Spatiotemporal Analysis of COVID-19 Incidence Data

(1) Background: A better understanding of COVID-19 dynamics in terms of interactions among individuals would be of paramount importance to increase the effectiveness of containment measures. Despite this, the research lacks spatiotemporal statistical and mathematical analysis based on large datasets. We describe a novel methodology to extract useful spatiotemporal information from COVID-19 pandemic data. (2) Methods: We perform specific analyses based on mathematical and statistical tools, like mathematical morphology, hierarchical clustering, parametric data modeling and non-parametric statistics. These analyses are here applied to the large dataset consisting of about 19,000 COVID-19 patients in the Veneto region (Italy) during the entire Italian national lockdown. (3) Results: We estimate the COVID-19 cumulative incidence spatial distribution, significantly reducing image noise. We identify four clusters of connected provinces based on the temporal evolution of the incidence. Surprisingly, while one cluster consists of three neighboring provinces, another one contains two provinces more than 210 km apart by highway. The survival function of the local spatial incidence values is modeled here by a tapered Pareto model, also used in other applied fields like seismology and economy in connection to networks. Model’s parameters could be relevant to describe quantitatively the epidemic. (4) Conclusion: The proposed methodology can be applied to a general situation, potentially helping to adopt strategic decisions such as the restriction of mobility and gatherings.

Fractal properties of forest fires in Amazonia as a basis for modelling pan-tropical burned area

Current methods for modelling burnt area in Dynamic Global Vegetation Models involve complex fire spread calculations, which rely on many inputs, including fuel characteristics, wind speed and countless parameters. They are therefore susceptible to large uncertainties through error propagation. Using observed fractal distributions of fire scars in Brazilian Amazonia, we propose an alternative burnt area model for tropical forests, with fire counts as sole input and few parameters. Several parameterizations of two possible distributions are calibrated at multiple spatial resolutions using a satellite-derived burned area map, and compared. The tapered Pareto model most accurately simulates the total area burnt (only 3.5 km2 larger than the recorded 16 387 km2) and its spatial distribution. When tested pan-tropically using MODIS MCD14ML fire counts, the model accurately predicts temporal and spatial fire trends, but produces generally higher estimates than the GFED3.1 burnt area product, suggesting higher pan-tropical carbon emissions from fires than previously estimated.

Estimation of the upper cutoff parameter for the tapered Pareto distribution

The tapered (or generalized) Pareto distribution, also called the modified Gutenberg-Richter law, has been used to model the sizes of earthquakes. Unfortunately, maximum likelihood estimates of the cutoff parameter are substantially biased. Alternative estimates for the cutoff parameter are presented, and their properties discussed.

Estimation of the upper cutoff parameter for the tapered Pareto distribution

The tapered (or generalized) Pareto distribution, also called the modified Gutenberg-Richter law, has been used to model the sizes of earthquakes. Unfortunately, maximum likelihood estimates of the cutoff parameter are substantially biased. Alternative estimates for the cutoff parameter are presented, and their properties discussed.