This paper investigates rumor transmission over online social networks, such as those via Facebook or Twitter, where users liberally generate visible content to their followers, and the attractiveness of rumors varies over time and gives rise to opposition such as counter-rumors. All users in social media platforms are modeled as nodes in one of five compartments of a directed random graph: susceptible, hesitating, infected, mitigated, and recovered (SHIMR). The system is expressed with edge-based formulation and the transition dynamics are derived as a system of ordinary differential equations. We further allow individuals to decide whether to share, or disregard, or debunk the rumor so as to balance the potential gain and loss. This decision process is formulated as a game, and the condition to achieve mixed Nash equilibrium is derived. The system dynamics under equilibrium are solved and verified based on simulation results. A series of parametric analyses are conducted to investigate the factors that affect the transmission process. Insights are drawn from these results to help social media platforms design proper control strategies that can enhance the robustness of the online community against rumors.

本文调查了在线社交网络上的谣言传播，例如通过 Facebook 或 Twitter，用户可以自由地向他们的追随者生成可见内容，并且谣言的吸引力会随着时间的推移而变化，并引起反谣言等反对。社交媒体平台中的所有用户都被建模为有向随机图的五个部分之一中的节点：易感、犹豫、感染、缓解和恢复 (SHIMR)。该系统用基于边缘的公式表示，过渡动力学导出为常微分方程组。我们进一步允许个人决定是否分享、无视或揭穿谣言，以平衡潜在的得失。这个决策过程被表述为一个博弈，并导出了达到混合纳什均衡的条件。基于仿真结果求解并验证了平衡状态下的系统动力学。进行了一系列参数分析以研究影响传输过程的因素。从这些结果中得出的见解可帮助社交媒体平台设计适当的控制策略，从而增强在线社区抵御谣言的稳健性。