“It’s human nature to want the greatest outcome for the least amount of work,” says Filippo Simini a post-doctorate researcher in Northeastern’s Center for Complex Network Research, directed by Albert-László Barabási.
Simini is quoting the American linguist George Kingsley Zipf who, in the early 1940s, introduced a model based on this “principle of least effort” to predict individuals’ inter-city movements.
Later variations of Zipf’s original model are based on an analogy with Newton’s law of gravitation: larger and closer cities attract people more than smaller and more distant cities. The so-called “Gravity Law” of mobility, which accounts for the size and distance between a commuter’s origin and destination, help contemporary network scientists build larger mobility maps, which can help them predict the spread of disease.
But the Gravity Law has several limitations: It depends on parameters that are not universal to all regions of the globe, its predictions are sometimes flat out wrong and, perhaps most importantly, it cannot be used in regions without sufficient traffic data, which often correlate to areas most affected by infectious diseases.
“The Gravity Law works,” says Simini, “But maybe it’s not the best we can do.” In research published online Sunday in the journal Nature, Simini and Barábasi, along with collaborators Marta González from the Massachusetts Institute of Technology and Amos Maritan from University of Padua in Italy, present a more accurate approach, which they call the “Radiation Model.”
Instead of looking only at origin and destination populations, it also takes into account the population density throughout the entire region in which a commuter may find work. Since it depends only on population density data, which is widely available across the globe, it is more versatile than the Gravity Law.
To illustrate the difference between the two models, the team analyzed census data from two pairs of counties with similar populations in Utah and Alabama, respectively. Because the Gravity Law looks only at origin and destination populations, it predicts identical commuting patterns in the two regions. But census data reports 10 times more trips between the two counties in Utah than in Alabama.
“If you live in a city that lies in a densely populated region” says Simini, “then you will probably find good employment close to home. If your city is surrounded by a desert, you’ll have to travel farther to find comparable job opportunities.” Predictions from the Radiation Model come much closer to the actual data.
The team applied their equation to other data sets, such as hourly trips detected by mobile phone use, migration data from the IRS and freight shipment data. The equation accurately predicts the number of trips made between two places using any of these sets.
Network scientists have already put the equation to use in current studies modeling the spread of disease and report that it can give more accurate results than their current methods.
“We enter an era in which predicting the large-scale mobility of individuals is essential for epidemic prediction and transportation planning,” says Barabási, the principal investigator on the work. “The results obtained in the paper offer a rational tool to quantify these movements.”
Photo by Mary Knox Merrill