Online dynamic rumour propagation model considering punishment mechanism and individual personality characteristics

In the Internet era, rumours will spread rapidly in the network and hinder the development of all aspects of society. To create a harmonious network environment, it is essential to take punitive measures against malicious rumour mongers on social platforms. Take the measure of forbidden as an example. The forbidden one may stop spreading rumours because of being punished, or he may become a disseminator again because of paranoia. Other people who know rumours may become alert and stop propagating rumours or temporarily forget rumours. And therefore, the forbidden state is added to describe the above phenomenon, and the SIFR (Ignorant–Disseminator–Forbidden–Restorer) model is proposed. Taking the vigilance and paranoia derived from punishment measures into account, the connection edges from the forbidden to the disseminator and from the disseminator to the restorer are increased in this model. And then, the stability of SIFR model is proved by using the basic regeneration number and Routh–Hurwitz stability theorem. The simulation results demonstrate that individual paranoia may do harm to the control of rumour dissemination. While the punishment mechanism, individual forgetting mechanism and vigilance can effectively curb the spread of rumours.