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

##### October 11, 2011

Using 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 . In the AIP's journal , 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.

Explore further: Human behavior is 93 percent predictable, research shows

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.

## Related Stories

#### Human behavior is 93 percent predictable, research shows

February 23, 2010

(PhysOrg.com) -- Human behavior is 93 percent predictable, a group of leading Northeastern University network scientists recently found. Distinguished Professor of Physics Albert-László Barabási and his ...

#### Congestion Charge: potentially unsafe for motorcyclists, claim researchers

August 17, 2007

The London congestion charge may be having an adverse effect on motorcyclist and cyclist casualties, according to research now published online in the journal Transportation.

#### Travelling epidemics: Human mobility patterns and their impact on the spread of epidemics

August 31, 2011

(PhysOrg.com) -- In a globalized world, infectious diseases such as SARS, swine flu or seasonal influenza can be transmitted over the entire planet by travellers. To enable a more effective response to this threat, scientists ...

#### Habitable zones

August 22, 2011

(PhysOrg.com) -- The "habitable zone" is the region around a star where a suitable planet could sustain the conditions necessary for life. Most astronomers take it to be the region where the balance between stellar radiation ...

#### How common are terrestrial, habitable planets around sun-like stars?

September 28, 2011

Once again news from the Kepler mission is making the rounds, this time with a research paper outlining a theory that Earth-like planets may be more common around class F, G and K stars than originally expected.

#### Java Mobile Phones Find the Way – New Mobile Navigation

December 6, 2005

Java-enabled mobile phones are becoming mobile pathfinders. VDO Dayton has become the first supplier to launch a navigation system for cell phones that feature the widely used programming language Java. Navigation solutions ...

## Recommended for you

#### Experts uncover hidden layers of Jesus' tomb site

October 27, 2016

In the innermost chamber of the site said to be the tomb of Jesus, a restoration team has peeled away a marble layer for the first time in centuries in an effort to reach what it believes is the original rock surface where ...

#### Important ancient papyrus seized from looters in Israel

October 27, 2016

(Phys.org)—Eitan Klein, a representative of the Israel Antiquities Authority, has announced that an important papyrus document dated to 2,700 years ago has been seized from a group of Palestinian looters who reportedly ...

#### Fossilized dinosaur brain tissue identified for the first time

October 27, 2016

An unassuming brown pebble, found more than a decade ago by a fossil hunter in Sussex, has been confirmed as the first example of fossilised brain tissue from a dinosaur.

#### Money can buy happiness but it's costly to bank on that without measuring debt

October 26, 2016

Yes, money can lead to happiness, but how much debt one has should also be considered in the money-happiness equation, according to a new a study from Purdue University.

#### Upper Paleolithic humans may have hunted cave lions for their pelts

October 26, 2016

Upper Paleolithic humans may have hunted cave lions for their pelts, perhaps contributing to their extinction, according to a study published October 26, 2016 in the open-access journal PLOS ONE by Marián Cueto from the ...

#### Ancient parrot fossil found in Siberia

October 26, 2016

(Phys.org)—A Russian paleontologist has discovered a parrot fossil uncovered in Siberia several years ago—the first evidence of parrots living in Asia. In his paper published in Biology Letters, Nikita Zelenkov describes ...