SIR-IM: SIR rumor spreading model with influence mechanism in social networks

Rumor, with the fast speed of transmission, may bring us panic, even economic loss. Thus, it is significant for us to take effective steps to control the rumor spreading. Unfortunately, most of the existing works ignore that the spreading probability is not a constant, but depends on the number of spreaders currently. That is to say, the more spreaders, the larger spreading probability. In order to overcome this shortcoming, in this paper, we propose a novel susceptible–infected–removed (SIR) rumor spreading model with the influence mechanism, called SIR-IM, which first incorporates the number of current spreaders into the spreading probability. Then, it employs time function to describe the rate of people from spreader to stifler as time goes on. Moreover, we not only derive mean-field equations to describe the dynamics of our SIR model, but also give theoretical analysis. Numerical simulations are conducted on social networks, which show that the influence mechanism can accelerate the rumor spreading.