SIRaRu rumor spreading model in complex networks

•SIRaRu rumor spreading model is established and mean-field equations are derived.•There exists the spreading threshold in the SIRaRu model.•The final size of a rumor is greatly impacted by the forgetting rate.•For rumor control, the targeted immunization is more effective than the random immunization.

Compared with the epidemic spreading, rumor spreading has some specific characteristics. In this paper, we supplement some realistic conditions on previous rumor spreading models, then develop a new rumor spreading model called SIRaRu model. The mean-field equations are derived to describe the dynamics of the SIRaRu rumor spreading in complex networks, associated with which the steady-state analysis is carried out, indicating the spreading threshold existing in both homogeneous networks and inhomogeneous networks. Meanwhile, we discuss the rumor immunization strategy and obtain the immunization threshold and spreading thresholds in homogeneous and inhomogeneous networks, respectively. Numerical simulations are conducted in complex networks, showing that the network topology exerts significant influence on the rumor spreading. The final size of the rumor is greatly impacted by the forgetting rate.