We propose a model based on discrete latent variables, which are spatially associated and time specific, for the analysis of incident cases of SARS-CoV-2 infections. We assume that for each area the sequence of latent variables across time follows a Markov chain with initial and transition probabilities that also depend on latent variables in neighboring areas. The model is estimated by a Markov chain Monte Carlo algorithm based on a data augmented scheme, in which the latent states are drawn together with the model parameters for each area and time. As an illustration we analyze incident cases of SARS-CoV-2 collected in Italy at regional level for the period from February 24, 2020, to January 17, 2021, corresponding to 48 weeks, where we use number of swabs as an offset. Our model identifies a common trend and, for every week, assigns each region to one among five distinct risk groups.

我们提出了一个基于离散潜变量的模型，这些变量在空间上相关且特定于时间，用于分析 SARS-CoV-2 感染的事件病例。我们假设对于每个区域，潜变量随时间的序列遵循马尔可夫链，其初始概率和转移概率也取决于相邻区域的潜变量。该模型由基于数据增强方案的马尔可夫链蒙特卡罗算法估计，其中潜在状态与每个区域和时间的模型参数一起绘制。作为说明，我们分析了 2020 年 2 月 24 日至 2021 年 1 月 17 日期间在意大利地区收集的 SARS-CoV-2 事件病例，对应 48 周，我们使用拭子数量作为补偿​​。我们的模型确定了一个共同趋势，并且每周，