Algebraic growth of infected clusters on heterogeneous networks

We study a spreading pattern of epidemics over a complex network. In susceptible-infected (SI) model, it has been well known that the initial growth of infected nodes follows the exponential form as a function of time t with a time scale described by degree statistics, and that so does the final growth with an infection rate as a time scale. We put focus on the dynamics in the intermediate range except for both the early- and late- time regime and examine on the complex networks governed by degree distribution P_d(k)^{-γ}. It is observed that, for 2 < γ < 3, infected nodes increase with a power law such as t^{-1/(3-γ)} whereas a growth of infected nodes maintains the exponential form in the homogeneous network for γ > 3.