The Flu Equation
Mathematicians’ computer models on vaccine distribution, human behavior help decision-makers fight H1N1 flu
Sept. 21, 2009
The new H1N1 flu is spreading like a wildfire across the globe. It’s the first flu pandemic the world has seen since 1968, and many people are holding their breath. Whether or not swine flu will leave a massive amount of destruction in its wake or smolder along like a typical seasonal flu is a question that may only be answered two years (or two months) from now.
As the school year kicks into high gear and flu season begins in earnest in the northern hemisphere, the buzz is palpable. And big questions loom: how many vaccines for preventing H1N1 will be ready and when? With a limited number of vaccines available, who should be getting them? How should antivirals that treat flu, like Tamiflu and Relenza, be distributed? How will the transmission of flu change when people change their behavior?
The drive to find answers to these questions is keeping mathematical biologist Lauren Ancel Meyers very busy these days, and she is creating a variety of models to help answer them.
“What are the optimal choices that policy-makers can make to best save lives and prevent the spread of the swine flu?” says Meyers, an associate professor of integrative biology. “Our models can help answer those questions.”
Mathematicians aren’t normally credited with saving lives, but in this case, some of the recommendations that come from Meyers’ models could help do just that.
Take, for example, a recommendation for distributing antivirals that recently emerged from a model she ran this past summer. (Antivirals are generally taken to combat infection once a person already has the flu, but can also be given to healthy people as a preventative measure. This differs from vaccines, which are given solely to prevent infection.)
Between state and federal holdings in the U.S., there are about 80 million courses of antivirals available. The U.S. population hovers around 300 million, and federal decision-makers must decide how to distribute their stock to the states.
Should states with the highest numbers of H1N1 cases be the first recipients? Should the entire stockpile be released at one time? Or, should there be another pattern of distribution entirely?
The models incorporate things like patterns of contact between people and various rates at which the antivirals actually reach people who truly have H1N1 (and not just the seasonal flu).
Meyers found there are many exceptionally complex ways the government could distribute its antiviral stockpile to reduce H1N1′s spread, but there is also a very simple release schedule that would be equally effective: the feds can release five million courses of antivirals each month over the next 10 to 12 months, distributed to each state proportional to that state’s population size.
“This simple and equitable plan should work as well as more complex delivery schedules,” says Meyers, who’s delivered her results to officials at the U.S. Centers for Disease Control and Prevention (CDC), BARDA (the authority at the U.S. Department of Health & Human Services responsible for distributing vaccines) and others.
She also says the power of antivirals in stopping the spread of the pandemic should not be overlooked.
“Antivirals can decrease the transmission of the H1N1 flu if a large fraction of people with H1N1 take them shortly after developing symptoms,” she says. “Public health officials are focusing on vaccines, which are critical to controlling this pandemic, but we really should be thinking about what we can do over the next six to eight weeks before any vaccines are available.”
Meyers is referring to the fact that the H1N1 vaccines are not expected to become available until late October of this year, at the earliest, and the number of vaccines available at that time will not be nearly enough to vaccinate all 300 million U.S. citizens. It’s still not clear yet, for example, how many vaccines will be distributed to this university’s University Health Services.
On that front, another part of Meyers’ modeling work focuses on determining which target groups should get the limited number of vaccines and when.
“When you have limited resources, competing interests and complexities in the system, distributing vaccines to the right people is going to be critical for reducing the number of H1N1 infections and deaths,” she says.
Meyers and her former graduate student Shweta Bansal (now a postdoctoral researcher at Penn State University) recently created models that showed that during the first year of a pandemic, the largest outbreak of flu will be in children.
“Children have very high contact patterns in the fall because of school,” says Meyers.
Adults are hit harder than children in the second season, the model shows, because the large number of kids infected during the first season have immunity to the circulating flu strain.
Bansal and Meyers compared the results of their model with data from the three major flu pandemics in the 20th century. Those pandemics show the same pattern as the model, proving its relevance. Kids get hit the first season, while more adults are infected the second.
Notably, the model also predicts there can be a transition period toward the end of the first flu season when fewer kids are becoming infected and adult infection rates are gaining steam.
These results point toward strategies for distributing vaccines. During the first season, the model suggests targeting children is best, with a transition to adults toward the end of the season.
“The second season, vaccinating kids may not be as important in limiting the spread of flu as targeting adults,” says Meyers. “But of course, protecting the high-risk groups should always be the highest priority. Flu vaccines should be given directly to those most likely to experience serious complications and then to those most likely to spread the disease.”
The Human Element
The way people react to the pandemic–their perceptions and their behaviors–also greatly contributes to how and when the disease spreads.
With a $3 million grant from the National Institutes of Health’s Models of Infectious Disease Agent Study (MIDAS) program, Meyers, mathematician Paul Damien from the McCombs School of Business and Allison Galvani from Yale University are studying this complex interplay between human behavior and the spread of disease.
Within 48 hours of learning that a new swine flu was infecting people in Mexico this past April, they effectively started their MIDAS research by posting an in-depth survey to look at how people across the nation were reacting to the pandemic. By then, it was kicking into full gear.
“People have a lot of misperceptions,” Meyers says. “For example, they tend to overestimate the risk of becoming infected by flu. They tend to underestimate the efficacies of vaccines. And it depends on age group. These misperceptions can lead people to behaving in a way that’s suboptimal for themselves and for society as a whole.”
Some of the first results from the survey have come in, and the scientists have already shared them with other MIDAS teams and their colleagues at the CDC.
It turns out that, during the first weeks of the H1N1 pandemic, women were more likely to take precautions against the flu-such as following news about H1N1 and limiting social interactions-than men. People from larger households (for example, with larger families) were also more likely to take precautions than people from smaller households. And strangely, as news about the swine flu pandemic began to taper off in the media early this past summer, people didn’t stop worrying, but they did start becoming less and less interested in the idea of seeing a doctor or getting the vaccine.
These results can help policy-makers target certain groups in an effort to change their behaviors in ways that limit disease transmission.
A second survey now under way will be used to model what’s going on in four U.S. cities: Washington, D.C. and Los Angeles (which had low rates of H1N1 infection during the early stages of the pandemic) and New York City and Milwaukee (which had high rates of infection). The researchers want to determine how people are behaving differently in these cities and aim to link that with disease transmission patterns.
Meyers and Damien are also looking at school closures, which are not taken lightly by policy-makers. They are costly and disruptive, and depending on the context, they might not do much to limit transmission or save lives.
“It’s challenging to assess when and where to close schools,” says Damien. “Based on what metric? Percent infected? Percent likely to be infected? Only by using mathematical methods can we best quantify these uncertainties.”
In the end, Meyers says, “Collectively, individual decisions can have a huge impact on the fate of a pandemic and the success of intervention efforts.”
The antiviral distribution modeling was done in collaboration with engineering postdoctoral researcher Ned Dimitrov, physics graduate student Sebastian Goll and public health officials from the U.S. CDC and the British Columbia CDC in Canada.
For more information, contact: Lee Clippard, Lady Bird Johnson Wildflower Center, 512-232-0104;
On the banner: A worker produces A/H1N1 flu vaccines at the domestic pharmaceutical company
Sinovac Biotech Ltd., Sept. 3, 2009, in Beijing, China. Photo: China Photos/Getty Images.