I-BioStat, Data Science Institute, Hasselt University, 3500, Hasselt, Belgium.
I-BioStat, KU Leuven, 3000, Leuven, Belgium.
Sci Rep. 2023 Mar 15;13(1):4322. doi: 10.1038/s41598-023-30948-7.
Understanding the local dynamics of COVID-19 transmission calls for an approach that characterizes the incidence curve in a small geographical unit. Given that incidence curves exhibit considerable day-to-day variation, the fractal structure of the time series dynamics is investigated for the Flanders and Brussels Regions of Belgium. For each statistical sector, the smallest administrative geographical entity in Belgium, fractal dimensions of COVID-19 incidence rates, based on rolling time spans of 7, 14, and 21 days were estimated using four different estimators: box-count, Hall-Wood, variogram, and madogram. We found varying patterns of fractal dimensions across time and location. The fractal dimension is further summarized by its mean, variance, and autocorrelation over time. These summary statistics are then used to cluster regions with different incidence rate patterns using k-means clustering. Fractal dimension analysis of COVID-19 incidence thus offers important insight into the past, current, and arguably future evolution of an infectious disease outbreak.
理解 COVID-19 传播的本地动态需要一种方法，该方法可以描述小地理区域的发病率曲线。鉴于发病率曲线表现出相当大的日常变化，因此针对比利时的佛兰德斯和布鲁塞尔地区研究了时间序列动态的分形结构。对于每个统计部门，即比利时最小的行政地理实体，基于滚动时间跨度为 7、14 和 21 天，使用四种不同的估计器（盒子计数，霍尔伍德，变差函数和 madogram）估算了 COVID-19 发病率的分形维数。我们发现，分形维数在时间和位置上存在不同的变化模式。进一步通过其平均值，方差和随时间的自相关来总结分形维数。然后，使用 k-均值聚类将具有不同发病率模式的区域进行聚类。因此，对 COVID-19 发病率的分形维数分析为传染病爆发的过去，现在和未来的发展提供了重要的见解。
