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.”