PEMODELAN MATEMATIKA PENYEBARAN PERILAKU PERUNDUNGAN DI SEKOLAH MENGGUNAKAN MODEL SBVR - Titania Aulia; Bayu Prihandono; Nilamsari Kusumastuti (Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat, 2026)
Bullying in the school environment is a social issue that adversely affects students’ psychological, social, and academic well-being. Understanding the dynamics of bullying behavior can be approached through mathematical modeling. This study develops a mathematical model of bullying behavior using the SBVR framework, which divides the population into four subpopulations: susceptible individuals, bullies, victims, and recovered individuals, to represent the dynamics of bullying behavior and evaluate the role of interventions in controlling it. The contribution of this study lies in the inclusion of a recovery compartment, which enables a more realistic representation of victim dynamics.The model is formulated as a system of nonlinear differential equations and analyzed to determine equilibrium points, compute the basic reproduction number as a key indicator of transmission potential, and evaluate the local stability of these equilibria. The results show that the model has two equilibrium points, namely a bullying-free equilibrium and a bullying-endemic equilibrium. The bullying-free equilibrium is locally asymptotically stable when the basic reproduction number is less than one, whereas the endemic equilibrium is stable when it exceeds one, indicating that this value acts as a threshold for the spread of bullying behavior. Numerical simulations show that increasing the effectiveness of interventions reduces the basic reproduction number and accelerates the decline in the number of bullies and victims. In addition, higher transition rates contribute to a faster spread of bullying behavior. These findings indicate that effective interventions play a crucial role in controlling bullying dynamics and can serve as a basis for developing strategies to reduce bullying in schools.