A high-accuracy Hermite wavelet scheme for fractional epidemic models

Abstract In this study, we present a novel operational matrix framework constructed using Hermite wavelets for the numerical solution of a fractional order susceptible-infected-recovered epidemic dynamical system modeling childhood diseases. The fractional derivative is formulated in the sense of Caputo definition. The proposed approach employs the exact analytical representation of the Riemann–Liouville fractional integral operator in the Hermite wavelet domain and applies it to the fractional epidemic model, providing new insight into its dynamic behavior. This newly developed operational matrix enables the transformation of the original fractional differential equations into an equivalent system of algebraic equations, thereby simplifying the computational procedure. For comparison and validation, the well-established Adam-Bashforth predictor-corrector scheme is also employed to solve the same problem. A detailed comparative study between the Hermite wavelet method and the Adams-Bashforth predictor-corrector approach is conducted to evaluate the accuracy, efficiency, and practical applicability of the proposed method. Moreover, a comprehensive error and convergence analysis is performed to rigorously establish the validity and reliability of the Hermite wavelet approach.