Mathematical Model Illuminates Potential of Safe Consumption Sites

    New research aims to put numbers on how safe consumption sites (also known as overdose prevention sites, or OPS) can reduce overdose deaths in different cities across the United States.

    Published in Letters in Biomathematics in December, the research deploys a mathematical model called a Markov chain. Provided with data, this model is used to project the movement of people in a city between different “states”— such as “Not Currently Using Drugs,” or “Using Drugs (in an OPS)”—as well as fatal and non-fatal overdoses depending on the presence of OPS and other factors.

    According to the paper, the model allows “quantitative predictions of the benefits of harm reduction strategies such as overdose prevention sites, enabling policy makers to make data-driven decisions.”

    The model showed that if San Francisco, as an example, had 25,000 people who use drugs and set up 10 OPS, each able to accommodate 30 people, there would be 176 fewer overdose deaths per year. It also found that 668 of the total would be in treatment or recovery after one year under this scenario.

    The researchers are aware of how many variables, some of which they sought to account for, could impact effectiveness. Ami Radunskaya, a mathematician at Ponoma College in Claremont, California, and one of the authors of the paper, said the work suggests that OPS are most helpful in conjunction with other harm reduction strategies, such as helping people find work and housing, programs offering medications for opioid use disorder, and others.

    “What could you say about the effects of not just, say, safe injection sites, but also putting resources into harm reduction programs that involve counseling or helping people get jobs?” she asked Filter.

    Radunskaya added that this is something that California, among other states, could keep in mind, considering the influx of settlement money it’s receiving from pharmaceutical companies that manufactured various opioid painkillers.

    “We wanted to delve more deeply … into the mathematical possibilities of such a model.”

    According to Radunskaya, the model can also be used to gauge the effectiveness of other interventions. For instance, some of her students used it to look at buprenorphine treatment in San Bernardino County, California.

    As the US overdose crisis continues, opposition to safe consumption sites hinders their rollout. For instance, the government of Colorado recently blocked efforts that would have allowed the sites to be created.

    The authors of the recent paper had written a previous article specifically modeling Philadelphia. Published in the Harm Reduction Journal in 2021, it showed that an OPS would, indeed, help reduce deaths in the city. According to Radunskaya, the team involved members of the city’s public health sector, meaning they had access to a “lot of very specific data” about factors such as the number of people using drugs, providing the model with enough information to work.

    At the time, the city was mulling over allowing a safe consumption site to open, though both the municipal government a long-running federal lawsuit have since blocked efforts to establish OPS.

    From this first effort, the team learned more about other factors they wanted to include in the second paper. “We wanted to sort of delve more deeply … into the mathematical possibilities of such a model,” Radunskaya said.

    “The first thing [a city] should do if they have a pile of money is to set up the safe injection sites and spread them around so they’re accessible.”

    For the new model, they added new data from sources such as the cities of Seattle and Vancouver (which has OPS), and various jurisdictions in Europe. From these places, they had surveys about how likely people would be to attend an OPS given certain conditions (how close it was, etc.). Combined, this information enabled the team to look at how OPS could impact different US cities.

    However, Radunskaya noted that all models have their limitations. Going forward, she said that she hopes to fine-tune this one, including by calibrating it for different types of behavior, such as for people who have only recently started using drugs.

    “The first thing [a city] should do if they have a pile of money is to set up the safe injection sites and spread them around so they’re accessible,” she said. “And then, hold on to some of the resources and use them to have these social services.”



    Photograph by Photo Claude TRUONG-NGOC via Wikimedia Commons/Creative Commons 3.0

    • Doug is a writer, editor and journalist whose work has appeared in National Geographic, Undark Magazine, New Scientist and Hakai, among others. He lives in Alberta, Canada.

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