In 2016, more than 11 million Americans abused prescription opioids. The National Institute on Drug Abuse considers the opioid crisis a national addiction epidemic, as an increasing number of people are affected each year. Using the framework developed in mathematical modelling of infectious diseases, we create and analyse a compartmental opioid-abuse model consisting of a system of ordinary differential equations. Since $40\%$ of opioid overdoses are caused by prescription opioids, our model includes prescription compartments for the four most commonly prescribed opioids, as well as for the susceptible, addicted and recovered populations. While existing research has focused on drug abuse models in general and opioid models with one prescription compartment, no previous work has been done comparing the roles that the most commonly prescribed opioids have had on the crisis. By combining data from the Substance Abuse and Mental Health Services Administration (which tracked the proportion of people who used or misused one of the four individual opioids) with data from the Centers of Disease Control and Prevention (which counted the total number of prescriptions), we estimate prescription rates and probabilities of addiction for the four most commonly prescribed opioids. Additionally, we perform a sensitivity analysis and reallocate prescriptions to determine which opioid has the largest impact on the epidemic. Our results indicate that oxycodone prescriptions are both the most likely to lead to addiction and have the largest impact on the size of the epidemic, while hydrocodone prescriptions had the smallest impact.

中文翻译：

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计算四种最常用处方阿片类药物的处方率和成瘾概率，并使用隔室模型评估其对成瘾的影响。

2016年，超过1100万美国人滥用处方阿片类药物。国家药物滥用研究所认为阿片类药物危机是一种全国成瘾的流行病，因为每年都有越来越多的人受到影响。使用在传染病数学建模中开发的框架，我们创建和分析由常微分方程组组成的隔室阿片类药物滥用模型。由于40 %%的阿片类药物过量是由处方阿片类药物引起的，因此我们的模型包括针对四个最常用的阿片类药物以及易感人群，成瘾者和康复人群的处方区室。尽管现有研究集中在具有一个处方隔室的普通和阿片类药物模型中的药物滥用模型上，以前没有做过任何工作来比较最常用的阿片类药物在危机中所起的作用。通过将药物滥用和精神卫生服务管理局（跟踪使用或滥用四种阿片类药物之一的人的比例）的数据与疾病控制与预防中心的数据（计算处方总数）相结合，我们估算了四种最常用的阿片类药物的处方率和成瘾可能性。此外，我们进行敏感性分析并重新分配处方，以确定哪种阿片类药物对该流行病影响最大。我们的结果表明，羟考酮处方不仅最容易导致成瘾，而且对流行病的影响最大，