Modeling And Research Of Si-SIR Rumor Propagation Model In Complex Social Networks

With the development of the information age,social networks relying on the Internet make people’s life more convenient.Meanwhile,rumors inevitably spread on social networks.It is of practical significance and important value to study the rumor spreading mechanism on complex social networks for understanding the rumor spreading rules and formulating effective rumor control measures.Considering that there are few studies on spreader individuals which exist psychological differences in social networks,a Si-SIR(Silent-Susceptible-Infected-Removed)rumor propagation model is established,considering stochastic noise interference and optimal control models to study dynamic behaviors and rumor control measures in the rumor propagation process.The main contents of this paper are as follows:(1)Considering that the psychological difference of spreaders cannot be ignored in the process of rumor spreading,a Si-SIR rumor propagation model is proposed,and the mean field equations of the model is established on the homogeneous network and heterogeneous network respectively,and the rumor spreading threshold is deduced.Runge-Kutta numerical solution and Monte Carlo simulation are used to verify the rationality of the proposed model.The simulation results show that final scale of rumor in the network obeys the relation “Facebook network >WS network >BA network”.The silent-return mechanism improves the maximum impact of the rumor,reduces the density of the final removed nodes,and extends the time of rumor extinction.The simulation results of rumor propagation threshold are basically consistent with the theoretical derivation.(2)Complex social network is usually affected by environmental factors,which is reflected in the dynamic change of network topology.Such change is acted on the connectivity variation and described as Gaussian white noise.The stochastic differential dynamic equations are established on the homogeneous network and the heterogeneous network respectively,the existence and uniqueness of the global positive solution is demonstrated and a sufficient condition of rumor extinction is proved.The changes of network topology under the disturbance of weak noise intensity and strong noise intensity are analyzed through simulation experiments,and the effect of stochastic noise on rumor diffusion process is studied.The simulation results show that the rumor spreading process can be accelerated and improve maximum influence and final scale of rumor as long as add the appropriate noise intensity,and reduces the density of final silent nodes.(3)On the basis of the Si-SIR rumor propagation model considering the psychological differences of spreaders,three control variables which are preventive therapy,immunotherapy and positive transformation are introduced to establish the optimal control models on homogeneous network and heterogeneous network,and the necessary conditions of the optimal control models are proved by using the Pontryagin’s Minimum Principle.The numerical simulation results show that the sooner preventive therapy control measure is implemented,the more effective it will be.And the control measures of immunotherapy and positive transformation should follow the development trend of rumors.Comprehensive consideration of the three control measures can reduce the maximum influence of rumors,decrease the density of silent individuals,effectively suppress the harm of rumor spreading,and reduce the harm brought by rumors.