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

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          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.

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          Most cited references27

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          New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model

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            New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

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              Pulse vaccination strategy in the SIR epidemic model

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                Author and article information

                Journal
                Fractals
                Fractals
                World Scientific Pub Co Pte Ltd
                0218-348X
                1793-6543
                August 2022
                May 27 2022
                August 2022
                : 30
                : 05
                Affiliations
                [1 ]Department of Mathematics, Hanshan Normal University, Chaozhou 515041, P. R. China
                [2 ]School of Mathematical Science, Shanghai Jiao Tong University, Shanghai, P. R. China
                [3 ]Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhwa, Pakistan
                [4 ]Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia
                [5 ]Department of Mathematics, University of Malakand, Chakdara Dir (Lower), 18000 Khyber Pakhtunkhwa, Pakistan
                [6 ]Department of Computer Engineering, Biruni University, Istanbul, Turkey
                [7 ]Department of Mathematics, Faculty of Science, Firat University, 23119 Elaziğ, Turkey
                [8 ]Department of Medical Research, China Medical University, Taichung, Taiwan
                [9 ]Department of Mathematics, Lafayette College, Easton, PA, USA
                Article
                10.1142/S0218348X22401442
                0d81e4d2-2f31-4207-afa4-33a658b7ea36
                © 2022
                History

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