基于媒体报道的随机谣言传播模型

A Stochastic Rumor Spreading Model Based on Media Reports

摘要: 随着信息技术的发展，谣言传播的速度比过去更快，范围更广，而媒体发布信息可以在一定程度上阻止或控制谣言的传播。此外，由于个体间连接的变化，真实社交网络的拓扑结构会受到随机扰动。基于媒体报道和网络的连通性变化，本文通过引入媒体发布信息的透明度、媒体公信力参数，构建随机谣言传播模型。首先，对于同构网络上的模型，证明了解的全局存在唯一性。然后，通过对随机模型进行稳定性分析，推导了谣言消亡的充分条件，讨论了同构网络和异构网络上谣言的传播阈值。最后，在WS网络、BA网络和真实世界Facebook网络上进行数值模拟，验证了理论分析，并测试了相关参数对模型的影响。结果表明，随机噪声扰动加速了谣言传播消亡的过程，减小了同构网络上的传播阈值。此外，提高媒体的公信力和发布信息的透明度可以降低谣言的最大影响和最终规模。

Abstract: With the advancement of information technology, rumors propagate at a faster speed and broader scope than ever before, whereas the dissemination of information by media outlets can, to some extent, hinder or control the spread of rumors. Moreover, due to the variability of connections among individuals, the topological structure of real-world social networks is subject to random perturbations. Incorporating the transparency of media-released information and media credibility parameters, this paper constructs a stochastic rumor spreading model based on media reports and network connectivity changes. Firstly, for the model on a homogeneous network, the global existence and uniqueness of the solution are proved. Subsequently, through stability analysis of the stochastic model, sufficient conditions for rumor extinction are derived, and the rumor spreading thresholds on both homogeneous and heterogeneous networks are discussed. Finally, numerical simulations are conducted on WS networks, BA networks, and the real-world Facebook network to validate the theoretical analysis and examine the influence of relevant parameters on the model. The results indicate that random noise perturbations accelerate the process of rumor extinction and reduce the spreading threshold on homogeneous networks. Furthermore, enhancing media credibility and the transparency of released information can mitigate the maximum impact and final scale of rumors.