Fractal dimension based geographical clustering of COVID-19 time series data

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.

Automated summary

Understanding the local dynamics of COVID-19 transmission in small geographical units requires characterizing the incidence curve. This study investigates the fractal structure of time series dynamics in the Flanders and Brussels Regions of Belgium, estimating the fractal dimensions of COVID-19 incidence rates using four different estimators. Varying patterns of fractal dimensions across time and location were found, and summary statistics were used to cluster regions with different incidence rate patterns. Fractal dimension analysis offers important insight into the past, current, and future evolution of infectious disease outbreaks.