An individual-based dynamic model to assess interventions to mitigate opioid overdose risk

Abstract

Background: Illicit opioid overdose continues to rise in North America and is a leading cause of death. Mathematical modeling is a valuable tool to investigate the epidemiology of this public health issue, as it can characterize key features of population outcomes and quantify the broader effect of structural and interventional changes on overdose mortality. The aim of this study is to quantify and predict the impact of key harm reduction strategies at differing levels of scale-up on fatal and nonfatal overdose among a population of people engaging in unregulated opioid use in Toronto.

Methods: An individual-based model for opioid overdose was built featuring demographic and behavioural variation among members of the population. Key individual attributes known to scale the risk of fatal and nonfatal overdose were identified and incorporated into a dynamic modeling framework, wherein every member of the simulated population encompasses a set of distinct characteristics that govern demographics, intervention usage, and overdose incidence. The model was parametrized to fatal and nonfatal overdose events reported in Toronto in 2019. The interventions considered were opioid agonist therapy (OAT), supervised consumption sites (SCS), take-home naloxone (THN), drug-checking, and reducing fentanyl in the drug supply. Harm reduction scenarios were explored relative to a baseline model to examine the impact of each intervention being scaled from 0% use to 100% use on overdose events.

Results: Model simulations resulted in 3690.6 nonfatal and 295.4 fatal overdoses, coinciding with 2019 data from Toronto. From this baseline, at full scale-up, 290 deaths were averted by THN, 248 from eliminating fentanyl from the drug supply, 124 from SCS use, 173 from OAT, and 100 by drug-checking services. Drug-checking and reducing fentanyl in the drug supply were the only harm reduction strategies that reduced the number of nonfatal overdoses.

Conclusions: Within a multi-faceted harm reduction approach, scaling up take-home naloxone, and reducing fentanyl in the drug supply led to the largest reduction in opioid overdose fatality in Toronto. Detailed model simulation studies provide an additional tool to assess and inform public health policy on harm reduction.

Keywords: Drug checking; Harm reduction; Individual-based model; Interventions; Mathematical model; Microsimulation model; Opioid use disorder; Opioids; Overdose risk; PWID; Take-home naloxone.

Fig. 1

A graphical representation of the model flow at one timestep. Black lines indicate flow pathways between events. ‘Y’ indicates yes for an event that occurs, whereas ‘N’ indicates no for an event that does not occur. Dotted arrows indicate probability dependencies from the individual attributes (grey) to a given event. Removal refers to an individual who is removed from the population

Fig. 2

Population-level dynamics determined by the summation of individuals entering and leaving the model population. Solid arrows (black) indicate flows into and out of the population stock. The dotted arrow indicates model dependency on attribute (grey). At each timestep, population inflow is the sum of initiation of new persons by all individuals, and outflow is the sum of all OD fatality, cessation, and non-OD all-cause mortality by all individuals

Fig. 3

Parameter exploration of the four harm reduction strategies considered here: (a) supervised consumption site (SCS) use, (b) rate of presence of naloxone at overdose, (c) fraction of PWID population using opioid agonist treatment (OAT), and (d) fraction of population who use drug checking services prior to injection. Fatal overdoses (blue) and nonfatal overdoses (black) are plotted with standard error bars, and values corresponding to baseline parameters are indicated by blue and black circles, respectively

Fig. 4

Effect of the prevalence of fentanyl in the illicit drug supply on fatal overdoses (blue) and nonfatal overdoses (black), plotted with standard error bars. Results of fatal and nonfatal overdose based on current baseline prevalence (0.50) is indicated by blue and black circles, respectively