Rumor is an unauthenticated statement that gives significant changes in the social life of the people, financial markets (stocks and trades), etc. By incorporating the dissemination of rumor through groups in social, mobile networks and by considering the people’s cognitive factor (hesitate and forget), a new model on the rumor spreading process is presented in this paper. The spreading dynamics of rumor in homogeneous and heterogeneous networks is analyzed by using mean-field theory. The reproduction number is obtained by using the next-generation matrix. The global stability of the rumor-free equilibrium for the homogeneous and heterogeneous model is proved elaborately. An optimal control problem is developed to minimize the hesitators and infected persons and the existence of optimality is shown using Pontryagin’s Minimum Principle. The hesitating and forgetting mechanism has a great impact on the model and is similar to the real-life. Further, the control parameters work superior in controlling the spreading of rumors. Finally, the numerical results are verified by the analytical results.

中文翻译：

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复杂网络上群传播谣言模型的最优控制

谣言是一种未经证实的陈述，它使人们的社会生活、金融市场（股票和交易）等发生了重大变化。通过将谣言通过社交、移动网络中的群体传播并考虑到人们的认知因素（犹豫和忘记），本文提出了一种关于谣言传播过程的新模型。运用平均场理论分析了谣言在同构和异构网络中的传播动力学。通过使用下一代矩阵获得再生数。详细证明了同质和异质模型的无谣言均衡的全局稳定性。开发了一个最优控制问题，以最小化犹豫者和感染者，并使用 Pontryagin 最小原理显示最优性的存在。犹豫和遗忘机制对模型的影响很大，与现实生活相似。此外，控制参数在控制谣言传播方面表现出色。最后通过解析结果验证了数值结果。