  Despite its importance for rumors or innovations propagation, peer-to-peer
collaboration, social networking or Marketing, the dynamics of information
spreading is not well understood. Since the diffusion depends on the
heterogeneous patterns of human behavior and is driven by the participants'
decisions, its propagation dynamics shows surprising properties not explained
by traditional epidemic or contagion models. Here we present a detailed
analysis of our study of real Viral Marketing campaigns where tracking the
propagation of a controlled message allowed us to analyze the structure and
dynamics of a diffusion graph involving over 31,000 individuals. We found that
information spreading displays a non-Markovian branching dynamics that can be
modeled by a two-step Bellman-Harris Branching Process that generalizes the
static models known in the literature and incorporates the high variability of
human behavior. It explains accurately all the features of information
propagation under the "tipping-point" and can be used for prediction and
management of viral information spreading processes.
