Gravity model applicable to disease spread

Aug 9 2004

Tracking the spread of new or re-emergent diseases such as SARS or smallpox is essential in controlling disease epidemics, but horse-and-buggy concepts of how diseases spread have been supplanted by 21st-century realities.

"In the past, one expected the spread of disease to be based on distance, and the closest town would be the location of the next outbreak," said Ottar Bjornstad, assistant professor of entomology and biology. "Today, it is very different. Even excluding air transportation, someone like me is more likely to go to New York City than Lewistown, Pa., even though Lewistown is closer to where I live."

Borrowing from physics and transportation theory, the researchers are using an empirical gravity model along with the distance-based models to define a network of spatial spread of contagious disease.

"We are combining the basic theory of epidemiology with models from sociology and transportation theory to see what networks might look like," Bjornstad told attendees on Aug. 5 at the annual meeting of the Ecological Society of America. Bjornstad is working with Bryan T. Grenfell and Xia Yingcun, University of Cambridge, U.K.

Cities are like planets -- the larger they are, the more attractive they are, but the degree of attraction decreases with distance. From Central Pennsylvania, New York City or Philadelphia would be more an attractive destination than Chicago.

To test their model, the researchers used British data on the childhood disease measles because British records dating from 1940 to today are relatively complete. The records show, week-by-week and community-by-community, the spread of measles outbreaks. The U.K. has about 1,000 cities and 450 rural areas that report and outbreaks occur about every two years.

Measles belongs to an ecological class of disease that includes the traditional childhood illnesses – mumps, rubella, chickenpox, whooping cough – that are extremely contagious, but short-lived in the air. Smallpox, before eradication, was considered one of these diseases as well. To a smaller extent, influenza also is included in this category, although because influenza mutates so rapidly, each year brings a slightly different virus to infect even those who have contracted previous strains.

"We now have a class of models that bears great promise in capturing the transmission of known childhood infections," said Bjornstad. "We have just started work to see if the models are relevant to diseases of wildlife."

Laura M. Warlow, Penn State graduate student in biology, is working with Bjornstad on a wildlife model. Investigating the spread of distemper in harbor seals, Warlow looked first at a distance model and then at the gravity model. Unlike humans, harbor seals are not attracted to big city bright lights, but they are more attracted to large beaches close to food than to smaller beaches.

"The seals form clumps on beaches called haul-outs," Warlow said during her poster session at the Ecological Society of America meeting. "The clump size is related to the size of the beach and the closeness to food."

Harbor seals, like children, spread the disease by coughing on each other. Two recent outbreaks in 1988 and 2002 have decimated the population in the North Sea. Working with St. Andrews University, Warlow uses geographic positioning system tag data, aerial photos and actual counts of seals to study the 1988 outbreak.

"We looked at the 1988 data with the simple distance model first," said Warlow. "Then we used the gravity model. The gravity model more accurately predicted the spread of phocine distemper."

After modeling a children’s disease and an animal disease, the researchers now are looking at how adult diseases spread.

"Transmission of measles depends on the movement of children," said Bjornstad. "We need to think about applying the models to adult populations and to populations that have partial immunity."

The researchers are working with the National Institutes of Health John E. Fogerty International Center for Advanced Study in the Health Sciences. Influenza is one adult disease the group is studying but is a difficult one. Influenza, at least in the U.S., is not a disease that must be reported so data is spotty. The virus also mutates from year to year.