Rumor spreading model considering the activity of spreaders in the homogeneous network

There are some similarities between the rumor spreading and the infectious disease transmission. In this paper, we investigate rumor spreading dynamics with the activity of spreaders based on compartment model in the homogeneous network. Different from previous studies, each spreader individual in network rotates between high active and low active state according to certain probabilities. We introduce a dynamic model for the rumor spreading called I2SR, in which we consider the activity of nodes and divide spreaders into spreaders with the high rate of active state and the low rate of active spreaders. Then, the locally asymptotic stability of equilibrium is established by using Routh-Hurwitz criteria. The global stability of internal equilibrium of model is proved based on Lasalle's invariance principle. Finally, numerical simulations are carried to illustrate the impact of different parameters on the rumor spreading.