There are significant differences between rumor spreading and epidemic spreading in social networks, especially with consideration of the mutual effect of forgetting and remembering mechanisms. In this paper, a new rumor spreading model, Susceptible-Infected-Hibernator-Removed (SIHR) model, is developed. The model extends the classical Susceptible-Infected-Removed (SIR) rumor spreading model by adding a direct link from ignorants to stiflers and a new kind of people-Hibernators. We derive mean-field equations that describe the dynamics of the SIHR model in social networks. Then a steady-state analysis is conducted to investigate the final size of the rumor spreading under various spreading rate, stifling rate, forgetting rate, and average degree of the network. We discuss the spreading threshold and find the relationship between the final size of the rumor and two probabilities. Also Runge–Kutta method is used for numerical simulation which shows that the direct link from the ignorants to the stiflers advances the rumor terminal time and reduces the maximum rumor influence. Moreover, the forgetting and remembering mechanisms of hibernators postpone the rumor terminal time and reduce the maximum rumor influence.
