Analisis Dinamik pada Model Matematika Penyebaran Kekerasan Seksual dengan Pendekatan Rehabilitasi

Abstract

Sexual violence is a serious issue occurring in various countries, necessitating special attention in its prevention and management. Mathematical modeling of sexual violence is crucial for understanding the dynamics of its spread and the impact of interventions on sexual violence cases. In this study, a four-dimensional nonlinear dynamic system model is used to analyze the stability of a sexual violence model considering the influence of rehabilitation. The basic reproduction number is calculated using the next-generation matrix method to estimate the potential spread of new cases caused by a single perpetrator in a vulnerable population. Analytically, there are two equilibrium points in the model: the sexual violence-free equilibrium point and the endemic sexual violence equilibrium point. Both equilibrium points are asymptotically stable, depending on the value of the basic reproduction number . The sexual violence-free equilibrium point is asymptotically stable under the condition , and the endemic sexual violence equilibrium point is asymptotically stable under the condition . Numerical simulations are conducted using the fourth-order Runge-Kutta method, implemented in MATLAB. The numerical simulation results also demonstrate that both equilibrium points exhibit the same stability properties based on the parameters used in this study.