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.

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计算四种最常用的阿片类药物的处方率和成瘾概率，并使用隔间模型评估它们对成瘾的影响

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性的成瘾流行病，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，我们创建并分析了一个由常微分方程系统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，我们的模型包括四种最常用的阿片类药物以及易感、成瘾和康复人群的处方隔间。虽然现有的研究集中在一般的药物滥用模型和具有一个处方隔间的阿片类药物模型上，以前没有做过比较最常用的阿片类药物在危机中的作用的工作。通过将药物滥用和心理健康服务管理局的数据（跟踪使用或滥用四种阿片类药物之一的人的比例）与疾病控制和预防中心的数据（计算处方总数）相结合，我们估计了四种最常用的阿片类药物的处方率和成瘾概率。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流行病的影响最大。我们的结果表明，羟考酮处方最容易导致成瘾，对流行病的规模影响最大，