Nowadays rumors spread by virtual identities of people in online social networks. In order to study the influence of forcing silence on spreaders, we propose a rumor propagation model with a silence-forcing function in online social networks. The theoretical analysis of the rumor propagation model reveals the existence of the equilibrium points, the backward bifurcation and the local stability. Meanwhile, by choosing the key parameter and time delay as the bifurcation parameters, we have given some conditions of Hopf bifurcation that are easy to judge. Furthermore, the optimal control is discussed to reduce the frequency of rumor propagation. Finally, numerical simulations are presented to prove the correctness of the theoretical results.

如今，谣言是通过在线社交网络中人们的虚拟身份传播的。为了研究强迫沉默对传播者的影响，我们提出了一种具有沉默强迫功能的在线社交网络谣言传播模型。对谣言传播模型的理论分析揭示了平衡点的存在，向后的分叉和局部稳定性。同时，通过选择关键参数和时间延迟作为分叉参数，我们给出了易于判断的Hopf分叉条件。此外，讨论了最佳控制以减少谣言传播的频率。最后，通过数值模拟证明了理论结果的正确性。