SIR Rumor Spreading Model with Network Medium in Complex Social Networks

In this paper, taking into consideration the influence of the network medium, we propose a novel susceptible-infected-removed (SIR) model to study rumor spreading, and discuss by means of mean-field theory the dynamical behaviors of the SIR model on homogeneous networks and inhomogeneous networks, respectively. Theoretical analysis and simulation results show that, in both networks, the existence of the network medium greatly reduces the critical thresholds and increases the final rumor size. By numerical simulations, we also find that rumor spreading obviously accelerates with an increase of the infectivity between persons and the network medium, but the influence of the network medium on homogeneous networks is greater than on inhomogeneous networks. Therefore, to effectively control rumor spreading, it will not only be necessary to control the rumor spreading rate among different individuals, but one also needs to control the infectivity between persons and the network medium.