Analisis Numerik Model SEIRS pada Kasus Pengguna Judi Online Menggunakan Metode Runge-Kutta Orde 17

Abstract

Online gambling has become an increasingly widespread social phenomenon due to technological advancement and the ease of internet access, leading to a significant rise in the number of online gambling users. This study aims to analyze the dynamics of online gambling users using a SEIRS (Susceptible–Exposed–Infected–Recovered–Susceptible) mathematical model and to solve the resulting system using the seventeenth-order Runge–Kutta method. The population is classified into four compartments: susceptible individuals who are vulnerable to exposure, exposed individuals who have encountered online gambling advertisements, infected individuals who actively engage in online gambling, and recovered individuals who have stopped but remain at risk of relapse. The model is formulated as a system of ordinary differential equations with time as the independent variable. The seventeenth-order Runge–Kutta method is derived theoretically using Taylor series expansion and implemented computationally in MATLAB. Convergence analysis is conducted both theoretically and numerically by examining the error behavior for various step sizes and iteration levels. The results show that the method is convergent, as the error approaches zero under appropriate step sizes. Effectiveness testing indicates that the method produces relatively small errors within the specified iteration limits and demonstrates computational efficiency. The numerical solution of the SEIRS model yields final population values of 770 susceptible individuals, 67 exposed individuals, 136 infected individuals, and 85 recovered individuals. These findings confirm that the seventeenth-order Runge–Kutta method is effective and efficient in solving the SEIRS mathematical model for online gambling users.