具有复发的SEILR谣言传播模型的动力学分析

Dynamic analysis of the SEILR rumor spreading model with recurrence

基于谣言的传播机制,考虑人际因素导致的谣言复发,建立了一个SEILR谣言传播模型,研究了人际因素对谣言传播的影响。首先,给出谣言传播的阈值R 0,并分析了R 0<1时,无谣言平衡点的稳定性;其次,分析了多平衡态的存在性,并给出了模型发生后向分支的条件,然后通过构造Lyapunov函数证明了退化模型正平衡点的全局渐近稳定性;最后,通过数值模拟发现模型会出现退化的Hopf分支,模型存在2个极限环,其中大极限环不稳定,小极限环稳定。研究结果说明人际因素导致的谣言复发会改变谣言的动态传播趋势。

Based on the rumor spreading mechanism,considering the rumor recurrence caused by the interpersonal factor,this paper establishes a SEILR rumor spreading model,and studies the impact of this factor on rumor spreading.Firstly,the rumor spreading threshold R 0 is given,and the stability of the rumor-free equilibrium point is analyzed when R 0<1.Secondly,the existence of multiple equilibrium states is analyzed,and the condition of the occurrence of backward bifurcation is given.Then,the global asymptotic stability of the positive equilibrium point of the degenerate model is proved by constructing Lyapunov function.Finally,through numerical simulation,it is found that degenerate Hopf bifurcation appears and there are two limit cycles in the model,in which the large one is unstable and the small one is stable.The results show that the rumor recurrence caused by interpersonal factors can change the dynamic spreading trend of the rumors.