An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets

Sunil Kumar, Ali Ahmadian, Ranbir Kumar, Devendra Kumar, Jagdev Singh, Dumitru Baleanu and Mehdi Salimi
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Sunil Kumar: Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India
Ali Ahmadian: Institute of Industry Revolution 4.0, National University of Malaysia, UKM Bangi 43600, Selangor, Malaysia
Ranbir Kumar: Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India
Devendra Kumar: Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India
Jagdev Singh: Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
Dumitru Baleanu: Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No: 4, 06790 Etimesgut, Turkey
Mehdi Salimi: Center for Dynamics and Institute for Analysis, Department of Mathematics, Technische Universität Dresden, 01069 Dresden, Germany

Mathematics, 2020, vol. 8, issue 4, 1-22

Abstract: In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams–Bashforth–Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams–Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method.

Keywords: Bernstein wavelets; operational matrix; fractional differential equations; Adams–Bashforth–Moulton predictor correcter scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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