Modeling the dynamics of rumor diffusion over complex networks

Abstract

Rumor propagation on complex networks is rapidly affecting people’s life. As we all know, the regulatory control of rumors by regulators has a specific impact on the spread of rumors. Limited regulatory resources may saturate the regulatory level. Therefore, in this paper, we have introduced a saturation treatment function to model this phenomenon and further establish an SIS rumor propagation model with consideration of some comprehensive influence on rumor diffusion. First of all, we prove the boundedness of solutions, and the basic reproduction number R0 is obtained by the method of the next generation matrix. Secondly, by constructing Lyapunov function and applying the linearization method of differential equations, the stability conditions of the equilibrium points are derived. Further, we determine the condition for the backward bifurcation of the rumor propagation model. Moreover, in order to control the spread of rumors, we propose targeted immunization control, acquaintance immunization control and optimal control strategies based on complex networks. Finally, the sensitivity analysis of the basic reproduction number is carried out, and the correctness of the theoretical results is verified by numerical simulations. Our results may provide us with useful insights into the dynamics of online rumor propagation. For example, the basic reproduction number R0 gives the threshold of rumor propagation, which provides control conditions for suppressing the spread of rumors. Stability analysis indicates the likelihood of local or global outbreaks for rumors. In addition, the comparison of the effect for control strategies gives a variety of options for the control method.