Temporal behaviors of epidemic spreading on the scale-free network

Exploring temporal behaviors of the epidemic spreading is of particular importance, in which field an interesting phenomenon of hierarchical spreading cascade has already been demonstrated. By taking into account the effect of density of infected neighbors around an individual in the definition of spreading rate, an infection mechanism modulated by a parameter is introduced in the present paper. Under the mechanism temporal behaviors on the scale-free network are shown to be different, corresponding to different parameters. Three distinct hierarchical spreading modes are typically exhibited. In addition, a novel way to depict the dynamical processes of the epidemic spreading is also developed and some new features are, thus, clearly displayed.