基于SI_(1)I_(2)R模型的舆情传播与最优控制  

Public Opinion Propagation and Optimal Control Based on SI_(1)I_(2)R Model

作　　者：葛青 徐慧玲[1] 王海侠[1] GE Qing;XU Hui-ling;WANG Hai-xia(School of Mathematics and Statistics,Nanjing University of Science and Technology,NanJing 210094,China)

机构地区：[1]南京理工大学数学与统计学院,江苏南京210094

出　　处：《数学的实践与认识》2025年第2期197-208,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金面上项目(12272062)。

摘　　要：结合改进的传染病模型和舆情传播特点,提出了一个包含四类人群用户的SI_(1)I_(2)R舆情传播模型,对该模型的平衡点进行了稳定性分析.引入控制变量后,进行了模型的能控性分析.同时,考虑成本效益,研究了终端时刻自由情况下的最优控制问题,并提出了相应的最优控制策略.数值仿真结果显示,所提策略在有效抑制虚假信息传播的同时还节约了成本,并揭示了网络警报阈值对舆情传播的影响.未来研究可探讨如何设计合适的网络警报阈值以维护网络安全。Combined with the improved infectious disease model and the characteristics of public opinion propagation in real life,this study proposes the SI_(1)I_(2)R public opinion propagation model of four categories of online social network users,analyzes stability of several equilibrium points.In order to avoid the publicity of false information on the Internet,control variables are introduced,and the controllability of SI_(1)I_(2)R with control is analyzed.In addition,considering the cost problem,the optimal control problem with terminal time free is proposed and the corresponding optimal control strategy is given.Finally we set the parameters for numerical simulation,the results show that the false information in the process of public opinion transmission can be suppressed under the premise of cost control,so as to protect the security of the network environment.The simulation also proves that the network alarm threshold has a certain impact on the dissemination of public opinion.Therefore,how to design an appropriate network alarm threshold to maintain network security can be considered in the future.

关 键 词：传染病模型 能控性分析 最优控制 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]