After a piece of information is released in Online Social Networks (OSNs), will it spread to the entirenetwork or reach only a small population of users? In a time window of interest, how many users will forward or comment on this information? Limited effort has been made at this point to develop an effective model to address these issues, as the time-sensitive nature of information spreading and the complexity of network structure make it a very challenging task. In this paper, we propose a continuous-time model for information diffusion with time-varying diffusion (infection) rate to address these issues, and provide an interface between our proposed model and the well-studied SI model with constant diffusion rate.

We prove that there exists an elegant time-rescaling relationship between these two cases, such that any available result on the standard SI model can readily carry over to our time-varying case. We then show how the shape of the time-dependent infection rate will influence the temporal evolution of the size of infection and the time until the information reaches a given node on a graph. This also explains why some information stops spreading before reaching the entire population. Simulation results on Digg graph validate our findings.