混合传染病模型的统一
Unifying Epidemic Models with Mixtures
摘要：
COVID-19疫情强调了对流行病模型的深入理解的必要性。目前流行病的模型分为机械模型和非机械模型：机械模型对疾病的动态做出明确的假设，而非机械模型对观察到的时间序列的形式做出假设。在这里，我们介绍了一个简单的基于混合的模型，该模型在保留两者优点的同时，将这两种方法连接起来。该模型将病例和死亡的时间序列表示为高斯曲线的混合，与传统的机械模型相比，提供了一个灵活的函数类来从数据中学习。虽然该模型是非机械的，我们表明，它是一个随机过程的基础上网络SIR框架的自然结果。与类似的非机械模型相比，这使得学习的参数能够进行更有意义的解释，我们使用COVID-19大流行期间收集的辅助流动性数据来验证解释。我们提供了一个简单的学习算法来识别模型参数，并建立了理论结果，表明该模型可以有效地从数据中学习。经验上，我们发现该模型具有较低的预测误差。该模型可在covidpredictions.mit.edu上获得。最终，这使我们能够系统地了解干预措施对COVID-19的影响，这对于开发控制流行病的数据驱动解决方案至关重要。
英文摘要：
The COVID-19 pandemic has emphasized the need for a robust understanding of epidemic models. Current models of epidemics are classified as either mechanistic or non-mechanistic: mechanistic models make explicit assumptions on the dynamics of disease, whereas non-mechanistic models make assumptions on the form of observed time series. Here, we introduce a simple mixture-based model which bridges the two approaches while retaining benefits of both. The model represents time series of cases and fatalities as a mixture of Gaussian curves, providing a flexible function class to learn from data compared to traditional mechanistic models. Although the model is non-mechanistic, we show that it arises as the natural outcome of a stochastic process based on a networked SIR framework. This allows learned parameters to take on a more meaningful interpretation compared to similar non-mechanistic models, and we validate the interpretations using auxiliary mobility data collected during the COVID-19 pandemic. We provide a simple learning algorithm to identify model parameters and establish theoretical results which show the model can be efficiently learned from data. Empirically, we find the model to have low prediction error. The model is available live at covidpredictions.mit.edu. Ultimately, this allows us to systematically understand the impacts of interventions on COVID-19, which is critical in developing data-driven solutions to controlling epidemics.
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