Numerical Investigation of SIR Epidemic Model using Fibonacci Wavelets

Abstract

The susceptible-infected-recovered (SIR) epidemic model consists of a system of non-linear ordinary differential equations that model the spread of non-fatal disease in the human population. In this article, the Fibonacci wavelet-based collocation method is proposed for solving the SIR epidemic model. The proposed scheme starts with the construction of operational matrices of integration based on Fibonacci wavelets. Operational matrices of integration are then employed to convert the given SIR epidemic model into a system of algebraic equations. Moreover, the Jacobian technique is utilized to linearize the given nonlinear model. Furthermore, the obtained results of the SIR epidemic model are then compared with other existing numerical methods, including the fourth-order Runge-Kutta and residual power series methods. At the end, the numerical simulations for the susceptible, infected, and recovered populations are carried out via graphs and tables.