Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

The scaling laws of human travel


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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Dispersal of bank notes and humans on geographical scales.
Figure 2: Spatiotemporal scaling of bank note dispersal.

Similar content being viewed by others


  1. Bullock, J. M., Kenward, R. E. & Hails, R. S. (eds) Dispersal Ecology (Blackwell, Malden, Massachusetts, 2002)

  2. Murray, J. D. Mathematical Biology (Springer-Verlag, New York, 1993)

    Book  Google Scholar 

  3. Clobert, J., Danchin, E., Dhondt, A. A. & Nichols, J. D. (eds) Dispersal (Oxford Univ. Press, Oxford, 2001)

  4. Nicholson, K. & Webster, R. G. Textbook of Influenza (Blackwell, Malden, Massachusetts, 1998)

    Google Scholar 

  5. Grenfell, B. T., Bjornstadt, O. N. & Kappey, J. Travelling waves and spatial hierarchies in measles epidemics. Nature 414, 716–723 (2001)

    Article  ADS  CAS  Google Scholar 

  6. Keeling, M. J. et al. Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape. Science 294, 813–817 (2001)

    Article  ADS  CAS  Google Scholar 

  7. Hudson, P. J., Rizzoli, A., Grenfell, B. T. & Heesterbeek, H. (eds) The Ecology of Wildlife Diseases (Oxford Univ. Press, Oxford, 2002)

  8. Hufnagel, L., Brockmann, D. & Geisel, T. Forecast and control of epidemics in a globalized world. Proc. Natl Acad. Sci. USA 101, 15124–15129 (2004)

    Article  ADS  CAS  Google Scholar 

  9. Grassly, N. C., Fraser, C. & Garnett, G. P. Host immunity and synchronized epidemics of syphilis across the United States. Nature 433, 417–421 (2005)

    Article  ADS  CAS  Google Scholar 

  10. Webby, R. J. & Webster, R. G. Are we ready for pandemic influenza? Science 302, 1519–1522 (2003)

    Article  ADS  CAS  Google Scholar 

  11. Kot, M., Lewis, M. A. & van den Driessche, P. Dispersal data and the spread of invading organisms. Ecology 77, 2027–2042 (1996)

    Article  Google Scholar 

  12. Shlesinger, M. F., Zaslavsky, G. M. & Frisch, U. (eds) Lévy Flights and Related Topics in Physics (Springer Verlag, Berlin, 1995)

  13. Klafter, J., Shlesinger, M. F. & Zumofen, G. Beyond Brownian motion. Phys. Today 49, 33–39 (1996)

    Article  Google Scholar 

  14. Brockmann, D. & Geisel, T. Lévy flights in inhomogeneous media. Phys. Rev. Lett. 90, 170601 (2003)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  15. Metzler, R. & Klafter, J. The random walks guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1–77 (2000)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  16. Shlesinger, M. F., Klafter, J. & Wong, Y. M. Random-walks with infinite spatial and temporal moments. J. Stat. Phys. 27, 499–512 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  17. Nathan, R. The challenges of studying dispersal. Trends Ecol. Evol. 16, 481–483 (2001)

    Article  CAS  Google Scholar 

  18. Viswanathan, G. M. et al. Lévy flight search patterns of wandering albatrosses. Nature 381, 413–415 (1996)

    Article  ADS  CAS  Google Scholar 

  19. Ramos-Fernandéz, G., Mateos, J. L., Miramontes, O. & Cocho, G. Lévy walk patterns in the foraging movements of spider monkeys. Behav. Ecol. Sociobiol. 55, 223–230 (2004)

    Article  Google Scholar 

  20. Levin, S. A., Muller-Landau, H. C., Nathan, R. & Chave, J. The ecology and evolution of seed dispersal: A theoretical perspective. Annu. Rev. Ecol. Evol. Syst. 34, 575–604 (2003)

    Article  Google Scholar 

  21. Nathan, R. et al. Mechanisms of long-distance dispersal of seeds by wind. Nature 418, 409–413 (2002)

    Article  ADS  CAS  Google Scholar 

  22. Gardiner, C. W. Handbook of Stochastic Methods (Springer Verlag, Berlin, 1985)

    Google Scholar 

  23. Montroll, E. W. & Weiss, G. H. Random walks on lattices. J. Math. Phys. 6, 167–181 (1965)

    Article  ADS  MathSciNet  Google Scholar 

Download references


We would like to thank the initiators of the bill tracking system ( 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

Authors and Affiliations


Corresponding author

Correspondence to D. Brockmann.

Ethics declarations

Competing interests

Reprints and permissions information is available at The authors declare no competing financial interests.

Supplementary information

Supplementary Notes 1

Calibration against independent human travel datasets (PDF 637 kb)

Supplementary Notes 2

Theory of Lévy flights and continuous time random walks (CTRW) (PDF 580 kb)

Supplementary Notes 3

Relaxation time of two dimensional pure Lévy flights in a confined region (PDF 38 kb)

Supplementary Notes 4

Similarities between the dispersal of bank notes and infectious diseases (PDF 86 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brockmann, D., Hufnagel, L. & Geisel, T. The scaling laws of human travel. Nature 439, 462–465 (2006).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing