Online social networks have recently become an effective and innovative channel for spreading information and influence among hundreds of millions of end users. Most of prior work either carried out empirical studies or focus on the information diffusion modeling in temporal dimension, little attempt has been given on understanding information diffusion over both temporal and spatial dimensions. In this paper, we propose a Partial Differential Equation (PDE), specifically, a Diffusive Logistic (DL) equation to model the temporal and spatial characteristics of information diffusion. We present the temporal and spatial patterns in a real dataset collected from a social news aggregation site, Digg, and validate the proposed DL equation in terms of predicting the information diffusion process. Our experiment results show that the DL model is able to characterize and predict the process of information propagation in online social networks. For example, for the most popular news with 24,099 votes in Digg, the average prediction accuracy of DL model over all distances during the first 6 hours is 92.08%. To the best of our knowledge, this paper is the first attempt to use PDE-based model to study the information diffusion process in both temporal and spatial dimensions in online social networks.
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