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Study of the Spreading Behavior of the Biological SIR Model of COVID-19 Disease Through a Fast Fibonacci Wavelet-Based Computational Approach

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Abstract

In this article, we introduce an innovative methodology based on the Fibonacci wavelet and collocation technique for solving the susceptible–infectious–recovered (SIR) model of COVID-19. The SIR model is represented by a system of nonlinear ordinary differential equations. Our approach begins by transforming the given differential equations into an equivalent algebraic form using the basis expansion of Fibonacci wavelets. The collocation technique is then applied, leading to a system of nonlinear equations. To simplify these nonlinear equations, we employ the Newton–Raphson method. Through the utilization of examples under various conditions, we demonstrate the superiority of our method compared to existing approaches. Moreover, we highlight the versatility of our method, showcasing its applicability in solving a range of linear and nonlinear ordinary and partial differential equations across diverse scientific and engineering domains. Figures and Tables are presented to illustrate the accuracy of our solution and the variation in error. Notably, our approach distinguishes itself by requiring less computational effort while delivering enhanced accuracy across a wide spectrum of scenarios. All calculations are performed using MATLAB Software, underscoring the practical implementation of our proposed methodology.

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Acknowledgements

The authors express their sincere gratitude to the esteemed reviewers and referees for their invaluable contributions to this research paper. The insightful comments and improved suggestions provided by the reviewers have played a pivotal role in refining and strengthening the paper, making it more robust and unique. The authors also extend their sincere appreciation to the reviewers for their time, expertise, and dedication to the advancement of scholarly work.

Funding

The research was supported in the form of the Homi Bhabha Teaching cum Research Fellowship vide Ref. No.: AKTU/2021/Dean PGSR/Fellowship Allotment/6263 Dated: 27 Nov 2021 by Dr. A. P. J. Abdul Kalam Technical University Uttar Pradesh, Lucknow 226031, India.

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  1. Applied Sciences and Humanities Department, Institute of Engineering and Technology, An Autonomous Constituent Institute of Dr. A.P.J. Abdul Kalam Technical University, Lucknow, U.P., 226021, India

    Vivek, Manoj Kumar & Suyash Narayan Mishra

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All authors contributed equally to the paper, including the conceptualization of the basic idea, preparation of the text, and execution of every stage of the research and proofreading process.

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Vivek, Kumar, M. & Mishra, S.N. Study of the Spreading Behavior of the Biological SIR Model of COVID-19 Disease Through a Fast Fibonacci Wavelet-Based Computational Approach. Int. J. Appl. Comput. Math 10, 106 (2024). https://doi.org/10.1007/s40819-024-01699-4

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