Dynamical behavior of rumor spreading under a temporal random control strategy

The propagation of rumors must be controlled due to their harm to society. Here, we analyze a probability master equation model of rumor spreading, which considers a temporal random control strategy that can be adopted at any time as soon as the authority is aware of the negative impact of the rumor. We find that this strategy can effectively reduce both the lifetime of a rumor (i.e. the so-called extinct time) and the proportion of a population hearing this rumor (i.e. the so-called infected density). In particular, the control effect is better if the control strategy is adopted at the early stage of rumor spreading. In addition, we find that (1) increasing the spreading amplitude (i.e. the difference between maximum and minimum of the spreading rate) can increase the infected density but reduces the extinct time; (2) increasing the noise intensity can reduce the infected density but enlarges the extinct time; (3) relaxing the control strategy can give rise to secondary outbreak of a rumor. Our results not only indicate that the temporal random control strategy is effective in preventing rumor diffusion, but that they could also help the authority make decisions for rumor control.