带时间延迟和强制静默的SICR谣言传播模型

A SICR Rumor Propagation Model with Time Delay and Enforced Silence

考虑谣言传播过程中传播者传播谣言时可能存在时间延迟以及受到网络监管者的强制静默而无法传播谣言等因素,在SIR模型的基础上,结合辟谣机制和空格理论,将网络中的节点分为易感节点S、感染节点I、辟谣节点C和免疫节点R,提出了一种新的SICR谣言传播模型。首先,通过平均场理论给出了均匀网络结构下谣言传播动力学方程,分析了平衡点的存在性,利用下一代矩阵法计算了模型的基本再生数,发现基本再生数与传播率、平均度、迁入率、迁出率、强制静默率和感染节点恢复率有关。其次,通过Routh-Hurwitz判据分析了平衡点处的局部渐近稳定性,并且通过LaSalle不变原理对无谣言平衡点的全局渐近稳定性进行分析。最后,利用数值仿真实验对理论结果的正确性进行验证,结果表明:考虑辟谣机制的SICR模型相较于SIR模型能够更好地抑制谣言的传播。基于Dataset_R6数据集,采用最小二乘法拟合了模型参数,模型的R^(2)为0.9508。

Considering the factors such as time delay in the propagation of rumors and the inability to spread rumors due to the forced silence of network regulators,in this study,based on the SIR model,combined with the rumor-refuging mechanism and the space theory,nodes in the network were divided into susceptible node S,infective node I,rumor-refuging node C and recovered node R,a new SICR rumor propagation model was proposed.Firstly,the dynamic equation of rumor propagation in homogeneous network structure was given by means of average field theory,the existence of equilibrium point was analyzed,and the basic reproduction number of the model was calculated by using the next generation matrix method.It was found that the basic reproduction number was related to the propagation rate,average degree,migration rate,migration rate,forced silence rate,and recovery rate of infective nodes.Secondly,the local asymptotic stability of the equilibrium point was analyzed by Routh-Hurwitz criterion,and the global asymptotic stability was analyzed by LaSalle′s invariance principle.Finally,the correctness of the theoretical results was verified by numerical simulation experiments.The simulation results showed that SICR model considering the rumor-refuting mechanism could suppress the rumor propagation better than SIR model.Based on Dataset_R6 dataset,the parameters of the model were fitted by least square method,and the R ^(2) of the model was 0.9508.