The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronize populations of interacting species, stabilize them, and diversify gene pools1,2,3. Human travel, for example, is responsible for the geographical spread of human infectious disease4,5,6,7,8,9. In the light of increasing international trade, intensified human mobility and the imminent threat of an influenza A epidemic10, the knowledge of dynamical and statistical properties of human travel is of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive, and the assumption that humans disperse diffusively still prevails in models. Here we report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Using a comprehensive data set of over a million individual displacements, we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale-free random walks known as Lévy flights. Second, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails that attenuate the superdiffusive spread. We show that human travelling behaviour can be described mathematically on many spatiotemporal scales by a two-parameter continuous-time random walk model to a surprising accuracy, and conclude that human travel on geographical scales is an ambivalent and effectively superdiffusive process.
We would like to thank the initiators of the bill tracking system (www.wheresgeorge.com). We thank cabinetmaker D. Derryberry for discussions and for drawing our attention to the wheresgeorge website, and B. Shraiman, D. Cohen and W. Noyes for critical comments on the manuscript. Author Contributions The project idea was conceived by D.B. and L.H., data pre-processing was done by L.H., data analysis by D.B. and L.H., the theory and model was constructed by D.B., and the manuscript was written by D.B., L.H. and T.G.
Calibration against independent human travel datasets
Theory of Lévy flights and continuous time random walks (CTRW)
Relaxation time of two dimensional pure Lévy flights in a confined region
Similarities between the dispersal of bank notes and infectious diseases