IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i10p2238-d1143847.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/10/2238/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/10/2238/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fu, Xinjie & Wang, JinRong, 2022. "Dynamic stability and optimal control of SISqIqRS epidemic network," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Yanan Liao & Kai Yang & Hua Wang & Qingtai Xiao, 2022. "An Alternative Approach for Identifying Nonlinear Dynamics of the Cascade Logistic-Cubic System," Mathematics, MDPI, vol. 10(12), pages 1-13, June.
    3. Kang, Daekook & Devi, S. Aicevarya & Felix, Augustin & Narayanamoorthy, Samayan & Kalaiselvan, Samayan & Balaenu, Dumitru & Ahmadian, Ali, 2022. "Intuitionistic fuzzy MAUT-BW Delphi method for medication service robot selection during COVID-19," Operations Research Perspectives, Elsevier, vol. 9(C).
    4. Farman, Muhammad & Sarwar, Rabia & Akgul, Ali, 2023. "Modeling and analysis of sustainable approach for dynamics of infections in plant virus with fractal fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. Khan, Muhammad Altaf & Atangana, Abdon, 2022. "Mathematical modeling and analysis of COVID-19: A study of new variant Omicron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    6. Abdulilah Mohammad Mayet & Seyed Mehdi Alizadeh & Karina Shamilyevna Nurgalieva & Robert Hanus & Ehsan Nazemi & Igor M. Narozhnyy, 2022. "Extraction of Time-Domain Characteristics and Selection of Effective Features Using Correlation Analysis to Increase the Accuracy of Petroleum Fluid Monitoring Systems," Energies, MDPI, vol. 15(6), pages 1-19, March.
    7. Oraby, T. & Suazo, E. & Arrubla, H., 2023. "Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    8. Daşbaşı, Bahatdin, 2023. "Fractional order bacterial infection model with effects of anti-virulence drug and antibiotic," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    9. Ameen, Ismail Gad & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2022. "Different strategies to confront maize streak disease based on fractional optimal control formulation," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Touqeer, Muhammad & Shaheen, Sadaf & Jabeen, Tahira & Sulaie, Saleh Al & Baleanu, Dumitru & Ahmadian, Ali, 2022. "A signed distance based ranking approach with unknown fuzzy priority vectors for medical diagnosis involving interval type-2 trapezoidal pythagorean fuzzy preference relations," Operations Research Perspectives, Elsevier, vol. 9(C).
    11. Noureddine Djenina & Adel Ouannas & Iqbal M. Batiha & Giuseppe Grassi & Taki-Eddine Oussaeif & Shaher Momani, 2022. "A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    12. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    13. Hassan Shokouhandeh & Mehrdad Ahmadi Kamarposhti & Fariba Asghari & Ilhami Colak & Kei Eguchi, 2022. "Distributed Generation Management in Smart Grid with the Participation of Electric Vehicles with Respect to the Vehicle Owners’ Opinion by Using the Imperialist Competitive Algorithm," Sustainability, MDPI, vol. 14(8), pages 1-17, April.
    14. Ashpazzadeh, Elmira & Chu, Yu-Ming & Hashemi, Mir Sajjad & Moharrami, Mahsa & Inc, Mustafa, 2022. "Hermite multiwavelets representation for the sparse solution of nonlinear Abel’s integral equation," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    15. Paul, James Nicodemus & Mbalawata, Isambi Sailon & Mirau, Silas Steven & Masandawa, Lemjini, 2023. "Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2238-:d:1143847. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.