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A New COVID-19 Pandemic Model including the Compartment of Vaccinated Individuals: Global Stability of the Disease-Free Fixed Point

Author

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  • Isra Al-Shbeil

    (Department of Mathematics, Faculty of Sciences, University of Jordan, Amman 11942, Jordan)

  • Noureddine Djenina

    (Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Ali Jaradat

    (Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan)

  • Abdallah Al-Husban

    (Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 2600, Jordan)

  • Adel Ouannas

    (Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Giuseppe Grassi

    (Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy)

Abstract

Owing to the COVID-19 pandemic, which broke out in December 2019 and is still disrupting human life across the world, attention has been recently focused on the study of epidemic mathematical models able to describe the spread of the disease. The number of people who have received vaccinations is a new state variable in the COVID-19 model that this paper introduces to further the discussion of the subject. The study demonstrates that the proposed compartment model, which is described by differential equations of integer order, has two fixed points, a disease-free fixed point and an endemic fixed point. The global stability of the disease-free fixed point is guaranteed by a new theorem that is proven. This implies the disappearance of the pandemic, provided that an inequality involving the vaccination rate is satisfied. Finally, simulation results are carried out, with the aim of highlighting the usefulness of the conceived COVID-19 compartment model.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:576-:d:1043378
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    References listed on IDEAS

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    1. Maurício de Carvalho, João P.S. & Moreira-Pinto, Beatriz, 2021. "A fractional-order model for CoViD-19 dynamics with reinfection and the importance of quarantine," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Manuel De la Sen & Asier Ibeas & Raul Nistal & Ya Jia, 2021. "About Partial Reachability Issues in an SEIR Epidemic Model and Related Infectious Disease Tracking in Finite Time under Vaccination and Treatment Controls," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-21, March.
    3. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    4. 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.
    5. D’Innocenzo, A. & Paladini, F. & Renna, L., 2006. "A numerical investigation of discrete oscillating epidemic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 497-512.
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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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