With the prevalence of online social networks, rumors spread rampantly online. The versatility and complexity of human attitudes make dissemination more challenging to portray, so it is meaningful to develop a more comprehensive diffusion model. To this end, an improved SEIHR model considering three attitudes towards rumors is proposed. Then we deduce the stability of the dynamics model and use two scenarios to validate its accuracy. Meanwhile, rumor diffusion generates extensive social threats. To mitigate such threats, we introduce three immunization strategies and forge bonds among their basic reproduction numbers. Besides, we develop three synergistic optimal controls that vary with the time and degree to impede rumor diffusion. The analysis of the optimal control problem is conducted by Pontryagin's maximum principle. Next, experiments are conducted to verify the efficacy of the SEIHR model and control strategies. Our simulations show that adding the exposed and the hibernated undermines the impact of rumors and puts off terminal time. Additionally, immunization strategies effectively curb rumor diffusion. Moreover, the combination of three synergistic optimal controls leads to the smallest rumor scale and the least cumulative total costs.

中文翻译：

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在线社交网络中SEIHR谣言传播模型的动态分析与控制策略


随着网络社交网络的盛行，谣言在网上泛滥成灾。人类态度的多样性和复杂性使得传播更加难以描绘，因此开发更全面的传播模型是有意义的。为此，提出了一种考虑对谣言的三种态度的改进SEIHR模型。然后我们推导了动力学模型的稳定性，并使用两个场景来验证其准确性。与此同时，谣言的传播产生了广泛的社会威胁。为了减轻此类威胁，我们引入了三种免疫策略，并在其基本繁殖数之间建立联系。此外，我们还开发了三种协同最佳控制，这些控制随时间和程度而变化，以阻止谣言传播。最优控制问题的分析采用庞特里亚金极大值原理进行。接下来，通过实验验证SEIHR模型和控制策略的有效性。我们的模拟表明，添加暴露和休眠会削弱谣言的影响并推迟终端时间。此外，免疫策略有效遏制谣言传播。此外，三种协同最优控制的组合导致谣言规模最小和累计总成本最小。