| Recently,the modern Internet has successfully created various ways for people to obtain information,which enhances the enthusiasm of people participating topic discussion.As a result,the effect of information in depth and breadth is enlarged,which means that one piece of the information people delivered on the Internet can receive great attention,cause some panic or even unnecessary economic loss.In this case,to study the mechanism of rumor spreading,node activity and individual reaction can make significant impact on the society.Rumor spreading is a complex process,based on the individual reaction and node activity on the process of rumor spreading,this paper aims to investigate the effects of activity rate and different ignorants'reaction to rumors on the rumor spreading scale.Taking these factors into consideration,different rumor spreading models are established to analyze final rumor spreading scales and their thresholds,and then numerical simulations are conducted to verify the theoretical analysis.These results all revealed that activity rate and spreading rate all could exert effects on final rumor spreading scales,furthermore,spreading rate and activity rate are interdependent,spreading rate takes effects on the threshold of node activity and node activity also have influence on the threshold of spreading rate.After the research,some findings are got as follows:(1)Considering different activities of individuals to the same rumor,adjusted rumor spreading model is established and the corresponding mean-field equations are obtained.Besides,the final rumor spreading scales in the homogeneous network and heterogeneous network are computed,it is found in the numerical simulations that activity rate of individuals does exert effects on final rumor spreading scales and the threshold of rumor spreading scale.Especially,as the activity rate gets larger,the threshold of spreading rate becomes smaller.(2)Considering the condition that different ignorants meet with the rumor may show different attitude to it,like believe and spread,doubt or just unbelieve it,SI_b I_n I_u(Susceptible-Believer-Incubator-Unbeliever)model considering node reaction is proposed to compute the final rumor spreading scale in the homogeneous network and heterogeneous network.According to the numerical simulation results,it reveals that when the transforming rates from ignorants to the spreader,from ignorants to incubators become larger,the final rumor spreading scales will be bigger as well.Besides,the transforming rate of incubators to spreaders will not change the final rumor spreading scales,but it will affect the time of the network reaching the steady state.(3)Taking both activity rate and the reaction of incubators to the rumor into consideration,it is assumed that once an ignorant node hears about the rumor,he will first get into the incubative state after reckoning about the truth of the rumor,then he will choose to believe the rumor or not.Based on such assumption,aS-I_n-I_b I_u(Susceptible-Incubator-Believer-Unbeliever)rumor spreading model with activity rate is proposed to explore effects of both node activity and individual reaction on rumor spreading progress,it is found that node activity rate and spreading rate both exert effects on final rumor spreading scales,and they will have influence on each other's threshold.To sum up,mean-field equations are established to study the dynamical analysis on final rumor spreading scale,considering node activity and different individuals'reaction to the same rumor.The findings reveal that node activity and spreading rate take mutual effects on final rumor spreading scale and spreading threshold,which further enrich the theory of rumor spreading and provide rumor-control workers with more practical suggestions. |
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