Drug overdose deaths continue to increase in the United States for all major drug categories. Over the past two decades the total number of overdose fatalities has increased more than five-fold; since 2013 the surge in overdose rates is primarily driven by fentanyl and methamphetamines. Different drug categories and factors such as age, gender, and ethnicity are associated with different overdose mortality characteristics that may also change in time. For example, the average age at death from a drug overdose has decreased from 1940 to 1990 while the overall mortality rate has steadily increased. To provide insight into the population-level dynamics of drug-overdose mortality, we develop an age-structured model for drug addiction. Using an augmented ensemble Kalman filter (EnKF), we show through a simple example how our model can be combined with synthetic observation data to estimate mortality rate and an age-distribution parameter. Finally, we use an EnKF to combine our model with observation data on overdose fatalities in the United States from 1999 to 2020 to forecast the evolution of overdose trends and estimate model parameters.

翻译：药物过量死亡在美国所有主要药物类别中持续增加。过去二十年间，过量死亡总数增加了五倍以上；自2013年以来，过量死亡率的激增主要由芬太尼和甲基苯丙胺驱动。不同药物类别及年龄、性别、种族等因素与不同的药物过量死亡率特征相关，这些特征也可能随时间变化。例如，药物过量死亡的平均年龄从1940年到1990年有所下降，而总体死亡率则稳步上升。为深入了解药物过量死亡率的人群水平动态，我们构建了一个年龄结构化的药物成瘾模型。通过使用增广集合卡尔曼滤波（EnKF），我们通过一个简单示例展示了如何将模型与合成观测数据结合，以估算死亡率及年龄分布参数。最后，我们利用EnKF将模型与1999年至2020年美国药物过量死亡观测数据结合，以预测过量死亡率趋势的演变并估计模型参数。