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The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time

Author

Listed:
  • Meriem Boukhobza

    (Department of Mathematics and Informatics, University of Mostaganem, Mostaganem 27000, Algeria)

  • Amar Debbouche

    (Department of Mathematics, Guelma University, Guelma 24000, Algeria)

  • Lingeshwaran Shangerganesh

    (Department of Applied Sciences, National Institute of Technology Goa, Ponda 403401, Goa, India)

  • Juan J. Nieto

    (CITMAga, Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain)

Abstract

This article introduces a discrete-time fractional variable order over a SEIQR model, incorporated for COVID-19. Initially, we establish the well-possedness of solution. Further, the disease-free and the endemic equilibrium points are determined. Moreover, the local asymptotic stability of the model is analyzed. We develop a novel discrete fractional optimal control problem tailored for COVID-19, utilizing a discrete mathematical model featuring a variable order fractional derivative. Finally, we validate the reliability of these analytical findings through numerical simulations and offer insights from a biological perspective.

Suggested Citation

  • Meriem Boukhobza & Amar Debbouche & Lingeshwaran Shangerganesh & Juan J. Nieto, 2024. "The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time," Mathematics, MDPI, vol. 12(8), pages 1-24, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1236-:d:1379074
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    References listed on IDEAS

    as
    1. Higazy, M., 2020. "Novel fractional order SIDARTHE mathematical model of COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Tirumalasetty Chiranjeevi & Raj Kumar Biswas, 2017. "Discrete-Time Fractional Optimal Control," Mathematics, MDPI, vol. 5(2), pages 1-12, April.
    3. Tyagi, Swati & Martha, Subash C. & Abbas, Syed & Debbouche, Amar, 2021. "Mathematical modeling and analysis for controlling the spread of infectious diseases," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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    1. Boukhobza, Meriem & Debbouche, Amar & Shangerganesh, Lingeshwaran & Torres, Delfim F.M., 2024. "Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

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