Cole Butler— 2019-20 Public Affairs Scholar – Using Mathematics to Understand Maine’s Opioid Epidemic (A mid-year progress report)

Cole Butler, a mathematics major at the University of Maine, is working alongside Margaret Chase Smith Policy Center Faculty Fellow Dr. Peter Stechlinski to develop a mathematical model for understanding the opioid crisis in the state of Maine. Butler, who received a Margaret Chase Smith Public Affairs scholarship from the Center, contends that the opioid epidemic is a dynamical system and thus it can be analyzed using mathematical tools to formulate and identify an optimized response, as well as a better understanding of the consequences of policy-makers’ actions in addressing this pressing problem. Building on his work creating dynamic models and simulations for infectious diseases—most notably control strategies for MRSA through patient screening policies—he plans to use mathematics to compare various strategies and methods of control for the opioid epidemic in an attempt to mitigate this crisis over the course of the next few decades.

Alongside his mid-year progress report, Butler added that “Opioid abuse has affected many communities in Maine and remains a very personal issue for me. The MCS Public Affairs scholarship has allowed me to study the epidemic from a mathematical perspective, so that through a qualitative analysis we may better understand its dynamics and work to mitigate its effects from a policy standpoint. Analyzing the opioid epidemic has been challenging, as social/behavioral contagions are difficult to quantify, but the resources and financial support of the MCS Policy Center have certainly made things easier.”

The following figure is a schematic of the mathematical model that Butler is using in his research. Here, the population is classified according to prescription status (Rx or No Rx) and their status of abuse (abusers or nonabusers). Each compartment is disjointed from the remaining compartments, and the dynamics of the opioid epidemic are captured by “movement” between compartments. Butler plans to use a system of nonlinear differential equations to quantify interactions between each compartment and hopefully be able to model the epidemic with an adequate level of accuracy.