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Fractional Mathematical Modeling To The Spread Of Polio With The Role Of Vaccination Under Non-Singular Kernel

Author

Listed:
  • XUAN LIU

    (Department of Mathematics, Hanshan Normal University, Chaozhou 515041, P. R. China)

  • MATI UR RAHMAN

    (School of Mathematical Science, Shanghai Jiao Tong University, Shanghai, P. R. China)

  • MUHAMMAD ARFAN

    (Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhwa, Pakistan)

  • FAIROUZ TCHIER

    (Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia)

  • SHABIR AHMAD

    (Department of Mathematics, University of Malakand, Chakdara Dir (Lower), 18000 Khyber Pakhtunkhwa, Pakistan)

  • MUSTAFA INC

    (Department of Computer Engineering, Biruni University, Istanbul, Turkey7Department of Mathematics, Faculty of Science, Firat University, 23119 ElaziÄŸ, Turkey8Department of Medical Research, China Medical University, Taichung, Taiwan)

  • LANRE AKINYEMI

    (Department of Mathematics, Lafayette College, Easton, PA, USA)

Abstract

This paper deals with the fractional mathematical model for the spread of polio in a community with variable size structure including the role of vaccination. The considered model has been extended with help of Atangana–Baleanu in the sense of the Caputo (ABC) fractional operator. The positivity and boundedness of solution (positively invariant region) are presented for the ABC-fractional model of polio. The fixed-point theory has been adopted to study the existing results and uniqueness of the solution for the concerned problem. We also investigate the stability result for the considered model using the Ulam–Hyers stability scheme by taking a small perturbation in the beginning. Numerical simulation is obtained with the help of the fractional Adams–Bashforth technique. Two different initial approximations for all the compartments have been tested for achieving stability to their same equilibrium points. The control simulation is also drawn at fixed infection and exposure rates at various fractional orders. The comparison at different available rates of infection and exposition is also plotted to show the decrease in the infection by decreasing these rates. Various graphical presentations are given to understand the dynamics of the model at various fractional orders.

Suggested Citation

  • Xuan Liu & Mati Ur Rahman & Muhammad Arfan & Fairouz Tchier & Shabir Ahmad & Mustafa Inc & Lanre Akinyemi, 2022. "Fractional Mathematical Modeling To The Spread Of Polio With The Role Of Vaccination Under Non-Singular Kernel," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-17, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401442
    DOI: 10.1142/S0218348X22401442
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    Cited by:

    1. Deepika, S. & Veeresha, P., 2023. "Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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