Entropy Ratio and Entropy Concentration Coefficient, with Application to the COVID-19 Pandemic

• Published in: Entropy (Basel, Switzerland) Vol. 22; no. 11; p. 1315
• Main Author: Bandt, Christoph
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 18-11-2020; MDPI
• Subjects: Coefficient of variation; concentration coefficient; Coronaviruses; COVID-19; Entropy; fractal; Fractals; Income distribution; Infections; Markov chains; Pandemics; Population density; relative entropy; Self-similarity; East Germany; United States > US; Germany; fractal; Covid-19; relative entropy; concentration coefficient
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e22111315

In order to study the spread of an epidemic over a region as a function of time, we introduce an entropy ratio
describing the uniformity of infections over various states and their districts, and an entropy concentration coefficient C=1-U. The latter is a multiplicative version of the Kullback-Leibler distance, with values between 0 and 1. For product measures and self-similar phenomena, it does not depend on the measurement level. Hence,
is an alternative to Gini's concentration coefficient for measures with variation on different levels. Simple examples concern population density and gross domestic product. Application to time series patterns is indicated with a Markov chain. For the Covid-19 pandemic, entropy ratios indicate a homogeneous distribution of infections and the potential of local action when compared to measures for a whole region.