基于辟谣机制的时滞谣言传播模型的动力学分析

Dynamic analysis of rumor-spread-delaying model based on rumor-refuting mechanism

在社交网络谣言传播模型中,考虑到辟谣机制和时滞效应对网络谣言传播的影响,建立基于辟谣机制和时滞效应的SIR谣言传播模型.利用再生矩阵谱半径方法得到R0;根据二次函数图像特征给出谣言盛行平衡点存在的条件;通过特征值理论和Routh-Hurwitz判据确定无谣言平衡点和谣言盛行平衡点的局部稳定性以及发生Hopf分支的条件;数值仿真结果表明政府和媒体发布的辟谣信息会加快谣言收敛的速度和降低谣言传播者的最大密度.

In this paper,we establish a susceptible-infected-removed(SIR)rumor spreading model based on the influence of rumor-refuting mechanism and time delay on internet rumor spreading.The threshold R0 of rumor spreading is obtained by using the spectral radius method of regenerative matrix;the conditions for the existence of rumor prevailing equilibrium point are given according to the quadratic function characteristics;the local stability of rumor-free equilibrium point and rumor prevailing equilibrium point are established by using eigenvalue theory and Routh-Hurwitz criterion;and the criterion for the occurrence of Hopf bifurcation is also established.The numerical simulation results show that the information about refuting rumors,released by the government and the media,can accelerate the convergence rate of rumors and reduce the maximum density of rumor-spreaders.