Published online 12 August 2004 | Nature | doi:10.1038/news040809-13

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# Gravity equations give rise to measles model

Disease shown to spread to big cities rather than small towns.

Large cities attract people and disease alike.© Alamy

The pattern of epidemics could be predicted more accurately by taking into account how attractive different sizes of cities are to visitors. A new model uses equations originally developed to calculate the gravitational pull between planets.

Theoretical ecologist Ottar Bjørnstad, from Penn State University in University Park, took inspiration from Andrew Cliff, an economic geographer from the University of Cambridge, UK. In the 1970s, Cliff proposed that the equations used to calculate how planets are attracted to each other could also be used to predict how people with contagious disease would move. The shared idea is that a bigger place, whether planet or city, is more attractive.

Bjørnstad and his colleagues have now tested the idea, using exhaustive data on childhood measles in England and Wales, and publish their results in The American Naturalist1. They combined a model of how an epidemic plays itself out locally with the idea that the infection is more likely to hop from a small town to the capital than to a nearby small town to predict where the disease was likely to move next.

“Everyone thought it was beautiful work.”

Pejman Rohani
Ecologist, Georgia University

The model has four parameters: relating to the likelihood that someone will travel to a distant place instead of a close one; the likelihood that if someone travels they will go to a place of a particular size; the transmission rate of the visitor in the visited place (for example, children visiting family are likely to be around fewer children than when they are in school); and a final factor involving the varying rates of travel of people from small and large towns.

The model was able to predict the course of the measles infections described by the British data. "The exciting thing for us was to go from the common sense to the predictive network," Bjørnstad says. "We can answer: which is going to be next? A town of 100,000 people that is 40 miles away or a town of 200,000 people that is 40 miles away?"

## Building patterns

The researchers are now collaborating with the John E. Fogarty International Center, a branch of the US National Institutes of Health that specializes in overseas projects. Bjørnstad is using the centre's global influenza data to determine whether the model applies to flu as well.

Bjørnstad presented his work at the Ecological Society of America meeting in Portland, Oregon, last week. "It got an excellent response," says Pejman Rohani, an ecologist from the University of Georgia in Athens, Georgia, who saw the talk. "Everyone thought it was beautiful work."

Rohani says he expects to use the model in his own research, but added a caveat: "The method that they developed is based on data from the pre-vaccine era, so there are important technical issues if you are trying to do what they've done in the modern vaccine era."

At the same meeting, Bjørnstad's student, Laura Warlow, showed that the model also did well at predicting the timing of outbreaks of phocine distemper virus, which causes a measles-like illness in seals. Seals tend to congregate on the beach in piles called haul-outs. Big haul-outs, like big cities, attract more infection.

Warlow says one advantage of the model is that it isn't necessary to worry about why certain haul-outs are popular, or why people like to go to big cities. "You definitely do not need to know why," she says. "The disease doesn't care."

Ecologist, Georgia University

• ## References

1. Xiz Y., Bjørnstad O. & Grenfell B. Am. Nat., 164. 267 - 281 (2004). | Article | PubMed |

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