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Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model

Author

Listed:
  • Tingting Xue

    (School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

  • Xiaolin Fan

    (School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

  • Yan Xu

    (School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China)

Abstract

The fractional-order calculus model is suitable for describing real-world problems that contain non-local effects and have memory genetic effects. Based on the definition of the Caputo derivative, the article proposes a class of fractional hepatitis B epidemic model with a general incidence rate. Firstly, the existence, uniqueness, positivity and boundedness of model solutions, basic reproduction number, equilibrium points, and local stability of equilibrium points are studied employing fractional differential equation theory, stability theory, and infectious disease dynamics theory. Secondly, the fractional necessary optimality conditions for fractional optimal control problems are derived by applying the Pontryagin maximum principle. Finally, the optimization simulation results of fractional optimal control problem are discussed. To control the spread of the hepatitis B virus, three control variables (isolation, treatment, and vaccination) are applied, and the optimal control theory is used to formulate the optimal control strategy. Specifically, by isolating infected and non-infected people, treating patients, and vaccinating susceptible people at the same time, the number of hepatitis B patients can be minimized, the number of recovered people can be increased, and the purpose of ultimately eliminating the transmission of hepatitis B virus can be achieved.

Suggested Citation

  • Tingting Xue & Xiaolin Fan & Yan Xu, 2023. "Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3642-:d:1223486
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    References listed on IDEAS

    as
    1. Anwarud Din & Yongjin Li & Abdullahi Yusuf & Aliyu Isa Ali, 2022. "Caputo Type Fractional Operator Applied To Hepatitis B System," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-11, February.
    2. Khan, Tahir & Ullah, Zakir & Ali, Nigar & Zaman, Gul, 2019. "Modeling and control of the hepatitis B virus spreading using an epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 1-9.
    3. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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    5. Ameen, I. & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2020. "An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
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