Dynamic Analysis Of Online Rumour Spread Based On Infectious Disease Model

With the rapid development of Internet technology,social networks are closely related to our lives,and every user in a social network is a recipient and publisher of information.The rapid spread of unconfirmed rumors can have a serious impact on our national development,social order and personal life.The process of spreading rumors in social networks is very similar to the process of spreading infectious diseases,and the process of spreading rumors on the Internet is studied by optimising and improving on the infectious disease model.The main research of this paper includes:(1)Based on the analysis of SEIR and other models,the IERSU model of Internet rumour propagation was constructed.In the IERSU model,the population in the system is divided into ignorant,exposed,rumour spreading,rumour resisting and disinterested people,and there is a certain transition probability between the various categories of people,while the dynamic change of the number of people in the system is considered,and the rate of increase of the number of people in the system and the rate of leaving the system for each category of people are added.A system of kinetic differential equations is used to describe the change in the number of people in the system during rumour propagation.The threshold parameters of the model are obtained using the next generation matrix method,which is used to discriminate between the invalid propagation equilibrium point and the effective propagation equilibrium point.The global stability of the rumour propagation equilibrium point and the effective propagation equilibrium point is proved.(2)In order to study the role of the IERSU model on the spread of Internet rumors,data related to the spread of a certain rumour in microblogs were selected,the data were correlated,the influence of different parameters on the number of people spreading Internet rumors was analyzed according to numerical simulations,and a series of effective control strategies for the corresponding parameters were given.(3)Based on the IERSU model,the IER1R2 DS Internet rumour propagation model is further optimised and improved by subdividing rumour spreaders into intentional rumour spreaders and unintentional rumour spreaders according to the psychological state of rumour spreaders,while replacing rumour resisters with rumour debunkers.The threshold parameters of the model are used to determine the final propagation state of the model.Using the determination and properties of the negative definite matrix,Lyapunov’s first method and La Salle’s invariant set principle,the local stability and global stability of the rumour propagation invalid equilibrium point and the propagation effective equilibrium point of the model are proved.Finally,numerical simulations are carried out to analyse the influence of various factors on the number of rumour spreaders in the two types of rumour spreading process,and relevant suggestions and measures are given.