Stability analysis of I2S2R rumor spreading model in complex networks

In this paper, we propose I2S2R rumor spreading model with general incidence function in homogeneous networks and I2S2R rumor spreading model in heterogeneous network. In the first model, we establish a dynamic model for rumor propagation called I2S2R, in which we consider two general incidence functions. Then the basic reproduction number, the locally stability and the global stability of rumor-free equilibrium are discussed. In the second model, we mainly consider another network structure, i.e. heterogeneous network. Thus, we propose a new dynamic model for rumor spreading. By deriving the mean-field equation, the basic reproduction number is obtained. Moreover, the global stability of rumor-free equilibrium is established by comparison principle. By using a monotone iterative algorithm, the global attractivity of the positive equilibrium is proved. Finally, we obtain some important conclusions with numerical simulations.