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

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.