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Model for tracking flu progression could reduce flu pandemic's peril

Engineer who survived pandemic of 1968 focuses on reducing influenza's death toll.
Richard Larson
Richard Larson
Photo / Donna Coveney

Nearly 40 years ago, MIT Professor Richard Larson spent a week sick in bed with the worst illness he'd ever had--the particularly virulent strain of flu that swept the globe in 1968. "That was the sickest I'd ever been," Larson recalled. "I really thought that was the end." It took him two or three months to recover fully from the illness.

Known as the Hong Kong flu, the virus killed 750,000 people worldwide, the second worst influenza pandemic the world has seen since the infamous 1918-1919 epidemic of so-called Spanish flu.

Now, many experts fear the world is on the brink of another deadly flu pandemic. And Larson wants to be sure that people are ready to deal with it.

To that end, he and his colleagues have developed a mathematical model to track the progression of a flu outbreak, and their results show that the death toll of an epidemic could be greatly reduced by taking steps such as minimizing social contacts and practicing good hygiene, such as frequent handwashing.

The report, "Simple Models of Influenza Progression within a Heterogeneous Population," will be published in the May-June issue of Operations Research, which comes out June 4.

"We can't reduce to zero the chance that any of us will get the next bad flu. But there is compelling evidence that we can reduce the chances of our loved ones and ourselves getting the flu by a significant factor," said Larson, the Mitsui Professor of Engineering Systems and of civil and environmental engineering.

The H5N1 strain of flu, also known as avian flu, has infected birds throughout Asia and Europe, with a few known cases among humans. So far, the disease has not mutated to a form where it can jump easily between humans, but if that happens, the disease could spread around the world in days or weeks.

Larson's research team decided to model the progress of such an epidemic, taking a unique approach. Unlike most existing models, theirs takes into account people's different levels of social activity and susceptibility to the flu.

One of the report's key findings is that "social distancing"--reducing the frequency and intensity of person-to-person contact--could be an effective way to limit the spread of the disease.

Influenza is normally spread by person-to-person contact, so people who have more contact with others have a higher risk of catching the disease and then spreading it. However, most existing influenza models assume that all individuals within a population have the same degree of social contact. They also assume that social behavior does not change over the course of the epidemic.

Such models "didn't do justice to the complexity of the problem," Larson says.

He and his team developed a dynamic mathematical model that assumes a heterogeneous population with different levels of flu susceptibility and social contact. They then used the model to compare different scenarios: one where people maintained their social interactions as the flu spread, and others where they did not.

Their results showed that reducing the social contacts of people who normally have the most interactions could dramatically slow early growth of the disease. Most of the disease spread is due to a minority of the population--the people with the most daily human contacts. Focusing on these individuals and reducing their daily contacts can change an exponentially exploding disease into one that dies out over time.

A key feature of the model deals with "R0," a popular parameter of most other models, which is defined as the average number of new infections caused by a recently infected person in a population of susceptible individuals. An R0 greater than 1.0 leads to exponential increase in the number of cases.

However, because R0 is an average over the entire population, it does not reflect the fact that only a fraction of the population is responsible for the majority of new infections. Averages can be misleading--for example, when a billionaire enters any establishment, on average everyone there instantly becomes at least a millionaire.

The researchers believe that splitting R0 into components, one for each level of activity or propensity to become infected, provides better policy guidance. In Larson's model, every population component is assigned different values for R0 , depending on factors such as that component's frequency of human contact and susceptibility to infection if exposed to the flu. Each of these factors can be at least partially controlled, suggesting that our individual and collective behaviors in response to the flu can greatly influence the numbers who become infected.

The researchers also found a striking difference in death toll depending on how early in the epidemic social distancing measures went into effect. For example, in a hypothetical population of 100,000 susceptible individuals, 12,000 fewer people were infected if social distancing steps were taken on day 30 of an outbreak instead of day 33. But intervention on Day 0 is best.

This finding is consistent with historical research reported in April by two research teams, one led by the National Institute of Allergy and Infectious Diseases and one from the United Kingdom, that demonstrated that those communities in 1918 that took aggressive social distancing actions early usually suffered less from the "Spanish Flu" than those who waited and debated.

The findings strongly suggest that influenza emergency plans should include measures to reduce social contact, such as encouraging people to work from home and avoid large gatherings, Larson said. This is especially important because it generally takes at least six months from the time of an outbreak to develop an effective vaccine. Those who must continue to work, such as doctors and other health care workers, should be the first to receive any available avian flu vaccine that might be developed, he said.

Larson says that large institutions like MIT, as well as state and local governments, should have emergency plans ready to put into action as soon as the first case of human-to-human H5N1 influenza is reported.

"We need to be aggressive. We need to be assertive. Don't dilly-dally, don't have a lot of political debate and foot-dragging," he said. "If people do take it seriously, the number of deaths could be greatly reduced. A key is to start taking aggressive steps well before the flu is at your doorstep."

Larson became interested in modeling influenza after reading a book about the 1918 outbreak, which killed between 50 and 100 million people around the world. He had never heard much about the epidemic, which in the United States claimed more victims than World War I.

"Reading the history of it, I became fascinated," he said. "The wonderful thing about being in OR (operations research) is you can go into any problem you think is important and relevant and really contribute to it."

Larson said he hopes that other operations researchers will take up influenza research and develop more detailed models.

"Any mathematical model of the disease is bound to be incorrect," Larson wrote in the Operations Research paper. "But we are not seeking multidecimal accuracy, but rather insights on how to limit the spread of the disease. We firmly believe that fresh eyes from the OR community can play a significant role in this quest."

Other members of the MIT research team include undergraduate Kelley Bailey; Stan Finkelstein, senior research scientist in the Engineering Systems Division; Karima Robert Nigmatulina, graduate student in the Operations Research Center; Robert Rubin, faculty member at the Harvard-MIT Division of Health Sciences and Technology; and Katsunobu Sasanuma, a graduate student in the Engineering Systems Division and the Operations Research Center.

The research was funded in part by an IBM Faculty Research Award.

A version of this article appeared in MIT Tech Talk on June 6, 2007 (download PDF).

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