A new paper by Professor Isabelle Rao in the Department of Mechanical & Industrial Engineering (MIE) uses mathematical modelling to show the impact of providing stable housing to people experiencing homelessness and opioid addiction.
The paper published in JAMA Network Open shows that a ‘housing first’ approach to treating homelessness and addiction can minimize the likelihood of fatal overdoses and decrease healthcare costs.
“Homelessness, substance abuse disorders and a disconnect from healthcare services are all intertwined,” says Rao, who joined MIE in 2024. “For example, homelessness increases the likelihood of developing an addiction, while addiction increases the likelihood of losing housing options.”
Approaches to treating these interrelated issues typically fall into two general categories: housing first and treatment first. Housing first emphasizes providing permanent housing as quickly as possible, with other supportive services following afterward, while treatment first advocates for the opposite.
During the COVID-19 pandemic, opioid use spiked and fentanyl became a leading cause of overdose deaths. This motivated Rao and her former advisor, Professor Margaret Brandeau of the Management Science and Engineering Department at Stanford University, to create a dynamic mathematical model that incorporated housing, a key social determinant of health, into the analysis of the opioid epidemic.
The model simulated treatment and health outcomes for 1,000 unhoused people with opioid addiction, with and without the provision of stable housing. The model encompassed men and women over a range of ages, projected overdoses and deaths over five years, as well as lifetime healthcare and housing costs, and quality-adjusted life years (QALYs).
The results of their simulations demonstrated that investing in stable housing for marginalized populations was cost-effective, improved health outcomes, increased entry into and retention in addiction treatment, and saved lives.
“The most successful outcome in our analysis came when stable housing was provided,” says Rao. “This improved addiction treatment success and reduced mortality rates among individuals who had experienced homelessness.”
The team found that implementing the housing intervention reduced total overdoses and fatal overdoses over the five years by 11% and 9% respectively. The housing intervention costs $96,000 USD per person and increases QALYs by 3.59, leading to an incremental cost of $26,800 USD per QALY gained compared to the scenario with no housing. Accounting for savings in criminal justice system costs that accrue when individuals are no longer homeless, such housing programs may even be cost-saving.
“The results from the mathematical modelling demonstrate that providing stable housing is both life-saving and cost-effective,” says Rao. “This study has the potential to help inform local policies for funding and demonstrate the cost-effectiveness of Housing First programs.”
Rao and Brandeau have engaged with officials in California’s Santa Clara County, where Stanford University is located, to inform policies around homelessness.
They are also looking to do outreach with other local health communities, and expand into Toronto, and are currently seeking funding opportunities from the US National Institutes of Health (NIH).
“I have always been invested in having an impact on policies to improve the lives of marginalized communities,” says Rao. “My engineering and mathematical background allows me to use modelling to inform critical decisions in public health. It’s very motivating to see the positive and long-term healthcare and personal care impacts that stable housing can provide to people experiencing homelessness.”
– This story was originally published on the University of Toronto’s Faculty of Applied Science and Engineering News Site on July 2, 2025, by Kendra Hunter.