The overwhelming spatio-temporal nature of the spread of the ongoing Covid-19 pandemic demands urgent attention of data analysts and model developers. Modelling results obtained from analytical tool development are essential to understand the ongoing pandemic dynamics with a view to helping the public and policy makers. The pandemic has generated data on a huge number of interesting statistics such as the number of new cases, hospitalisations and deaths in many spatio-temporal resolutions for the analysts to investigate. The multivariate nature of these data sets, along with the inherent spatio-temporal dependencies, poses new challenges for modellers. This article proposes a two-stage hierarchical Bayesian model as a joint bivariate model for the number of cases and deaths observed weekly for the different local authority administrative regions in England. An adaptive model is proposed for the weekly Covid-19 death rates as part of the joint bivariate model. The adaptive model is able to detect possible step changes in death rates in neighbouring areas. The joint model is also used to evaluate the effects of several socio-economic and environmental covariates on the rates of cases and deaths. Inclusion of these covariates points to the presence of a north-south divide in both the case and death rates. Nitrogen dioxide, the only air pollution measure used in the model, is seen to be significantly positively associated with the number cases, even in the presence of the spatio-temporal random effects taking care of spatio-temporal dependencies present in the data. The proposed models provide excellent fits to the observed data and are seen to perform well for predicting the location specific number of deaths a week in advance. The structure of the models is very general and the same framework can be used for modelling other areally aggregated temporal statistics of the pandemics, e.g. the rate of hospitalisation.

持续的 Covid-19 大流行蔓延的压倒性时空特性需要数据分析师和模型开发人员的紧急关注。从分析工具开发中获得的建模结果对于了解持续的大流行动态以帮助公众和政策制定者至关重要。这场大流行已经产生了大量有趣的统计数据，例如许多时空分辨率中的新病例数、住院人数和死亡人数，供分析师调查。这些数据集的多元性，以及固有的时空依赖性，给建模者带来了新的挑战。本文提出了一个两阶段分层贝叶斯模型，作为英格兰不同地方当局行政区域每周观察到的病例数和死亡人数的联合双变量模型。作为联合双变量模型的一部分，针对每周 Covid-19 死亡率提出了一种自适应模型。自适应模型能够检测邻近地区死亡率的可能阶跃变化。该联合模型还用于评估几个社会经济和环境协变量对病例率和死亡率的影响。包含这些协变量表明病例和死亡率都存在南北差异。二氧化氮是模型中使用的唯一空气污染指标，与病例数呈显着正相关，即使存在时空随机效应，也会处理数据中存在的时空依赖性。所提出的模型为观察到的数据提供了极好的拟合，并且被认为在提前一周预测特定地点的死亡人数方面表现良好。模型的结构非常通用，相同的框架可用于对流行病的其他区域汇总时间统计数据进行建模，例如住院率。