随着移动互联网的快速发展和社交网络的广泛应用，谣言突破了地理限制，其传播速度更快、传播范围更广。相较于传统信息媒介，社交网络低门槛、高自由度的特性增加了谣言传播能力和控制难度。研究社交网络谣言传播模型，揭示谣言传播内在机理，并提出有效的谣言控制策略，可为社交网络谣言防治提供参考。目前社交网络谣言传播建模和控制策略研究存在一些不足：在谣言传播建模方面，需要考虑坚定传谣群体和时滞机制对谣言传播的影响。在谣言控制策略方面，大多研究使用单一控制策略，且缺少对控制策略最优成本问题的研究。针对上述问题，本文聚焦于社交网络谣言传播仿真和控制策略的研究。本文主要研究内容如下：

(1) 社交网络时滞谣言传播建模与仿真。考虑坚定传谣者和时滞机制等因素对谣言传播的影响，建立一类时滞谣言传播动力学模型。计算该模型的平衡点和基本再生数，对该模型的动力学行为进行了分析：通过李雅普诺夫定理和罗斯-赫尔维茨准则判断无谣言平衡点和谣言盛行平衡点的稳定性，利用霍普夫分岔理论计算霍普夫分岔阈值；利用真实数据拟合模型参数，验证模型的有效性；通过仿真分析了时滞机制和坚定传谣者对谣言传播过程的影响，阐释了基本再生数和霍普夫分岔阈值对谣言传播趋势的评估作用，验证了理论结果的有效性。该研究为制定谣言管控措施提供一定理论支撑。

(2) 谣言传播混合控制策略研究。针对单一保护策略和单一阻断策略存在的不足之处，提出一类混合控制策略，建立一类谣言传播混合控制策略模型，分析该模型的动力学行为。通过庞特里亚金极小值原理，量化混合控制策略性能，建立混合控制策略最优控制问题。通过理论分析与计算，证明最优控制的存在性，从控制策略目标函数出发求解最优控制参数。通过仿真实验，验证了混合控制策略的效果优于单一谣言控制策略，且最优混合控制策略相较于其他控制策略具有更低控制成本，并能使传谣者密度最小化。

本文针对社交网络中的谣言传播行为，侧重于社交网络谣言传播的仿真需求及控制需求，基于社交网络用户群体及谣言传播机制的特殊性，提出了一类时滞谣言传播模型和谣言传播控制策略模型，对于促进社交网络中谣言传播行为内在规律的理解，协助谣言事件的防控及决策等方面具有重要意义。

With the rapid development of mobile Internet and the wide applications of social networks, rumors propagation is not limited to geographical conditions, and the speed is faster and scale is more extensive. Compared with traditional information media, the characteristics of social networks perform as low threshold and high freedom, which increases the capacity of spreading and the difficulty of controlling rumors. The research on rumor propagation models, revealing the intrinsic mechanism of rumor propagation, providing effective rumor control strategies, and providing references for preventing rumor propagation. There are still some insufficiencies in the research on modeling and controlling rumor propagation. In terms of modeling rumor propagation, it is necessary to consider the influence of the stubborn rumor spreading population and the time delay mechanism on rumor propagation. In terms of rumor control strategies, most studies use a single control strategy and there lacks research on optimal cost of the control strategies. In response to the above-mentioned issues, this thesis focuses on the research of rumor propagation and control strategies in social networks. The research contents of this thesis are as follows.

(1) Modeling and simulations of rumor propagation with time delay in social networks. A dynamics model of time delay rumor propagation is proposed considering the firm rumor spreaders and time delay mechanism. The equilibrium point and the basic regeneration numbers of the model are calculated, and the dynamical behaviors of the model are analyzed as follows: the stability of the rumor-free equilibrium point and the rumor-prevalent equilibrium point are judged by Lyapunov’s theorem and Routh-Hurwitz criterion, and the Hopf bifurcation threshold is calculated by using Hopf bifurcation theory; the model parameters are fitted with real practical data to verify the validity of the model; the simulation results verify the validity of the theoretical results, show that firm rumor spreaders have an important influence on rumor propagation, and explain the role of basic regeneration number and Hopf bifurcation threshold in evaluating the trend of rumor propagation.

(2) Research on hybrid control strategies for rumor propagation. To address the shortcomings of single protection strategy and single blocking strategy, a rumor hybrid control strategy is proposed, and a rumor propagation model including this hybrid control strategy is established, and the dynamic behaviors of the model are analyzed. The effect of the hybrid control strategy is verified to be better than the single rumor control strategy through comparative experiments. The performance of the hybrid control strategy is evaluated with the Pontryagin’s principle of minimal value, and the optimal control problem of the hybrid control strategy is established. The existence of the optimal control is proved by theoretical analysis and calculation, and the optimal control parameters are found from the control strategy objective function. The experimental results show that the optimal hybrid control strategy has the lower control cost and it can minimize the density of rumor spreaders compared with other control strategies.

This thesis mainly concerns the behaviors of rumor propagation in social networks, it focuses on the requirements of simulation and control of rumor propagation in social networks, and it proposes a rumor propagation model with time delay and a rumor propagation strategy model, and it is of important significance in promoting the understanding of the mechanism of rumor propagation behaviors in social networks and assisting with the prevention and control of rumor events and decision making.