A Hybrid Daubechies Wavelet Collocation Approach for a Fractional-Order SIR Epidemic Model with Delay Effects

This work investigates a fractional-order SIR epidemic model with a discrete delay to describe the short-term transmission dynamics of influenza. The model incorporates memory effects via the Caputo fractional derivative and accounts for biologically motivated delays, such as incubation periods or delayed immune responses. To solve this model, we propose a hybridized collocation method based on the Dubecshi wavelet basis, which effectively handles both the fractional-order nature and the delay structure of the system. The accuracy and robustness of the proposed scheme are assessed through comparison with established numerical methods, including the classical Runge-Kutta method (RK4), the Rational Polynomial Spectral Method of order 7 (RPSM7), the Generalized Wavelet Collocation Method (GWCM), and the Genocchi wavelet method. Numerical simulations clearly demonstrate that our Dubecshi wavelet-based approach yields superior performance in terms of convergence, stability, and the ability to capture both memory and delay effects. Furthermore, it outperforms previously employed techniques by achieving better approximation accuracy with lower computational complexity. Mathematics Subject Classification. 34K37, 65M70, 92D30