mathematical analysis is carried out to illustrate some biological properties of the differential model SEIRS-VB, such as the non-negativity, boundedness, existence, and uniqueness. Using the next-generation method, the basic reproduction number associated with the model in the autonomous case is defined. The local stability of the disease-free equilibrium point is studied. Finally, a sensitivity analysis of the basic reproduction number is performed.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2238-:d:1143847
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    References listed on IDEAS

    as
    1. Zai-Yin He & Abderrahmane Abbes & Hadi Jahanshahi & Naif D. Alotaibi & Ye Wang, 2022. "Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    2. Mohammad Mehdizadeh Khalsaraei & Ali Shokri & Higinio Ramos & Shao-Wen Yao & Maryam Molayi, 2022. "Efficient Numerical Solutions to a SIR Epidemic Model," Mathematics, MDPI, vol. 10(18), pages 1-15, September.
    3. Md Rafiul Islam & Angela Peace & Daniel Medina & Tamer Oraby, 2020. "Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles," IJERPH, MDPI, vol. 17(6), pages 1-19, March.
    4. Isra Al-Shbeil & Noureddine Djenina & Ali Jaradat & Abdallah Al-Husban & Adel Ouannas & Giuseppe Grassi, 2023. "A New COVID-19 Pandemic Model including the Compartment of Vaccinated Individuals: Global Stability of the Disease-Free Fixed Point," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    5. 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.
    6. De-gang Xu & Xi-yang Xu & Chun-hua Yang & Wei-hua Gui, 2015. "Global Stability of a Variation Epidemic Spreading Model on Complex Networks," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, December.
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