Hawkes processes are used in statistical modeling for event clustering and causal inference, while they also can be viewed as stochastic versions of popular compartmental models used in epidemiology. Here we show how to develop accurate models of COVID-19 transmission using Hawkes processes with spatial-temporal covariates. We model the conditional intensity of new COVID-19 cases and deaths in the U.S. at the county level, estimating the dynamic reproduction number of the virus within an EM algorithm through a regression on Google mobility indices and demographic covariates in the maximization step. We validate the approach on both short-term and long-term forecasting tasks, showing that the Hawkes process outperforms several models currently used to track the pandemic, including an ensemble approach and an SEIR-variant. We also investigate which covariates and mobility indices are most important for building forecasts of COVID-19 in the U.S.

霍克斯过程用于事件聚类和因果推理的统计建模，同时它们也可以被视为流行病学中使用的流行区室模型的随机版本。在这里，我们展示了如何使用具有时空协变量的霍克斯过程开发准确的 COVID-19 传播模型。我们对美国县级新的 COVID-19 病例和死亡的条件强度进行建模，通过对谷歌流动性指数和最大化步骤中的人口协变量进行回归，估计 EM 算法内病毒的动态繁殖数量。我们在短期和长期预测任务上验证了该方法，结果表明霍克斯过程优于目前用于追踪大流行的几种模型，包括集成方法和 SEIR 变体。我们还调查了哪些协变量和流动性指数对于构建美国 COVID-19 的预测最重要