A Data-Driven Mathematical Model of the Heroin and Fentanyl Epidemic in Tennessee.

Opioid addiction represents a major national health issue spanning decades. In recent years, prescription opioid use disorder has increasingly led to heroin and fentanyl use, with subsequent increases in mortality rates due to overdose. In this paper, we present a mechanistic, epidemic model for prescription opioid addiction and illicit heroin or fentanyl addiction which aims to better understand and predict the dynamics between these two stages of opioid use disorder. Our model aims to be both parsimonious and robust: as a system of five differential equations it is appropriate for use in theory advancement and yet it remains powerful enough to capture state-level data from Tennessee for the period 2013-2018. A key finding from our data-driven analysis is that, in the face of changing policy around prescription opioids, heroin and fentanyl are now the driving force behind the Tennessee opioid epidemic. Model projections suggest that both addictions and overdoses related to heroin and fentanyl will continue to increase in the next few years (2020-2022), even as addiction to prescription drugs continues to fall. Finally, management strategy analysis suggests that in the changing face of the epidemic, the most successful approach will target availability of treatment with subsequent monitoring of stably recovered individuals to see that they do not relapse, coincident with direct efforts to decrease opioid overdose fatalities (e.g., further availability of Naloxone).