A Mathematical Approach to the Analysis of Harm Reduction Efforts in the Opioid Crisis

Abstract

Opioid addiction in the United States is a national crisis. Various harm reduction strategies have been proposed, including safe injection sites, whose goals are to reduce deaths and improve the health of addicts. Many of these proposed strategies are controversial because their impact is unknown. In this paper we present a discrete time Markov model that captures essential probabilities in the description of the U.S. opioid epidemic, while remaining tractable to analysis. We use the model to analyze the impact of an overdose prevention site and other harm reduction strategies on the number of fatal overdoses and recovery rates, and make quantitative predictions about the consequences of implementing specific policies.