Document Type

Honors Thesis

Major

Mathematics

Advisor(s)

Peter Stechlinski

Committee Members

François G. Amar, David Hiebeler, Andre Khalil, Deborah Saber

Graduation Year

August 2020

Publication Date

Summer 8-2020

Abstract

For the past two decades the United States has been embroiled in a prescription drug epidemic that has since grown in magnitude and complexity. The ripples of this epidemic have been especially apparent in the state of Maine, which has fought hard to mitigate the damage caused by addiction to pharmaceutical and illicit opioids. Us- ing data from state and federal sources, we construct a mathematical model capturing the dynamics of the opioid epidemic in the state of Maine, specifically as it pertains to pharmaceutical opioids and heroin. Parameter fitting is performed followed by an uncertainty analysis to quantify potential error in parameter estimates. The model is analyzed to determine effective ways of controlling opioid abuse prevalence (both in the form of heroin and pharmaceutical opioid use) at different points in time, and stochastic simulations are run to test the effect of various control strategies on the number of opioid abusers in the system. These results are then presented with the hope of helping to inform public policy as to the most effective means of intervention.

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