## A new mathematical model explains patterns of human movement by considering the costs

October 11, 2011 in Other Sciences / MathematicsUsing previously published data on the time-stamped locations of 100,000 anonymous cell-phone users, a researcher from Duke University has identified three distinct patterns of human mobility for short, medium, and long distance trips. In 2008, a separate research team that was not involved in the current study published a paper in which they had plotted data on cell-phone users' movements, and then fitted the data with a single, downward-sloping curve. The curve captured an intuitive relationship: the longer a trip, the less likely it was to occur.

Nicola Scafetta, however, thought deeper patterns might be hidden by the simple curve. In the AIP's journal *Chaos*, Scafetta proposes a finer-resolution analysis of the cell-phone data. He divided the data set up into three separate sections, one each for short (from 1 to 10 km), medium (from 10 to 300 km), and long (above 300 km) distance trips. He then fit each chunk of data with a separate curve. Surprisingly, the exponents from the three separate curve fits were simple numbers – 1, 2 and 3 – that illustrated a different relationship between distance and trip frequency for each zone. For all three zones, the likelihood of a trip decreases with increased distance, but the rate of decrease is faster in the higher-numbered zones.

Scafetta offers a physical and statistical explanation for this pattern. In zone one, people are running short-distance errands within an urban area, and may just consider one cost mechanism, like the time or the fuel cost of the trips, when deciding where and when to go. In the more distant zone two people are, for example, taking day-trips to nearby towns of specific interest. These trips might require travelers to consider both time and fuel costs in their decisions. And in zone three, people take multi-day trips and may consider time and fuel costs, as well as additional overnight lodging costs.

The increase in the number of considered costs for each zone could help explain the increase in the curve-fit exponent for each zone. Scafetta also rescaled the model and found that it could be used to interpret data gathered on the movements of volunteers who walked to their destinations, either in zone one (within 200 m) or zone two (from 200 to 1000 m).

The critical benefit of the alternative fitting method, Scafetta writes, is that it suggests clear physical and geographical mechanisms to explain the observations. Accurate models of human displacement have applications in traffic forecasting, urban planning, and in the study of social networks and the spread of diseases.

**More information:**
"Understanding the complexity of the Lévy-walk nature of human mobility with a multi-scale cost/benefit model" by Nicola Scafetta is accepted for publication in *Chaos: An Interdisciplinary Journal of Nonlinear Science.*

Provided by American Institute of Physics

"A new mathematical model explains patterns of human movement by considering the costs" October 11, 2011 http://phys.org/news/2011-10-mathematical-patterns-human-movement.html