The scaling laws of human travel

TL;DR

This paper quantitatively analyzes human travel patterns using bank note circulation data, revealing anomalous, scale-free dispersal characterized by Levy flights and long-tailed residence times, modeled effectively by a continuous time random walk.

Contribution

It provides the first comprehensive quantitative assessment of human travel statistics on geographical scales using real-world data, highlighting anomalous superdiffusive behavior.

Findings

Travel distances follow a power-law distribution, indicating Levy flight characteristics.

Residence times in regions have algebraically long tails, affecting spread dynamics.

Human travel can be modeled accurately by a two-parameter continuous time random walk.

Abstract

The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3]. Human travelling, e.g. is responsible for the geographical spread of human infectious disease [4-9]. In the light of increasing international trade, intensified human mobility and an imminent influenza A epidemic [10] the knowledge of dynamical and statistical properties of human travel is thus 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. 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 Levy flights. Secondly, the probability of remaining in a small, spatially confined region for a time T is dominated by algebraically long tails which 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 effectively superdiffusive process.