标题： 学校欺凌动态的数学模型 显示英文标题

标题： A mathematical model for the bullying dynamics in schools

摘要： 我们分析一个数学模型以了解学校中欺凌行为的动态。 该模型考虑了一个分为四个群体的人口：易受欺凌者、欺凌者、遭受欺凌的个体以及暴力个体。 这些状态之间的转换以设计好的速率发生，以捕捉学生之间的复杂互动，这些互动受到诸如浪漫拒绝、与同学和教师的冲突以及其他学校相关挑战等因素的影响。 这些互动可能会升级为欺凌和暴力行为。 该模型还包含了家长和学校管理者通过干预策略减轻欺凌的作用。 结果表明，如果学校实施的反欺凌计划足够强大，就可以有效控制欺凌。 此外，还探讨了欺凌持续存在的条件。 显示英文摘要

摘要： 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.