# Dresden 2006 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 12: Statistical Physics of Complex Networks II

### DY 12.7: Hauptvortrag

### Montag, 27. März 2006, 12:30–13:00, H\"UL 186

**The scaling laws of human travel** — •Dirk Brockmann^{1}, Lars Hufnagel^{2}, and Theo Geisel^{1} — ^{1}MPIDS, Göttingen — ^{2}KITP, UCSB, Santa Barbara, USA

In the light of increasing international trade, intensified human mobility and an imminent influenza A epidemic 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. I will report on a solid and quantitative assessment
of human travelling statistics by analysing the circulation of bank notes in the United States. Based on a
comprehensive dataset 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. Secondly, the probability of
remaining in a small, spatially confined region for a time *T* is dominated by algebraic tails which attenuate
the superdiffusive spread. We show that human travel 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 effectively superdiffusive process.

[1] Brockmann, D., L. Hufnagel, and T. Geisel, The scaling laws of human travel. Nature, 2006 (to be published).

[2] Hufnagel, L., D. Brockmann, and T. Geisel, Forecast and control of epidemics in a globalized world. PNAS, 2004. 101(42): p. 15124-15129.