Stability analysis of an SDILR model based on rumor recurrence on social media

Rumors can pose a damaging effect on individuals, organizations, and even public safety. It is of great value to precisely characterize the process of rumor spreading, since it can help provide corresponding countermeasures to contain the propagation. The main goal of this paper is to explore the phenomenon of rumors mongering repeatedly on social media, using a mathematical model, named SDILR. In this model, we describe different contact status for different users including the Susceptible, the Dangerous, the Infective, the Latent and the Recovered in an online social network. Compared to the traditional SIR spreading model, we supplement some realistic constraint condition i.e., the obstinacy of some rumor spreaders and the filtering function of online social medias are taken into account. Furthermore, the mean-field equations are derived to describe the dynamics of the SDILR rumor spreading model, associated with which the steady-state analysis is carried out, indicating the existence of equilibrium. Meanwhile, we investigate rumor control strategies over the Susceptible, the Dangerous, the Infective, the Latent and the Recovered. Simulation results show that there is great potential for an effective method to combat repeated rumors, in terms of lessening the recurrence rate θ and increasing the control rate γ. •Dangerous state represents those who have neighbors spreading the rumor.•Latent state is established for the consideration of rumor recurrence.•The stabilities of the two equilibria are proved.•Numerical simulation experiments validate the effectiveness of the SDILR model.