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传染病模型是微分动力系统成熟的应用,在研究了模型适用性的基础上,将微分动力系统模型引入到群体性事件的传播机理分析中,构建了群体性事件的微分动力系统模型。在此基础上,应用求解常微分方程模型再生矩阵谱半径的方法,得到判断群体性事件传播势态的关键阈值——基本再生数的解析式,并证明基本再生数小于1时,系统全局渐进稳定;基本再生数大于1时,模型有唯一的群体性事件平衡点,且系统在该点局部渐进稳定。应用基本再生数的解析式可判断群体性事件处于不同发展阶段的传播势态并提出相应的解决措施。最后指出,事件的萌芽期是阻止事件大规模爆发的黄金期,事件爆发期危害最大,稳定期要防止事件出现反复,并提出各个时期外部力量的应对策略。
The infectious disease model is a mature application of differential dynamical system. On the basis of studying the applicability of the model, the differential dynamical system model is introduced into the analysis of the propagation mechanism of mass incidents, and a differential dynamical system model of mass incidents is constructed. On this basis, by applying the method of solving the spectral radius of the regenerative matrix of ordinary differential equation model, the analytic formula of critical regenerative number, which is the judgment of the propagating state of mass incidents, is obtained and it is proved that the basic regenerative number is less than 1, the global asymptotic stability of the system ; When the number of basic regeneration is more than 1, the model has the only group event equilibrium point, and the system is gradually stable at this point. The analytic formula of the number of basic regeneration can be used to judge the spread of group events in different stages of development and propose corresponding solutions. Finally, it points out that the infancy of the incident is the golden period to prevent the massive outbreak of the incident. The outbreak of the incident is hardest hit and the stabilization period is to prevent the recurrence of the incident. The strategy of coping with external forces in various periods is also proposed.