一类具有自发行为的SIRI谣言传播模型研究

刘芳,李明涛

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (7) : 1257-1269.

PDF(713 KB)
PDF(713 KB)
系统科学与数学 ›› 2020, Vol. 40 ›› Issue (7) : 1257-1269. DOI: 10.12341/jssms13922
论文

一类具有自发行为的SIRI谣言传播模型研究

    刘芳1,李明涛2
作者信息 +

Research on SIRI Rumor Spreading Model with Spontaneous Behavior

    LIU Fang1, LI Mingtao2
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摘要

基于传染病动力学理论, 建立了具有自发行为的SIRI 谣言传播微分方程动 力学模型, 通过非负平衡点的存在性给出影响谣言传播效果的阈值. 利用Jacobian矩阵和 Bendixson-Dulac判别法分析了非负平衡点的全局稳定性, 提出了影响谣言传播的主要因素 及治理谣言的策略. 理论证明, 自发行为存在是谣言传播的必要条件, 当阈值大于1时, 谣 言持续, 否则谣言灭绝. 数值仿真为理论结果提供了支持. 复杂的动力学性质表明, 该模型对参 数的变化非常敏感, 对控制和治理谣言传播起了重要作用.

Abstract

Based on the theory of epidemic dynamics, a dynamic SIRI model of differential equation about rumor spreading with spontaneous behavior was established. By analyze the existence of non-negative equilibria, the threshold which effect the rumor spreading result is determined. Jacobian matrix and bendixson-dulac discriminant method were used to analyze the stability of the non-negative equilibria. Furthermore, the main factors affecting the rumor spreading and the strategies in order to control rumor spreading are given. The theoretical analysis shows that the existence of spontaneous behavior is a necessary condition for rumor spreading. If the threshold is more than 1, the rumor will last, otherwise the rumor will die out. Numerical simulations are provided to support the theoretical results. The complicated dynamics properties exhibit that the model is very sensitive to variation of parameters, which play an important role on controlling and administering the rumor spreading.

关键词

传染病动力学 / SIRI模型 / 自发行为 / 谣言传播 / 稳定性.

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刘芳 , 李明涛. 一类具有自发行为的SIRI谣言传播模型研究. 系统科学与数学, 2020, 40(7): 1257-1269. https://doi.org/10.12341/jssms13922
LIU Fang , LI Mingtao. Research on SIRI Rumor Spreading Model with Spontaneous Behavior. Journal of Systems Science and Mathematical Sciences, 2020, 40(7): 1257-1269 https://doi.org/10.12341/jssms13922
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