随着互联网技术的发展和在线社交媒体的出现，谣言的传播方式变得更复杂，传播速度更迅速，影响范围更广，造成的社会危害更严重。我们亟需了解谣言传播规律，抑制谣言传播，从而降低谣言传播带来的损失。因此，研究谣言传播模型、揭示谣言传播机理，并在此基础上提出有效的控制策略，具有重要的现实意义。目前，针对社交网络谣言传播建模和控制的研究还存在着一些不足；在建模和分析方面，没有考虑只讨论谣言话题的人群对谣言传播的影响，并且没有使用真实数据集验证模型的有效性。在控制谣言传播方面，大多使用单一的控制策略，没有考虑控制策略的成本问题。针对上述问题，本文致力于社交网络谣言传播建模和控制研究，主要研究内容和创新点如下：

(1) 社交网络谣言传播建模和分析。本文提出一种考虑讨论者的谣言传播模型，将总人口划分为四类：未知者、讨论者、传播者和免疫者。通过计算模型的平衡点和基本再生数，分析平衡点的局部和全局渐进稳定性、跨临界分岔现象，揭示谣言传播机理。利用数值仿真验证上述理论分析的正确性。通过与现有模型对比，仿真结果表明讨论者对谣言传播有重要影响。在真实数据集的基础上，使用最小二乘拟合方法估计模型的参数，并根据拟合得到的参数值预测谣言传播趋势，从而对模型进行验证。仿真结果表明，该模型的拟合优度R²值为0.9544，说明该模型能够准确模拟真实社交网络中的谣言传播。 

(2) 谣言传播控制策略研究。在所建模型的基础上，提出一种结合保护策略和阻断策略的谣言混合控制策略，并进行动力学行为分析。利用实际数据集，预测谣言传播者和真相传播者在真实社交网络上的传播趋势。与无控制策略、单一保护策略、单一阻断策略比较，数值仿真结果表明混合控制策略的有效性。为了能最大限度地控制谣言传播，并且使其控制成本最小化，提出混合控制策略的最优控制方案。使用庞特里亚金极小值原理，证明最优控制的存在性，并得到最优控制系统。实验结果表明最优控制的成本相比于混合控制策略、单一保护策略、单一阻断策略是最低的，并能最小化谣言传播者密度。

With the development of Internet technology and the emergence of online social media, the ways of rumor propagation become more complex, the propagation speed is more rapid, and the range of influence become more wider, which cause more serious social harm. We are urgently required to understand the rule of rumor propagation, restrain the spread of rumor, thereby reducing the loss caused by rumor propagation. Therefore, it is of great practical significance to study rumor propagation model, reveal rumor propagation mechanisms, and propose effective control strategies to restrain rumor propagation. Until now, there are still some deficiencies in researching on the modeling and controlling of rumor propagation in social networks. In the aspects of modeling and analysis of rumor propagation, current studies are presented without considering the influence of the people who just discuss rumor topics and without using real datasets to verify the validity of the proposed model; while as for the aspects of controlling rumor propagation, most researches use a single control strategy but the cost of the control strategy is not taken into account. To address the above issues, this thesis aims to conduct research on modeling and controlling of rumor propagation. The specific research contents and innovations of this thesis are as follows.

(1) Modeling and analysis of rumor propagation in social networks. This thesis proposes a rumor propagation model that considers the influence of discussants, which divides the entire population into four categories: ignorances, discussants, spreaders and removers. By calculating equilibria and the basic regeneration number of the model, and analyzing the local and global asymptotic stability of equilibria and the transcritical bifurcation phenomenon, the rumor propagation mechanism is revealed. The correctness of the above theoretical analysis is verified by carrying out numerical simulation experiments. By comparing with the existing models, the results show that discussants have an important influence on the spread of rumor. Based on a real dataset, the least square fitting method is used to estimate all the parameters of the model, and the parameter values obtained by the fitting method can be used to predict the rumor propagation trend, thus the model can be verified. The simulation results show that the value of the goodness-of-fit R² of the model is 0.9544, which indicates that the model can accurately simulate the rumor propagation in real social networks.

(2) Research on rumor propagation control strategy. On a basis of the proposed model, a rumor hybrid control strategy that combines protection and blocking strategies is proposed, and the dynamic behaviors of the proposed strategy are analyzed. A real dataset is used to predict the propagation trend of rumor spreaders and truth spreaders in real social networks. The effectiveness of the hybrid control strategy is illustrated by comparing with the following cases namely without control strategy, a single protection strategy, and a single blocking strategy. In order to achieve best control of the rumor propagation with lowest cost, an optimal control scheme of the hybrid control strategy is proposed. Using the Pontryagin’s minimum principle, the existence of the optimal control is proved and the optimal control system is obtained. The experimental results illustrate that the cost of the optimal control is the lowest by comparing with the cost of the hybrid control strategy, the single protection strategy, and the single blocking strategy, and minimize the density of rumor spreaders.

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