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A mathematical model for the bullying dynamics in schools

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  • Crokidakis, Nuno

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.

Suggested Citation

  • Crokidakis, Nuno, 2025. "A mathematical model for the bullying dynamics in schools," Applied Mathematics and Computation, Elsevier, vol. 492(C).
    • Handle: RePEc:eee:apmaco:v:492:y:2025:i:c:s009630032400715x
    DOI: 10.1016/j.amc.2024.129254
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    References listed on IDEAS

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    1. Sooknanan, J. & Comissiong, D.M.G., 2018. "A mathematical model for the treatment of delinquent behaviour," Socio-Economic Planning Sciences, Elsevier, vol. 63(C), pages 60-69.
    2. Oestereich, André L. & Pires, Marcelo A. & Crokidakis, Nuno & Cajueiro, Daniel O., 2023. "Optimal rewiring in adaptive networks in multi-coupled vaccination, epidemic and opinion dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    3. Nuno Crokidakis, 2023. "Radicalization phenomena: Phase transitions, extinction processes and control of violent activities," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(08), pages 1-12, August.
    4. Crokidakis, Nuno, 2024. "Nonequilibrium phase transitions and absorbing states in a model for the dynamics of religious affiliation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    5. Serge Galam & Marco Alberto Javarone, 2016. "Modeling Radicalization Phenomena in Heterogeneous Populations," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-15, May.
    6. Crokidakis, Nuno & Sigaud, Lucas, 2021. "Modeling the evolution of drinking behavior: A Statistical Physics perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    Full references (including those not matched with items on IDEAS)

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