Global stability of a two-mediums rumor spreading model with media coverage

Rumor spreading is a typical form of social communication and plays a significant role in social life, and media coverage has a great influence on the spread of rumor. In this paper, we present a new model with two media coverage to investigate the impact of the different mediums on rumor spreading. Then, we calculate the equilibria of the model and construct the reproduction number ℜ0. And we prove the global asymptotic stability of equilibria by using Lyapunov functions. Finally, we can conclude that the transition rate of the ignorants between two mediums has a direct effect on the scale of spreaders, and different media coverage has significant effects on the dynamics behaviors of rumor spreading.