考虑举报机制的SIMR谣言传播模型

SIMR Rumor Propagation Model of Considering Reporting Mechanism

摘要: 近年来，社交网络的流行使谣言的扩散性显著增强，谣言泛滥给政府相关部门带来了新的挑战。因此，研究社交网络中的谣言传播意义重大。考虑到社交网络中举报机制对谣言传播的影响，针对现实生活中谣言传播者可能被他人举报而暂时无法传播谣言的现象，在SIR谣言模型中引入被禁言者，提出了一种考虑举报机制的SIMR谣言传播模型。首先，构建了该谣言模型在同质与异质网络上的平均场方程。其次，讨论了模型在同质与异质网络中谣言的传播阈值，并利用Routh-Hurwitz准则分析了模型在无谣言平衡点处的局部渐进稳定性。最后，利用龙格库塔法求出了系统的数值解，并通过蒙特卡洛方法分别在WS网络、BA网络以及Facebook网络中进行仿真，研究举报机制及具体参数对谣言传播的影响。结果表明，在WS、BA以及Facebook网络中举报机制均能有效抑制谣言传播；举报率越高，谣言传播峰值越小；提高转化率或者降低恢复率不仅能降低谣言传播峰值还能缩短谣言消亡时间。

Abstract: In recent years, the popularity of social networks has significantly enhanced the spread of rumors, posing new challenges to government departments. Therefore, studying the spread of rumors in social networks is of great significance. Considering the impact of the reporting mechanism on rumor spread in social networks, where rumor spreaders may be reported by others and temporarily unable to spread rumors in real life, a SIMR rumor spread model considering the reporting mechanism is proposed by introducing the muted in the SIR rumor model. Firstly, the average field equations of the model on homogeneous and heterogeneous networks are constructed. Secondly, the rumor spread threshold of the model on homogeneous and heterogeneous networks is discussed, and the local asymptotic stability of the model at the rumor-free equilibrium point is analyzed. Finally, the numerical solution of the system is obtained by the Runge-Kutta method, and the impact of the reporting mechanism and specific parameters on rumor spread is studied by Monte Carlo simulations on WS small-world networks, BA scale-free networks, and Facebook networks. The results show that the reporting mechanism can effectively suppress the spread of rumors in WS, BA, and Facebook networks; the higher the reporting rate, the smaller the peak value of rumor spread; increasing the conversion rate or reducing the recovery rate can not only reduce the peak value of rumor spread but also shorten the time for rumor extinction.