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Fighting Epidemics With Math

Researchers tame the complicated social dynamics of infection by re-thinking reality.
(Photo: Maridav/Shutterstock)

(Photo: Maridav/Shutterstock)

Understanding how a disease spreads is a tough business. The biology of infection aside, it's difficult to sort out how diseases transmit through social groups. Typically, epidemiologists deploy simplifying assumptions—say, assuming friendship networks don't change with time—to deal with complex disease dynamics. But doing so moves their models, and potentially their ability to predict and track epidemics, a little further from reality. Now, researchers have found a clever way to sidestep invalid assumptions: Rather than repair the assumptions to match reality, re-frame the problem so that those assumptions are correct.

Understanding when a disease will become an epidemic "is of the utmost importance," a research team led by Eugenio Valdano at the Pierre Louis Institute of Epidemiology and Public Health writes in Physical Review X. But the truth is, modeling real-word disease dynamics is hard, so it's common to make simplifying assumptions, such as assuming social networks don't change. That's silly; akin to assuming we're in constant physical contact with everyone we know. Nevertheless, researchers struggle to take the dynamic nature of social networks into account when analyzing how illnesses spread.

Rather than think of an individual's health on one day depending on her health yesterday, think of yesterday's self as a separate person.

Fortunately, Valdano and colleagues seem to have figured out way to deal with constantly changing social networks. The researchers observed that the probability a person is sick on a given day depends on who was sick the previous day. If that person came in contact with a sick person yesterday or she herself was sick yesterday, her probability of being sick today goes up. That observation sets up a crucial step: Rather than think of an individual's health on one day depending on her health yesterday, think of yesterday's self as a separate person.

Here's an example: Matt and Monica meet for lunch on Monday. In the old perspective, Matt's health on Tuesday depends on whether either he or Monica was sick on Monday. According to the new outlook, there's someone named Tuesday-Matt, and how likely he is to be sick depends on whether Monday-Matt or Monday-Monica were sick. In other words, the question is whether Monday-Matt or Tuesday-Matt is sick; not whether Matt became sick. By re-framing the problem that way, time becomes part of the social network, rather than a separate complicating variable, so that researchers can compute epidemic thresholds using existing techniques for fixed, unchanging networks.

It sounds goofy, but the trick works. The team's calculations matched the results of computer simulations of epidemics on three real social networks—high school students' contacts with each other over a day, scientists' interactions at a conference, and meetings between prostitutes and their clients over a year.

Though the results are entirely theoretical—they were tested against computer simulations of disease spread, not real-world epidemiological data—they provide a set of tools to determine, for example, the likelihood of epidemics and the optimal window for collecting data on disease outbreaks. That should make them of "both fundamental and practical interest" to researchers and health officials hoping to head off the next epidemic, the researchers argue.

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