The mathematics of flu

Different cities have different influenza seasons, statistics show. Richard A Lovett reports.

Police in Mexico City during a flu epidemic in 2009. Climate and transport can both influence the spread of the virus.
Police in Mexico City during a flu epidemic in 2009. Climate and transport can both influence the spread of the virus.
LUIS ACOSTA / AFP / Getty Images

As Australia braces for what is expected to be an unusually bad flu season, an American researcher has discovered that the pattern of influenza outbreaks differs markedly from city to city.

Part of that difference is due to variations in climate, Benjamin Dalziel, a biologist at Oregon State University, Corvallis, said recently at a meeting of the Society for Industrial and Applied Mathematics (SIAM), in Portland, Oregon, US.

Low total humidity during the winter promotes transmission because the dry air makes for smaller water droplets when we cough.

Smaller droplets can travel farther, increasing what Dalziel calls the “cloud of risk” around an infected person. Humidity also affects the time the virus can survive in the environment, after someone coughs it out.

But in a study of weekly influenza rates in 603 US cities, Dalziel found that even among those in similar climates, flu season can vary sharply. In some, it tends to be spread out over much of the winter. In others, it starts slowly then peaks fast and hard; then, just as quickly, it’s over.

“Year after year, some cities have intense epidemics and others are spread out,” he says. “There’s something at the city level that’s generating differences.”

Surprisingly, larger cities have less-intense epidemics.

Dalziel believes the reason lies in the way people move around in settlements of different sizes.

“As cities get bigger, the movement patterns of their inhabitants get more organised,” he says.

Transportation networks, combined with other factors that increase urban density, crowd people together, increasing the risk of catching the flu early in the season, even though the humidity has not yet dropped to the levels that most strongly encourage transmission.

After all, if someone coughs directly in your face or spreads flu virus in any other tight-packed environment, you’re going to be exposed, regardless of whether weather conditions are conducive to long-distance droplet spread.

If people get the flu early in the season, they won’t get it later on. That means that when the climate-driven peak season arrives, it is likely to be shallower and broader, rather than a steep short-lived spike.

Dalziel is careful to point out that his work is a statistical analysis, with no specific policy recommendations.

“How that’s used will be up to public health,” he says. And, he adds, it isn’t a reason to flee one city for another. Within any climate zone, residents of both types of cities probably have the same overall risk of getting the flu, he says. It’s just the timing that’s different.

That variation, however, might be useful information for health officials trying to figure out how to prepare for flu season. The needs for a short, intense season, in which, Dalziel says, “we have everyone showing up in the emergency room within the same two weeks,” are different from those for a longer but less intense one.

Also, since climate and urbanisation interact to affect flu season, the fact that both are expected to change in coming decades could provide useful information to public health planners.

Influenza isn’t the only disease with a spread that can be addressed with advanced mathematics. In another presentation at the SIAM meeting, Kyle Gustafson of the US Navy used a combination of genomics and statistics to study the spread of the Ebola virus in Sierra Leone during the 2013 to 2016 West African Ebola outbreak.

During the epidemic, he says, about 1000 virus genomes were sequenced, allowing epidemiologists to link cases via similarities and differences in their particular virus strains.

Based on this and the location in which each case showed up, he explains, it is possible to track how the virus moved as people either conducted their normal business or fled for safety, inadvertently carrying it with them.

The goal, Gustafson says, is to create a modelling framework that can be used by public health officials in future outbreaks, not only of Ebola, but of other diseases, allowing them to understand how and where they might spread.

Similar statistical modelling can also be used in the fight to eradicate polio, which now exists in only three counties: Pakistan, Afghanistan, and Nigeria — and even there only at an extremely low rate.

“This year in Pakistan there’s just been three cases,” says Laina Mercer, a statistician at the Institute for Disease Modeling, Bellevue, Washington.

But resources are limited, and to get rid of the disease entirely, she says, it’s necessary to use statistical models to help government officials determine where immunisations are most needed.

At the moment, she notes, 200,000 Pakistanis are involved, at least part-time, in the effort to stomp out the last traces of a disease that only 30 years ago struck 350,000 people per year, worldwide.

“It’s expensive,” she says. “As soon as we eradicate it, we can spend the money on something else.”

Mathematical approaches can also be used in the fight against AIDS, says Florencia Tettamanti Boshier, an applied mathematician from Fred Hutchinson Cancer Research Center, Seattle, Washington. In this case, however, the goal is to look at the cells of a single human’s body, rather than at millions of people in distant parts of the world.

One of the great breakthroughs in the treatment of AIDS is the development of antiretroviral therapy (ART) treatments that can stop the virus from proliferating. But these treatments do not eliminate the virus and thus cure the disease, Boshier says. Instead, if treatment is stopped or interrupted, the virus will rebound.

What this means is that it continues to hide out in infected immune cells known as T-cells.

T-cells have finite lives, but they can replicate. In the process, they also replicate the virus, if it is hiding in their genome.

There are two ways in which the cells reproduce, Boshier says. One is normal replication, designed to keep their numbers from dropping and opening the body to infections. The other is when they are called into action to fight a disease, in which case they multiply rapidly.

By tabulating small variations in the HIV genome of infected T-cells in any given patient, Boshier says, it may be possible to figure out which of these mechanisms is causing the virus to persist in the descendants of long-ago infected cells.

And that, she says, could lead to HIV treatments that might truly provide cures.

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Richard A. Lovett is a Portland, Oregon-based science writer and science fiction author. He is a frequent contributor to COSMOS.
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