A mathematical model for the bullying dynamics in schools

TL;DR

This paper develops a mathematical model to analyze bullying dynamics in schools, considering various student states and intervention strategies, to identify conditions for effective bullying control.

Contribution

It introduces a novel compartmental model capturing complex interactions and intervention effects in school bullying dynamics.

Findings

Bullying can be controlled with sufficiently robust anti-bullying programs.

The model identifies conditions under which bullying persists or diminishes.

Interventions involving parents and administrators are crucial for effective mitigation.

Abstract

We analyze a mathematical model to understand the dynamics of bullying in schools. The model considers a population divided into four groups: susceptible individuals, bullies, individuals exposed to bullying, and violent individuals. Transitions between these states occur at rates designed to capture the complex interactions among students, influenced by factors such as romantic rejection, conflicts with peers and teachers, and other school-related challenges. These interactions can escalate into bullying and violent behavior. The model also incorporates the role of parents and school administrators in mitigating bullying through intervention strategies. The results suggest that bullying can be effectively controlled if anti-bullying programs implemented by schools are sufficiently robust. Additionally, the conditions under which bullying persists are explored.