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What do relapses of alcohol or drug addictions have in common with forest infestations by the mountain pine beetle? Turns out, they are similarly cyclical events that can be predicted mathematically.

At least that is the finding of a Winona State applied mathematics researcher, Jacob Duncan. After studying and measuring the cycle of rapid forest destruction, slow growth, and then destruction again that can occur because of insects, Duncan said it revealed striking similarities to the relapse cycles that occur for many people with addictions.

“The more I thought about it, the more I saw a similarity between periodic insect outbreaks and forest recovery, and the periodic relapses and recoveries of drug addicts,” he said. “Insects can wipe out acres of trees and it takes many years for the forest to recover. Similarly, after a relapse, it takes time for the neurotransmitters in an addict’s brain to get back to normal levels.”

In a paper in the SIAM Journal on Applied Dynamical Systems, Duncan explored whether he could use similar mathematical formulas to predict relapses based on the moods and cravings of people with addiction disorders. Colleagues with expertise in neuroscience from St. Mary’s College in Notre Dame, Ind., assisted by providing some of the underlying assumptions for the mathematical model regarding the cycle of relapse addiction.

The “fast-slow dynamical” model accounted for the rapid rise and fall in mood for people who relapse, and the much more gradual development of cravings after they receive treatment and abstain from the activities or substances that fuel their addictions.

“We’re applying mathematics to solve the problem of addiction in a way that hasn’t been attempted before,” Duncan said. “If we can accurately tell an addict that they generally relapse every 5.5 days, for example, we’ve greatly increased their odds of breaking the cycle and maintaining abstention.”

Duncan said the idea partly came from personal experience with alcohol addiction, and addictions he has seen in others close to him. The next step is to test the theoretical model with historical clinical data of patients who have experienced the relapse cycle.

Duncan said he hopes the results will provide addiction specialists “another tool in their toolbox” to keep patients safe and healthy. The model is limited, he said, in that it plots an individual’s “natural relapse cycle” but doesn’t account for the numerous environmental and unpredictable factors that can affect it. Whether a person walks by a liquor store at a time of peak cravings could alter the risk.

Jeremy Olson • 612-673-7744 • Twitter: @stribjo