In view of the fact that the existing public opinion propagation aspects are mostly based on single-layer propagation network, these works rarely consider the double-layer network structure and the negative opinion evolution. This paper proposes a new susceptible-infected-vaccinated-susceptible negative opinion information propagation model with preventive vaccination by constructing double-layer network topology. Firstly, the continuous-time Markov chain is used to simulate the negative public opinion information propagation process and the nonlinear dynamic equation of the model is derived; secondly, the steady state condition of the virus propagation in the model is proposed and mathematically proved; finally, Monte Carlo method is applied in the proposed model. The parameters of simulation model have an effect on negative public opinion information propagation, the derivation results are verified by computer simulation. The simulation results show that the proposed model has a larger threshold of public opinion information propagation and has more effective control of the scale of negative public opinion; it also can reduce the density of negative public opinion information propagation and suppress negative public opinion information compared with the traditional susceptible infected susceptible model. It also can provide the scientific method and research approach based on probability statistics for the study of negative public opinion information propagation in complex networks.

中文翻译：

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基于连续时间马尔可夫链的双层网络负面舆论信息传播建模

鉴于现有的舆论传播方面大多基于单层传播网络，因此这些工作很少考虑双层网络结构和负面舆论的演变。通过构建双层网络拓扑结构，提出了一种新的带有预防接种的易感性，易感性，易感染性负面意见信息传播模型。首先，利用连续时间马尔可夫链对负面舆论信息的传播过程进行仿真，得出模型的非线性动力学方程。其次，提出了模型中病毒传播的稳态条件，并进行了数学证明。最后，将蒙特卡罗方法应用于该模型。仿真模型的参数对负面舆论信息的传播有影响，并通过计算机仿真验证了推导结果。仿真结果表明，提出的模型具有较大的舆论信息传播门槛，可以更有效地控制负面舆论的规模。与传统的易受感染的易感模型相比，它还可以减少负面舆论信息传播的密度并抑制负面舆论信息。它还可以为基于概率统计的科学方法和研究方法，为复杂网络中负面舆论信息传播的研究提供依据。仿真结果表明，提出的模型具有较大的舆论信息传播门槛，可以更有效地控制负面舆论的规模。与传统的易受感染的易感模型相比，它还可以减少负面舆论信息传播的密度并抑制负面舆论信息。它还可以为基于概率统计的科学方法和研究方法，为复杂网络中负面舆论信息传播的研究提供依据。仿真结果表明，提出的模型具有较大的舆论信息传播门槛，可以更有效地控制负面舆论的规模。与传统的易受感染的易感模型相比，它还可以减少负面舆论信息传播的密度并抑制负面舆论信息。它也可以为基于概率统计的科学方法和研究方法，为复杂网络中负面舆论信息传播的研究提供依据。与传统的易受感染的易感模型相比，它还可以减少负面舆论信息传播的密度并抑制负面舆论信息。它还可以为基于概率统计的科学方法和研究方法，为复杂网络中负面舆论信息传播的研究提供依据。与传统的易受感染的易感模型相比，它还可以减少负面舆论信息传播的密度并抑制负面舆论信息。它也可以为基于概率统计的科学方法和研究方法，为复杂网络中负面舆论信息传播的研究提供依据。