Numerical Analysis of the SIR Model Using the Fourth-Order Runge-Kutta Method

The Susceptible–Infected–Recovered (SIR) model is a fundamental mathematical framework for analyzing the transmission dynamics of infectious diseases. Due to its nonlinear structure, analytical solutions are generally difficult to obtain, making numerical analysis an essential approach. This study presents a numerical analysis of the SIR model using the fourth-order Runge–Kutta (RK4) method, with emphasis on numerical stability, solution accuracy, and epidemiological interpretability. Numerical simulations are conducted and compared with the first-order Euler method to examine differences in solution behavior. The results indicate that the RK4 method produces smoother solution trajectories, more accurate estimation of the infection peak, and better preservation of population consistency than the Euler method. These findings confirm that RK4 is not only computationally superior but also more reliable for interpreting epidemic dynamics, making it suitable for applied and educational epidemiological modeling. Keywords: SIR model, numerical analysis, Runge–Kutta method, epidemic modeling, numerical simulation