Nur Asyifa Khaylana Putri, Arrival Rince Putri, Mahdhivan Syafwan
Bullying in schools is a pervasive social issue that negatively affects students' psychological well-being and social development. This study proposes a compartmental mathematical model to describe the dynamics of bullying behavior in a school environment, where the transmission of bullying is influenced by violence-driven interactions among students. The population is divided into four compartments: Susceptible (S), Bullies (B), Exposed (E), and Violent (V). A nonlinear system of differential equations is formulated to represent the transition dynamics between these groups. The model is analyzed to determine equilibrium points and their stability properties. The basic reproduction number R0 is derived to characterize the threshold behavior of bullying spread. The analysis shows that the bullying-free equilibrium is locally asymptotically stable when R0 < 1, while the endemic equilibrium exists and is stable when R0 > 1, based on the Routh–Hurwitz Criterion. Numerical simulations are performed to support the analytical findings and illustrate the impact of violence-driven transmission on the spread of bullying behavior.