Department of Mathematics and Computer Science, University of Richmond, 204 Jepson Hall, 221 Richmond Way, Richmond, VA, 23173, USA.
Department of Mathematics and Statistics, The College of New Jersey, Ewing, NJ, 08628, USA.
Harm Reduct J. 2021 Oct 30;18(1):110. doi: 10.1186/s12954-021-00559-4.
Fatal overdoses from opioid use and substance disorders are increasing at an alarming rate. One proposed harm reduction strategy for reducing overdose fatalities is to place overdose prevention sites-commonly known as safe injection facilities-in proximity of locations with the highest rates of overdose. As urban centers in the USA are tackling legal hurdles and community skepticism around the introduction and location of these sites, it becomes increasingly important to assess the magnitude of the effect that these services might have on public health.
We developed a mathematical model to describe the movement of people who used opioids to an overdose prevention site in order to understand the impact that the facility would have on overdoses, fatalities, and user education and treatment/recovery. The discrete-time, stochastic model is able to describe a range of user behaviors, including the effects from how far they need to travel to the site. We calibrated the model to overdose data from Philadelphia and ran simulations to describe the effect of placing a site in the Kensington neighborhood.
In Philadelphia, which has a non-uniform racial population distribution, choice of site placement can determine which demographic groups are most helped. In our simulations, placement of the site in the Kensington neighborhood resulted in White opioid users being more likely to benefit from the site's services. Overdoses that occur onsite can be reversed. Our results predict that for every 30 stations in the overdose prevention site, 6 per year of these would have resulted in fatalities if they had occurred outside of the overdose prevention site. Additionally, we estimate that fatalities will decrease further when referrals from the OPS to treatment are considered.
Mathematical modeling was used to predict the impact of placing an overdose prevention site in the Kensington neighborhood of Philadelphia. To fully understand the impact of site placement, both direct and indirect effects must be included in the analysis. Introducing more than one site and distributing sites equally across neighborhoods with different racial and demographic characteristics would have the broadest public health impact. Cities and locales can use mathematical modeling to help quantify the predicted impact of placing an overdose prevention site in a particular location.
阿片类药物使用和物质障碍导致的致命过量用药呈惊人的速度增长。减少过量用药死亡的一种减少危害策略是在过量用药率最高的地方附近设立过量预防场所,通常称为安全注射设施。随着美国的城市中心在引入和定位这些场所方面面临法律障碍和社区质疑,评估这些服务对公共卫生可能产生的影响变得越来越重要。
我们开发了一个数学模型来描述前往过量预防场所的阿片类药物使用者的流动情况,以便了解该设施对过量用药、死亡、用户教育以及治疗/康复的影响。该离散时间、随机模型能够描述一系列用户行为,包括他们需要到该场所的距离的影响。我们对来自费城的过量用药数据进行了模型校准,并进行了模拟以描述在肯辛顿社区设立该场所的效果。
在费城,种族人口分布不均,选择场所的位置可以决定哪些人群最受益。在我们的模拟中,在肯辛顿社区设立该场所,将使白人阿片类药物使用者更有可能受益于该场所的服务。现场发生的过量用药可以被逆转。我们的结果预测,如果这些过量用药发生在该场所之外,每年将有 6 例在该 30 个站点的过量预防站点中的站点发生的过量用药死亡。此外,当考虑从 OPS 到治疗的转介时,我们预计死亡人数将进一步下降。
使用数学建模来预测在费城肯辛顿社区设立过量预防场所的影响。为了充分理解场所位置的影响,必须在分析中包含直接和间接的影响。在不同种族和人口特征的社区中引入更多的场所,并公平分配这些场所,将对公共卫生产生最广泛的影响。城市和地区可以使用数学建模来帮助量化在特定地点设立过量预防场所的预期影响。