The study of events distributed over time which can be quantified as point processes has attracted much interest over the years due to its wide range of applications. It has recently gained new relevance due to the COVID-19 case and death processes associated with SARS-CoV-2 that characterize the COVID-19 pandemic and are observed across different countries. It is of interest to study the behavior of these point processes and how they may be related to covariates such as mobility restrictions, gross domestic product per capita, and fraction of population of older age. As infections and deaths in a region are intrinsically events that arrive at random times, a point process approach is natural for this setting. We adopt techniques for conditional functional point processes that target point processes as responses with vector covariates as predictors, to study the interaction and optimal transport between case and death processes and doubling times conditional on covariates.

对随时间分布的事件（可以量化为点过程）的研究由于其广泛的应用，多年来引起了人们的广泛兴趣。由于与 SARS-CoV-2 相关的 COVID-19 病例和死亡过程是 COVID-19 大流行的特征，并且在不同国家都观察到，因此它最近获得了新的相关性。研究这些点过程的行为以及它们如何与流动限制、人均国内生产总值和老年人口比例等协变量相关是很有意义的。由于一个地区的感染和死亡本质上是随机发生的事件，因此点过程方法对于这种情况来说是很自然的。我们采用条件功能点过程技术，将点过程作为响应，以向量协变量作为预测变量，来研究病例和死亡过程之间的相互作用和最佳传输，以及以协变量为条件的倍增时间。