Online and Offline Rumor Spreading Dynamics on Scale-Free Networks

Nowadays, the impact of the Internet on human beings is growing. The spread of rumors on the Internet has also become a way of spreading rumors. In the paper, we investigate rumor spreading with the route of rumor spreading based on compartment model on scale-free networks. Different from previous studies, a new $SO_{1}O_{2}E$ (susceptible-offline-online-educated) rumor spreading model with demographics on scale-free networks is proposed. We consider the activity of nodes and divide spreaders into spreading of offline and the spreading of online. Then the basic reproductive number is obtained. Furthermore, the global asymptotical stability of rumor-free equilibrium and the permanence of the rumor are proved in detail. Finally, numerical simulations confirm the analytical results.