A Mathematical Model for Overdose in a Population of People Who Inject Drugs

The presence of synthetic opioids (fentanyl and carfentanil) in heroin and other drugs has greatly increased the risk of fatal overdose among people who inject drugs (PWID) across Canada and elsewhere in the world. We sought to represent the dynamics of the population of PWID and various public health interventions using a mathematical framework that hybridizes an individual-based model with a compartmental analysis model. The goal of this study was to accurately formulate a simulated population of users whose risk is uniquely and dynamically determined. The model construction involved a significant literature review, and synthesis and analysis of data from collaborators implementing drug policy. We calibrated the model to represent the PWID population in downtown Toronto, but it can be adapted to examine effects of similar interventions in any location. The model results suggest that recruitment to the at-risk population is currently over-reported, and the present values should be re-evaluated. The model results also suggest that various factors, including age, previous overdoses, and history of incarceration, have a significant effect on the individual risk of fatal overdose. The information we obtain can be used to strategically target intervention strategies, and guide future research on the PWID population.