Analisis Model Matematika Dinamika Perilaku Bullying di Sekolah dengan Faktor Kekerasan

Putri, Nur Asyifa Khaylana (2025) Analisis Model Matematika Dinamika Perilaku Bullying di Sekolah dengan Faktor Kekerasan. S1 thesis, Universitas Andalas.

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Abstract

This study proposes a mathematical model to capture the dynamics of bullying behavior in a school environment, modeling its spread analogously to infectious disease transmission. The model categorizes the student population into four compartments: Susceptible individuals (S), Bullies (B), Exposed victims (E), and Violent victims (V). A system of nonlinear differential equations is formulated to describe these transitions and analyzed to determine the equilibrium points and their stability. Analytical results reveal the existence of two equilibrium states: a bullying-free equilibrium and an endemic equilibrium. Stability is assessed using the basic reproduction number (R0) and the Routh-Hurwitz criteria, showing that the bullying-free equilibrium is locally asymptotically stable when the reproduction number is less than one, and the endemic equilibrium becomes stable when it exceeds one. Numerical simulations support the analytical findings and demonstrate how changes in key parameters influence the system’s dynamics. This study highlights the significance of mathematical modeling in understanding bullying behavior in schools and identifies critical leverage points for developing effective intervention strategies.

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