Math Model Shows Naloxone Kits at Transit Stops Could Save Lives

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State laws in many states in the U.S. mandate the existence and placement of automated external defibrillators (AED) in specific locations, including K-12 schools, health clubs, assisted living facilities and nursing homes. The placement is strategic given lived experience and the community of people typically found in these locations.

Researchers in Canada want to do the same thing with naloxone kits.

“Naloxone kits are somewhat analogous to AEDs in that they can reverse the effects of an opioid poisoning event, but only if they are available quickly, which means they need to be in the right locations,” said University of Toronto Engineering professor Timothy Chan.

Chan and his team recently published a paper showing that placing naloxone kits in transit stations could help ensure that the life-saving medication is present where it is needed most. 

“The opioid epidemic is a profound public health crisis, and it may not be obvious at first how engineering researchers can help,” said Chan. “In collaboration with doctors and other medical professionals, we can apply techniques from our field—operations research and mathematical optimization—to develop new solutions.”

Math and medicine

In the new paper published in the Canadian Medical Association Journal, Chan and team evaluated all opioid poisoning incidents recorded by British Columbia Emergency Health Services between December  2014 and August  2020 in Metro Vancouver, Canada—totaling to 14,089 opioid poisonings.

The team then built a computer model that could simulate how many of those incidents would have taken place within a 3-minute walk from a naloxone kit, based on three distribution strategies:

  1. existing locations participating in take-home naloxone programs (647 locations),
  2. blanket naloxone kit placement at chain businesses (10–233 locations), pharmacies (790 locations), and registered public-defibrillator locations (980 locations),
  3. optimization-based strategic kit placement at transit stops based on historical poisonings.

According to the data, existing locations participating in take-home naloxone programs covered 4,988 (35.4%) opioid poisonings—more than a third of past opioid poisonings.

Meanwhile, placing kits at chain restaurants and similar businesses did not result in good coverage. Chain businesses covered 6 to 1,165 (8.3%) opioid poisonings, and chain business categories, pharmacies, and public defibrillator locations covered 97 to 3,152 (22.4%) opioid poisonings.

Meanwhile, optimization-based strategic placement of naloxone kits at transit stops yielded generally higher coverage levels, ranging from 2,907 (20.6%) opioid poisonings covered with 10 kit locations, to 7,506 (53.3%) with 1,000 kit locations.

“There have been a few small pilot programs putting naloxone kits in public locations, but to our knowledge, this is the first time anyone has analyzed what large-scale distribution would look like using mathematical optimization techniques. By presenting these results, I think we can make a strong case for doing that,” said Ben Leung, lead author on the paper. Leung built the computer model while working as a PhD student in Chan’s lab. He is now a research fellow at Clinical Research Institute.

The researchers hope these results can spur even broader changes, as well.

“For example, in Japan, AEDs are widely available at vending machines,” explained Chan. “That has led to an association: if someone is having a cardiac arrest, you automatically know to go to the nearest vending machine for an AED. If we can do something similar for naloxone, it could help bystanders feel more empowered to step in when they are needed to save lives.”



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