Research On SIS Rumor Spreading Model Based On Uncertainty Theory

The rapid development of the Internet has brought us into the information age.All kinds of media provide good conditions for freedom of speech,but also greatly increase the possibility of people spreading rumors.The spread of rumors is easy to incite the masses,trigger group behaviors,and endanger social stability.Especially in the face of sudden social public events,the spread of rumors will cause unnecessary public panic and many other negative social effects in a short time.Therefore,we actively carry out research on the spread of rumors has practical significance and application value.The purpose of this article is to model the spread process of rumors,reveal its propagation rules and characteristics,provide theoretical basis for the formation of a reasonable rumor control strategy,enable us to predict the possible harm caused by the spread of rumors,and help authoritative organizations in case of an emergency make effective prevention and control strategies to purify the network environment.In recent years,the research on the mechanism of rumor spreading based on mathematical models has attracted extensive attention from scholars at home and abroad.However,the process of rumor spreading will inevitably be disturbed by noise in the social environment and become uncertain,and uncertainty theory is a kind of special mathematical tool used to describe and analyze uncertain information,it is very suitable for studying the spread of rumors.Therefore,this thesis applies the uncertainty theory to the study of the spread of rumors.Firstly,this thesis used uncertain variables to describe the uncertain factors in the process of rumor spreading,built an uncertain SIS rumor spreading model driven by a Liu process,the solution of the model is constructed by the successive approximation method,and we used the mathematical induction method,Weierstrass criterion and Gronwall’s inequality prove that the positive solution of the model exists and is unique,and further proves that the model is stable in measure.Numerical simulations were carried out using Euler’s method to discuss the influence of different parameters in the model on the spread of rumors.The results show that:the smaller the spread rate of rumors,the faster the rumors disappear.When the spread rate is high,the rumors will spread widely and even become popular.The greater the intensity of the uncertainty process,the greater the range of fluctuations in the number of rumor spreaders and audiences,and the less time the model will stabilize.Next,on the basis of the uncertain SIS rumor spreading model,considering the influence of the rebuttal mechanism on rumor spreading,a new objector role is added.A multi-dimensional uncertain differential equation is used to establish the uncertain SIAS rumor spreading model driven by multi-dimensional Liu processes,and the existence,uniqueness and stability of the solution of the model are proved.Finally,this thesis uses the α-path to transform the uncertain differential equation into ordinary differential equations,and conducts numerical simulations to find that:the larger the initial value of the objector,the smaller the peak value of the spreader,the shorter the time it takes for the spreader to reduce to 0,and the shorter the time for the model to stabilize,that is,the faster the rumor disappears.