The rapid spread of the SARS-CoV-2 epidemic has simultaneous time and space dynamics. This behaviour results from a complex combination of factors, including social ones, which lead to significant differences in the evolution of the spatiotemporal pattern between and within countries. Usually, spatial smoothing techniques are used to map health outcomes, and rarely uncertainty of the spatial predictions are assessed. As an alternative, we propose to apply direct block sequential simulation to model the spatial distribution of the COVID-19 infection risk in mainland Portugal. Given the daily number of infection data provided by the Portuguese Directorate-General for Health, the daily updates of infection rates are calculated by municipality and used as experimental data in the geostatistical simulation. The model considers the uncertainty/error associated with the size of each municipality’s population. The calculation of daily updates of the infection risk maps results from the median model of one ensemble of 100 geostatistical realizations of daily updates of the infection risk. The ensemble of geostatistical realizations is also used to calculate the associated spatial uncertainty of the spatial prediction using the interquartile distance. The risk maps are updated daily and show the regions with greater risks of infection and the critical dynamics related to its development over time.

中文翻译：

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葡萄牙的地统计 COVID-19 感染风险地图。

SARS-CoV-2流行病的快速传播具有同步的时间和空间动态。这种行为是包括社会因素在内的复杂因素组合的结果，导致国家之间和国家内部时空格局演变的显着差异。通常，空间平滑技术用于绘制健康结果图，很少评估空间预测的不确定性。作为替代方案，我们建议应用直接块顺序模拟来模拟葡萄牙大陆 COVID-19 感染风险的空间分布。鉴于葡萄牙卫生总局每天提供的感染数据数量，感染率的每日更新由市政当局计算，并用作地统计模拟中的实验数据。该模型考虑了与每个城市人口规模相关的不确定性/误差。感染风险地图每日更新的计算源自感染风险每日更新的 100 个地统计实现的一个集合的中值模型。地统计实现的集合还用于使用四分位数距离计算空间预测的相关空间不确定性。风险地图每天更新，显示感染风险较大的区域以及与感染随时间发展相关的关键动态。