# New Jersey High Schoolers Earn Top Honors for Mathematical Model of Substance Abuse

The use and subsequent abuse of substances like tobacco, alcohol, and narcotics are on the rise among teenagers in the United States. Electronic cigarettes and vaping—inhalation of an aerosol produced by vaporization of liquid chemicals like nicotine, a highly-addictive substance derived from tobacco—are popular with high school students, so much so that the U.S. Surgeon General declared e-cigarette use an epidemic among America’s youth in late 2018. Opioid addiction is also remarkably prevalent in the U.S., with increasingly more individuals abusing both prescription and non-prescription drugs. A 2019 report from the National Safety Council indicates that Americans are now more likely to die of accidental opioid overdose than in a motor vehicle accident.

Substance abuse affects the physical and mental health of users and can interfere with brain development in adolescents. The numerous, wide-ranging consequences of addictive behavior extend well beyond individual users to society as a whole. Besides the evident health-related repercussions, such behavior negatively impacts finances, school and workplace performance, and social and familial relationships. Regulatory efforts at the local, state, and national levels attempt to control and restrict access to and consumption of addictive substances. In order to truly find success, such efforts must be rooted in a deep understanding of the ways in which substance abuse spreads among vulnerable populations.

The complicated dynamics of substance abuse made it a particularly relevant topic for this year’s MathWorks Math Modeling (M3) Challenge, a high school mathematics contest sponsored by MathWorks and organized by SIAM. The competition, which awards a total of $100,500 in scholarship funds, invites U.S. teams of high school juniors and seniors to tackle a multifaceted, real-world problem with mathematical modeling and report their results in only 14 hours. After two rigorous rounds of online and in-person judging by nearly 150 professional applied mathematicians, the top six teams traveled to New York City to present their solution papers in front of one last panel of judges and compete for the grand prize of$20,000. This final event was hosted in late April by Jane Street, a New York-based quantitative trading firm.

The three-part Challenge problem asked students to create a mathematical model that predicts the spread of vaping in coming years; calculate the likelihood that certain individuals among a class of 300 high school seniors will use nicotine, marijuana, alcohol, and unprescribed opioids; and analyze the broader impacts of substance abuse. “This is a problem that can be approached from a variety of different ways, depending on the students’ comfort zone with mathematics but also because of their own experiences,” said judge Kathleen Kavanagh (Clarkson University), who co-wrote the 2019 problem with Karen Bliss (Virginia Military Institute) and Ben Galluzzo (Clarkson University). “I really feel like each student is going to have some sort of exposure to issues that are centered on addiction, and they can bring that into their solution. I think it’s something to which they can automatically relate.”

This year’s first-place team, from High Technology High School in Lincroft, NJ, likened the spread of conventional cigarette and e-cigarette use to that of an infectious disease during an epidemic. “In order to use a drug you have to know someone who uses it, or have watched someone online who’s used it, like in advertisements,” Eric Chai of High Technology said. “That’s kind of similar to how infections must be contracted from a person.” Chai and his teammates thus derived their initial model from a SIRS (susceptible-infected-recovered-susceptible) compartmental model and adapted it to acknowledge that a relapsing individual would re-enter the “infected” rather than “susceptible” category. Using their model, they solved a system of differential equations to analyze both cigarette and e-cigarette use in the coming decade. The students concluded that 26.63 percent of Americans will vape in 2029, while only 6.45 percent will smoke cigarettes.

When simulating the likelihood that a given individual will use nicotine, marijuana, alcohol, or unprescribed opioids, the New Jersey team utilized a binary multivariate logistic model to ensure inclusion of a variety of influencing factors and social attributes collected from the 2005-2006 Health Behavior in School-Aged Children survey. Their model assessed the effects of the following factors on substance abuse: age, gender, ethnicity, income, overall health, relationships with friends and parents, opinions on school, weapon possession, and experience with bullying. “We basically trained the logistic equation so that given new data, we could predict the output of probability that someone would use a substance,” team member Gustav Hansen said. The team then coded and employed a Monte Carlo simulation that generated 300 high school seniors with varying attributes. They found that 46.3 percent of those students would use nicotine, 17.3 would use marijuana, 66.0 percent would use alcohol, and 0.0 percent would use opiates.

Finally, the High Technology team developed a robust metric to rank the impact of the four aforementioned substances. They split the effects of these drugs into four categories: physical harm, social harm, dependence, and economic harm. The students measured the first three factors on a scale of 0 to 3 based on psychiatric survey results, and defined economic harm as the loss of gross domestic product from the decrease in life expectancy caused by substance abuse. “We also provided harm values on an individual and societal level,” Chai said. “Since certain drugs have a much lower population of use, we thought it would make sense to give both numbers, depending on how harmful the drugs are to one person or to the U.S. as a whole.” On an individual level, the ranking from most to least harmful was opioids, alcohol, cigarettes, and marijuana. But in terms of societal impact, the ranking switched to alcohol, cigarettes, marijuana, and opioids. In this case, alcohol was the most harmful despite the often-fatal effects of opioids because the latter has a much smaller population of users.

Chai and Hansen—along with teammates Emily Jiang, Kyle Lui, and Jason Yan—will split $20,000 in scholarship funds for their first-place finish. The group also received the third-place M3 Challenge Technical Computing Scholarship Award, which yields an additional$1,000. Instituted in 2018 under the MathWorks title sponsorship, this prize is awarded for “outstanding use of programming to analyze, design, and conceive a solution for the problem” and allocates a total of \$6,000 to three high-performing teams.

Seniors Chai and Lui are no strangers to the M3 Challenge; they also competed in last year’s competition as juniors and made it to the final round. As they prepare for college, Chai reflected on his potential career trajectory. “Before participating in this challenge, I was always interested in math and computer science,” he said. “But now I’m less interested in the purely theoretical stuff and more into data science, big data, analyzing trends and marketing, and things like that. I like how it has a real-world impact, and you can see the actual application in what you’re doing.”

In addition to presenting their solution papers in New York, all six finalist teams had the opportunity to hear from and converse with M3 Challenge alumnus Chris Musco, a current research instructor of computer science at Princeton University who will soon join the faculty of New York University’s Tandon School of Engineering. Musco was a member of the 2008 finalist team from the Wheeler School in Providence, RI. Following his team’s success, he studied applied mathematics and computer science at Yale University before earning his Ph.D. in computer science from the Massachusetts Institute of Technology.

Musco also served as a judge during the triage round of judging, reviewed an early draft of the problem statement, and was eager to encourage students and give back to the competition that first piqued his interest in applied mathematics. “I learned through the M3 Challenge that it’s actually possible to not just use math as a tool, but to spend a career building new mathematical tools to apply in all sorts of different fields,” he said. “This competition was a jumping-off point for me. At the time it really opened my mind to the fact that there’s a potential for careers where I can keep doing math, possibly for the rest of my life.”

High Technology High School’s winning paper is available online.

 Lina Sorg is the associate editor of SIAM News.