The influence of oblivion-recall mechanism and loss-interest mechanism on the spread of rumors in complex networks

Studying more realistic propagation mechanisms of rumors is crucial to controlling their spreading. Considering the reality of people’s forgetting and losing interest in the process of rumor spreading, the oblivion-recall mechanism and the loss-interest mechanism are both introduced in this paper to construct a novel susceptible-infected-removed (SIR) model. In our SIR model, the forgetting is regarded as an independent state type of the population, and we use the forgetting factor α and the recall factor β to characterize the oblivion-recall mechanism. The mean-field equations are established respectively to describe the transmission dynamics of rumors in homogeneous networks and inhomogeneous networks. By performing stable state analysis, the relationship between these two parameters α, β and the propagation critical thresholds λc is investigated. It shows that λc is directly proportional to α, which indicates that the loss-interest mechanism makes λc exist, and the oblivion-recall mechanism increases the value of λc. Thus, the oblivion-recall mechanism reduces the outbreak probability of rumor spreading. It also reveals that when considering the impact of oblivion-recall mechanism, both the final rumor size and the propagation velocity of rumors decrease. Moreover, in the case of considering the existence of oblivion-recall mechanism, it is still found that the network topology is an important factor affecting the spread of rumors. We wish that our study can offer a new angle of view on the issue of the spread of rumors.