From Classical to Fractional: A Numerical Perspective on the SIR Model with RK-2 and ABS Techniques

This paper presents a comparative study of the SIR (Susceptible-Infectious-Recovered) model implemented using both ordinary and fractional differential equations. We utilize numerical methods such as Runge-Kutta 2nd Order (RK-2), ABS-2 Step, and ABS-3 Step to investigate the dynamics of disease spread under these frameworks. The objective is to illustrate how fractional calculus, with its memory-dependent behavior, offers a more realistic and accurate modeling approach for real-world phenomena, particularly in epidemiology and mathematical biology. MATLAB-based simulations are used to visualize and analyze the differences in the evolution of infection curves. The outcomes are critically discussed to provide insight into the implications of each modeling approach.