Global Dynamics of Knowledge Transmission Model on Scale-free Networks

Human behaviors are known to spread through social contact, which means that knowledge transmission is a social process. In order to investigate the characteristics of knowledge transmission and heterogeneity of social networks, an ILSFI (ignoramus-learner-spreader-forgetter-ignoramus) model is presented on scale-free networks. The spreading dynamics of knowledge are analyzed in detail by using the theory of mean-field. The basic reproductive number R
0
is calculated by the next generation matrix method and two equilibria are derived. The theoretical analysis indicates that the basic reproductive number mainly depends on the knowledge transmission process and the topology of the underlying networks. Furthermore, the global stability of the knowledge loss equilibrium and the permanence of the knowledge transmission are also studied in detail. Finally, we analyze the interest degree and the benefit degree through numerical simulations.