Mathematical Modeling to Support Mental Health-Focused Policing and Substance Use Disorder Treatment

The opioid crisis has claimed over 1,000,000 American lives since 1999, while non-fatal overdoses, opioid-related arrests, and cases of opioid use disorder ( OUD) have surged. This rapid increase in opioid-related events has strained many organizations, systems, and personnel in hospitals, treatment facilities, and police departments, which often lack adequate resources and procedures to manage such crises. As a result, many individuals who use opioids never receive or finish the treatment they need and instead may have many interactions with hospitals or the criminal justice system. These interactions provide an opportunity for interventions that can divert individuals who use opioids to OUD treatment. Therefore, we hypothesize that policies that create new pathways and programs that utilize treatment services can lead to more opioid-resilient communities (e.g., communities with fewer adverse opioid-related outcomes).

Using causal inference, we measure the impact of a local arrest diversion program on recidivism, where individuals arrested for an illegal substance-related crime are instead diverted to substance use disorder treatment. We also introduce a discrete event simulation that evaluates various OUD treatment policies and estimates community outcomes–such as opioid use, deaths, hospital encounters, and treatment uptake–by simulating individuals’ trajectories through systems and organizations within a United States (US ) county. Many of these programs and policies require collaboration between medical professionals and law enforcement. These collaborations have resulted in variations in how mental health training and professionals are integrated into law enforcement operations and procedures. Therefore, queueing networks, modeled as discrete event simulations, are evaluated using newly developed performance metrics to understand the trade-offs of several police emergency response models that offer mental health-focused services.

All models use public and community-sourced data for the analyses. Case studies in Dane County, WI, and Seattle, WA, provide practical context for these analyses. The findings highlight policies that have the potential to lower opioid-related deaths, overdoses, and arrests and improve OUD treatment access. This dissertation contributes to the broader field of decision science and operations research by developing new mathematical models that inform responses to the opioid epidemic and the next generation of policing.