LAUSR

Social networks have become one kind of the most important information media in the world, and the study of the phenomena of rumor propagation in social networks is helpful to understand the intrinsic laws of propagation behavior. We distinguish two propagation channels, that is, point to point propagation and group propagation, of rumor spreading on social networks. Thus we propose an improved SIR model and establish the corresponding mean-field equation. By using the differential dynamics method and the next generation matrix theory, the equilibrium point and the basic regeneration number R0 are calculated. Moreover, the geometric method is used to prove the asymptotic stability of the model at the equilibrium point and the bifurcation phenomenon at R0=1. Finally, numerical simulations are carried out to verify the correctness of the theoretical results, and the influence of the rumor spreading mechanisms on the propagation process is analyzed.