| With the development of network technology,more and more social applications such as Weibo,wechat and QQ appear in our daily life.While promoting the exchange of information,they also lead to the rampant spread of rumors,which has an adverse impact on individuals’ daily life and social stability and development.Therefore,it is particularly important to establish a realistic rumor propagation model,study the inherent law of rumor propagation,and reduce the spread scope of rumors.In recent years,rumors spread more and more in groups,so it becomes more and more important to study the law of rumor spread in groups.Some scholars have proposed the SIHR model considering the forgetting mechanism.On this basis,this paper establishes a SIHR rumor propagation model based on group communication,and implements immune strategies and optimal control strategies to reduce the spread scale of rumors.The main research contents of this paper are as follows:(1)The SIHR rumor propagation model based on group propagation is established.The average field equations are established on homogeneous and heterogeneous networks respectively,and the stability of the model is analyzed.At the same time,it is found that there is no rumor propagation threshold.Monte Carlo simulation is carried out in artificial networks and real social networks.The simulation results show that,under the condition of the same network size,the rumor propagation time of BA scale-free network is smaller than that of WS small-world network,and the density peak of BA network propagation node is larger than that of WS small-world network.When the average size of the group is fixed,increasing the scale of the group can reduce the spread scale of the rumor comparing with increasing the size of the group.(2)It is found that the model has no immunity threshold on the homogeneous network.Through the simulation of random immune process in WS small world network,it is found that with the increase of immune proportion,the spread scale of rumors decreases.Random immunity,target immunity and acquaintance immunity are respectively implemented on heterogeneous networks.Monte Carlo simulation is carried out in BA scale-free network,and it is found that the three immunization strategies are effective in rumor control.In addition,under the condition of the same immunization ratio,the target immunization effect is the best,the acquaintance immunization effect is the second,and the random immunization effect is the worst.(3)Two control strategies,prevention and isolation,are introduced.The existence of the optimal control solution is proved by Cesari theorem,and the optimal control signal is calculated by Pontriagin principle.The effectiveness of the control measures is proved by simulation experiments.The simulation results show that the prevention and isolation measures should change dynamically with the propagation process of rumors.The two control measures can effectively reduce the scale of the propagation nodes and reduce the economic losses caused by rumors. |
