FRACTIONAL MATHEMATICAL MODELING TO THE SPREAD OF POLIO WITH THE ROLE OF VACCINATION UNDER NON-SINGULAR KERNEL

Xuan Liu, Mati Ur Rahman (), Muhammad Arfan, Fairouz Tchier, Shabir Ahmad, Mustafa Inc and Lanre Akinyemi ()
Additional contact information
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

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-17

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.

Keywords: Fractional Model of Polio; Existence Theory; Numerical Simulations; Adams–Bashforth Method (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0218348X22401442

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