Using Math to Help Predict Epidemics
(March 2008) Last summer, five mathematicians and one public health student converged on Rutgers University. Their mission: Develop an early-warning model that can “see” an epidemic before it claims many victims.
Center for Dynamic Data Analysis.(DyDAn), the lead on a DHS Center of Excellence that creates ways to see patterns and relationships hidden in massive amounts of data. “Our goal is to find evidence of an epidemic as early as possible, even before public health officials recognize it,” said Nina Fefferman, a research professor at the university’s Center for Discrete Mathematics and Theoretical Computer Science. Fefferman, an applied mathematician, served as her visitors’ research mentor and joint team leader.
The six researchers came from two historically black universities: Howard in Washington, D.C., and Morgan State in Baltimore. Each school sent a graduate student, an undergrad, and a faculty member. They were part of the DHS Summer Research Team Program for Minority Serving Institutions (MSIs), in which the department’s S&T Directorate fosters collaborative research between MSIs and the Centers of Excellence.
Epidemiologists study health reports and compare them to chart a disease’s course—the earlier, the better. But report data can seldom be compared “apples for apples.” For example, two neighboring counties may report an illness by ZIP code or by street, by week or by month. And to respect privacy laws, some of the most telling health data—such as a victim’s contact information, age, or race—may remain off-limits.
Therefore, epidemiologists often must interpolate, reading between the lines, even when they are eyeing an illness that has already claimed scores of victims. So imagine the challenge of charting an illness whose numbers seem to be growing in no discernible pattern. The earliest victims may fall ill sporadically—too sporadically to signal a pattern or raise an alarm. Are their illnesses the start of a mushrooming trend? Or are they just statistical “noise”—isolated accidents that foretell nothing?
Could the DyDAn researchers sort the noise from the signal? Using math, could they “see” a budding epidemic … before its death toll reached epidemic proportions?
Yes, they could—using a principle called information entropy, which is a measure of the uncertainty associated with a random variable. A single event that’s totally random—say, a coin toss or dice roll—has the greatest possible entropy. Its outcome is completely uncertain. But add weight to the coin or load the die, and the outcome is now less random, more predictable; it has less entropy.
The research teams exploited these properties to study disease. They first analyzed data that indicate the start of a possible disease spread (“Step one” in the diagram), selected just the right time-window for analysis (“Step two”), and grouped the disease’s daily incidence figures into just the right categories (“Step three”). In this way, they were able to tease out an unmistakable jump in entropy (or spike) early into the outbreak—earlier than disease watchers could have noticed using standard detection methods. Equally important, such a jump did not occur at any other time.
The researchers then tested how well their model “detected” actual historical outbreaks. They scored a bulls-eye, accurately detecting when each disease shifted from low, normal levels to become an epidemic, days in advance.
If DyDAn can maximize the model’s warning time, while retaining its accuracy, public health officials could intervene early, saving hundreds or even thousands of lives, Fefferman said. “We know what we want to accomplish, but we don’t know how long it will take,” she added. “But one thing is for sure: These students are up for the challenge.”