2019年美赛C题特等奖论文.docx

Random Walks and Rehab 353 Random Walks and Rehab: Analyzing the Spread of the Opioid Crisis Ellen Considine Suyog Soti Emily Webb University of Colorado Boulder Boulder, Colorado USA Advisor: Anne Dougherty Summary We classify 69 types of opioid substances into four categories based on synthesis and availability. Plotting use rates of each category over time re- veals that use of mild painkillers and natural alkaloids has stayed relatively constant over time, semi-synthetic drugs have declined slightly, and syn- thetic drugs such as fentanyl and heroin have increased dramatically. These ?ndings align with reports from the CDC. We select 54 of 149 socioeconomic variables based on their variance in?ation factor score (a common measure of multicollinearity) as well as on their relevance based on the public health literature. To model the spread of the opioid crisis across Kentucky, Ohio, Penn- sylvania, West Virginia, and Virginia, we develop two completely different models and then compare them. Our ?rst model is founded on common modeling approaches in epidemi- ology: SIR/SIS models and stochastic simulation. We design an algorithm that simulates a random walk between six discrete classes, each of which represents a different stage of the opioid crisis, using thresholds for opioid abuse prevalence and rate of change. We penalize transitions between cer- tain classes differentially based on realistic expectations. Optimization of parameters and coef?cients for the model is guided by an error function in- spired by the global spatial autocorrelation statistic Moran ’sI. Testing our model via both error calculation and visual mapping illustrates high accu- racy over many hundreds of trials. However, this model does not provide much insight into the in?uence of socioeconomic factors on opioid abuse The UMAP Journal 40 (4) (2018) 353 – 380c. Copyright 2019 by COMAP