Is there still time to dampen the flames of the SARS epidemic to the point where it can burn itself out? That's the most pressing question in medicine today. A research team in London is trying to answer it by the end of this week.

The researchers, at the University of London's Imperial College, are building a mathematical model that shows how the mysterious, sometimes fatal infection spreads. In numbers and equations, they are expressing the behavior of both people and the coronavirus that appears to cause SARS, or severe acute respiratory syndrome. Their goal is to provide insights useful to public health authorities in several countries who are trying hard to keep the epidemic from going worldwide.

For nearly two weeks, Roy Anderson, an epidemiologist at Imperial College, and five other scientists have been analyzing data collected from Hong Kong and Canada, the places the outbreak has been best chronicled. While SARS appears to have originated in China's Guangdong province last fall, the information from that country is not complete enough to be useful.

This is not the first time Anderson and his colleagues have worked under the gun with incomplete data and lives and fortunes at stake. Two years ago, they modeled the foot-and-mouth disease outbreak in Britain, and provided much of the objective evidence that led Prime Minister Tony Blair's government to order widespread extermination of livestock -- about 11 million animals in all -- to halt the outbreak.

This task is harder. Human lives are at stake, a global pandemic may be in the balance, and the draconian steps taken in the foot-and-mouth outbreak are obviously out of the question.

"The objective of this study is to determine what is the most efficient route of control. There are a limited number of options," Anderson said. "One way or another, you have to get potential patients into isolation quicker."

Some epidemic models are used primarily to project the number of cases of disease a population can expect to see at some point. But the type of model Anderson and his colleagues are creating is meant instead to represent the present. It is supposed to have the same "working" parts as the real thing, except the ones in the model are easier to manipulate.

The SARS model will be crude, Anderson conceded, but he hopes it will be good enough to achieve a very specific goal. Researchers want to use it to discover the conditions in which newly infected SARS patients infect, on average, less than one person each.

That number -- new infections created per infected person -- is the most important concept in epidemic modeling. It is called the "basic reproductive number" of infection. When it is greater than one, a disease spreads indefinitely and involves ever-larger numbers of people. When it is less than one, the disease still spreads, but it attacks fewer and fewer people with each round of infection. At that rate, an infectious disease cannot sustain itself. Eventually it dies out.

The number is clearly greater than one in Hong Kong and Canada, where SARS is still spreading. Anderson and his team are trying to calculate it precisely by evaluating the three factors that work together to produce the basic reproductive number.

The first of those factors is the number of times an infected person comes in contact with an uninfected person while he or she is capable of passing on the illness. The second is the probability of transmitting the infection in each contact. The third is simply the length of time a person remains infectious.

In theory, any one of these factors (or any combination of them) can be altered to change the basic reproductive number. In practice, some factors are more easily changed than others.

For example, it is possible to change the third factor -- how long a person remains infectious -- by giving drugs that reduce the amount of microbe the ill person is carrying. This can work even in rapidly moving, airborne infections, such as influenza, which SARS resembles in some ways. But with SARS, there is no such drug.

Even without medicines, it is possible to alter the second factor -- the likelihood of transmitting the microbe with each contact. People sense this intuitively, which is why face masks are so popular with healthy Hong Kong residents these days. Other, less visible measures, such as repeated hand-washing, can also help.

But as a practical matter, the first factor -- the number of contacts -- is the most important.

Public health authorities can dramatically alter the number of contacts an infected person has per hour or day. Already, authorities are isolating SARS patients. Although they have not made it routine yet, they could also begin tracing, observing and quarantining everyone who has had contact with a SARS patient.

So far in the epidemic, most people are seeking hospital treatment three to seven days after their first symptoms appear. One of the key questions the Imperial College researchers are trying to answer -- by the end of this week, they hope -- is how much that delay would have to be shortened to limit contacts to the point that the outbreak would begin to burn itself out.

"If I imagine I can shift the average time from six days to one or two days, would that suffice? Only analysis can give you that sort of guidance," Anderson said.

Public health authorities could reduce this time by asking everyone with certain symptoms to go to the hospital immediately; those who report and appear to be potential SARS cases might then be asked to quarantine themselves until the illness "declares itself." At the involuntary -- and far more disruptive -- end of the spectrum is contact tracing and the forced quarantine of anyone who has had a specified contact with a SARS patient.

Even under ideal circumstances, controlling SARS will be difficult. Unlike with some viral infections, the period between infection and serious illness is quite variable -- between three and 12 days. In addition, there appear to be some people -- called "super-spreaders" -- who pass the infection to a much higher than average number of contacts. Both of these variables allow an outbreak to stay alive in one place even if it is receding overall.

What is clear is that SARS will have to be stamped out very soon if it is to be stamped out at all: It is on the verge of spreading too widely, and some experts think it is already past that point.

"It's pretty clear to me that SARS is not going to go away," said Ira M. Longini Jr., an epidemic modeler at the Rollins School of Public Health at Emory University. He thinks very soon it will join the legion of seasonal respiratory viruses -- influenza, rhinovirus, respiratory syncytial virus -- that flare up in the northern and southern hemispheres during their respective winters. Practically speaking, those infections are ineradicable.

If Longini is right, then the next role for epidemic modeling of SARS will involve decisions about the deployment of a vaccine -- when, and if, one becomes available.