{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:23:48Z","timestamp":1760239428279,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,18]],"date-time":"2020-11-18T00:00:00Z","timestamp":1605657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In order to study the spread of an epidemic over a region as a function of time, we introduce an entropy ratio U describing the uniformity of infections over various states and their districts, and an entropy concentration coefficient C=1\u2212U. 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, C is an alternative to Gini\u2019s 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.<\/jats:p>","DOI":"10.3390\/e22111315","type":"journal-article","created":{"date-parts":[[2020,11,18]],"date-time":"2020-11-18T07:41:00Z","timestamp":1605685260000},"page":"1315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Entropy Ratio and Entropy Concentration Coefficient, with Application to the COVID-19 Pandemic"],"prefix":"10.3390","volume":"22","author":[{"given":"Christoph","family":"Bandt","sequence":"first","affiliation":[{"name":"Institute of Mathematics, University of Greifswald, 17487 Greifswald, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,18]]},"reference":[{"key":"ref_1","unstructured":"Wikipedia (2020, October 06). Gini Coefficient. 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