Date of Award
2024
Document Type
Thesis
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
Dr. Joanna Wares
Second Advisor
Dr. Saif Mehkari
Abstract
The opioid epidemic is prevalent in countless communities throughout the United States and has yet to be mitigated. Treatments for OUD (opioid use disorder) include Medication-Assisted Treatment (MAT) and treatment without medication (non-MAT), with the former being judged as more effective in terms of lower relapse rates, death rates, and criminal activity (U.S. Food & Drug Administration, 2023; SAMHSA, 2024). Motivated by the promising research on MAT, this paper models the relationship
between the treatment and addicted populations using a system of ordinary differential equations. In addition to producing closed-form equilibrium solutions, the model leads to the conclusion that expanding access to MAT, while important for decreasing the addicted population, is not a sufficient policy measure in isolation. Instead, policymakers should endeavor to increase access to all forms of treatment. Furthermore, varying the rate of addiction to prescription opioids causes significantly different equilibrium populations, indicating that the prescription of opioids requires further monitoring.
Recommended Citation
Akram, Maniha Zehra, "Modeling the Opioid Crisis in Virginia: A Differential Equations Model Assessing the Impact of Medication-Assisted Treatment on the Addicted Population" (2024). Honors Theses. 1751.
https://scholarship.richmond.edu/honors-theses/1751