Letter

The scaling laws of human travel

  • Nature volume 439, pages 462465 (26 January 2006)
  • doi:10.1038/nature04292
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Abstract

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.

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Acknowledgements

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.

Author information

Affiliations

  1. Max-Planck Institute for Dynamics and Self-Organisation, Bunsenstr. 10, 37073 Göttingen, Germany

    • D. Brockmann
    •  & T. Geisel
  2. Department of Physics, University of Göttingen, 37073 Göttingen, Germany

    • D. Brockmann
    •  & T. Geisel
  3. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA

    • L. Hufnagel
  4. Bernstein Center for Computational Neuroscience, 37073 Göttingen, Germany

    • T. Geisel

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Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Corresponding author

Correspondence to D. Brockmann.

Supplementary information

PDF files

  1. 1.

    Supplementary Notes 1

    Calibration against independent human travel datasets

  2. 2.

    Supplementary Notes 2

    Theory of Lévy flights and continuous time random walks (CTRW)

  3. 3.

    Supplementary Notes 3

    Relaxation time of two dimensional pure Lévy flights in a confined region

  4. 4.

    Supplementary Notes 4

    Similarities between the dispersal of bank notes and infectious diseases

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