负面思想传播的IHSRI模型研究
A study on IHSRI model of negative ideological propagation

针对目前各类负面思想传播多采用定性分析，未能揭示思想传播内在规律的问题，引入病毒传播理论与数学建模的方法，提出了负面思想传播的IHSRI (Ignorant-Hidden-Spread-Removed-Ignorant)模型。首先分析系统中无知者(I)、潜伏者(H)、传播者(S)和移出者(R)这四种状态的网民之间的转换关系，接着建立相应的数学传播模型，求得该模型的平衡点，对模型的局部稳定性进行分析并证明，当基本再生数R0小于等于1时，无负面平衡点局部渐进稳定，当基本再生数R0大于1时，负面平衡点渐进稳定。仿真结果表明，潜伏者(H)到移出者(R)的转移速率ε从0.04增加到0.2，可以使基本再生数R0从5.71减小到2.67；比例系数α从0.8减小到0.15，可以使R0从5.71减小到1.07，可知通过增加ε和减小α可以减小R0的取值，可实现模型趋近于无负面平衡点，提出的IHSRI模型能够准确的描述负面思想传播的过程，证明此模型是合理、有效的。
The negative ideological are mostly qualitative analyzed at present, whichfailed to reveal the inherent law of ideological propagation. In order to solve the problem, the IHSRI (Ignorant Hidden Spread Removed Ignorant)model is proposedutilizing the method of virus propagation theory and mathematical modeling. Firstly, the authors analyze the conversion relationship between of Internet users under four states, that is, ignorant(I), hidden (H), spread (S) and removed (R).Then, the authorsestablish the corresponding mathematical propagation model. The equilibrium point of the model is calculated and the local stability of the model is analyzed and proved. The no negative equilibrium is locally asymptotically stable when the basic reproduction number R0 is less than or equal to 1; the negative equilibrium is locally asymptotically stable as the number R0 is greater than 1.Finally,the simulation result shows that the basic reproduction number R0 can be reduced from 5.71 to 2.67 when the transfer rate ε (transforming from H to R) increases from 0.04 to 0.2;R0 can be reduced from 5.71 to 1.07 when the proportionality coefficient αdecreases from 0.8 to 0.15.It can be seen that the value of R0 can be reduced by increasing ε and decreasing α, and the model can be approximated to the non negative equilibrium. The research shows that the IHSRI model can accurately describe the process of negative ideology propagation, which proved that this modelis reasonable and effective