Spreading Dynamics of an Advertisement Model with Time Delay on Scale-free Networks

In this developed information age, the advertisement exists around real life. Considering the attractive degree of the advertisement, time delay and the heterogeneity of social networks, a novel INSRI(ignorant-insider-spreader-resister) advertising information spreading model is put forward on scale-free networks. By the mean-field theory, the spreading dynamic behaviors of advertising information are analyzed in detail. Firstly, the basic reproductive number R
0
is derived. Then, advertisement-free equilibrium and advertisement-prevailing equilibrium are obtained. Both the existence of advertising information equilibriums and the dynamic behaviors of the model are determined by the basic reproductive number R
0
. Furthermore, the global stability of the advertisement-free equilibrium E
0
and the permanence of advertisement spreading are studied in detail. Finally, numerical simulations are performed to confirm the analytical results.