The COVID-19 pandemic provided many modeling challenges to investigate the evolution of an epidemic process over areal units. A suitable encompassing model must describe the spatio-temporal variations of the disease infection rate of multiple areal processes while adjusting for local and global inputs. We develop an extension to Poisson Auto-Regression that incorporates spatio-temporal dependence to characterize the local dynamics while borrowing information among adjacent areas. The specification includes up to two sets of space-time random effects to capture the spatio-temporal dependence and a linear predictor depending on an arbitrary set of covariates. The proposed model, adopted in a fully Bayesian framework and implemented through a novel sparse-matrix representation in Stan, provides a framework for evaluating local policy changes over the whole spatial and temporal domain of the study. It has been validated through a substantial simulation study and applied to the weekly COVID-19 cases observed in the English local authority districts between May 2020 and March 2021. The model detects substantial spatial and temporal heterogeneity and allows a full evaluation of the impact of two alternative sets of covariates: the level of local restrictions in place and the value of the Google Mobility Indices. The paper also formalizes various novel model-based investigation methods for assessing additional aspects of disease epidemiology.

翻译：COVID-19大流行对研究区域单元上流行病过程的演化提出了诸多建模挑战。一个合适的综合模型必须能够描述多个区域过程中疾病感染率的时空变异，同时调整局部和全局输入的影响。我们开发了一种泊松自回归的扩展方法，该方法引入时空依赖性以刻画局部动态特性，同时从相邻区域中借用信息。模型规范包括至多两组时空随机效应以捕获时空依赖性，以及一个依赖于任意协变量集的线性预测因子。所提出的模型采用全贝叶斯框架，并通过Stan中新颖的稀疏矩阵表示实现，为评估研究整个时空域上的局部政策变化提供了框架。该模型通过大量模拟研究验证，并应用于2020年5月至2021年3月期间英格兰地方当局行政区每周COVID-19病例数据。模型检测到显著的时空异质性，并允许全面评估两组替代协变量的影响：即地方限制措施等级和谷歌移动指数值。本文还系统化提出了多种基于模型的新型研究方法，用于评估疾病流行病学的其他方面。