Modeling the opioid epidemic

Opioid addiction has become a global epidemic and a national health crisis in recent years, with the number of opioid overdose fatalities steadily increasing since the 1990s. In contrast to the dynamics of a typical illicit drug or disease epidemic, opioid addiction has its roots in legal, prescription medication a fact which greatly increases the exposed population and provides additional drug accessibility for addicts. In this paper, we present an epidemic model for opioid prescription, addiction, and treatment. Through mathematical analysis of our model, we show that no addiction-free equilibrium exists without stringent control over how opioids are administered and prescribed, effectively transforming the dynamics of the opioid crisis into those of a classic, illicit drug epidemic. Numerical sensitivity analysis suggests that relatively low states of endemic addiction can also be obtained by focusing primarily on medical prevention, followed by aggressive treatment of remaining cases even when the probability of relapse remains high. Further empirical study focused on understanding the rate of illicit drug dependence verses overdose risk, along with the current and changing rates of opioid prescription and treatment, would shed significant light on optimal control efforts and feasible outcomes for this epidemic and drug epidemics in general. N.A. Battista Dept. of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Road, Ewing, NJ 08628 E-mail: [email protected] L.B. Pearcy Dept. of Mathematics, University of North Carolina at Chapel Hill, CB 3250, University of North Carolina, Chapel Hill, NC, 27599 E-mail: [email protected] W.C. Strickland Dept. of Mathematics, University of Tennessee at Knoxville, 1403 Circle Drive, Knoxville TN, 37996 E-mail: [email protected] ar X iv :1 71 1. 03 65 8v 1 [ qbi o. PE ] 1 0 N ov 2 01 7 2 Nicholas A. Battista et al.