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Entropy
Volume 28
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10.3390/e28010082
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Article

Remarks on a Scaling Theory of Spread of COVID-19 with an Application to the Case of Bulgaria

by
Svetlan Kartalov
and
Nikolay K. Vitanov
*
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 4, 1113 Sofia, Bulgaria
*
Author to whom correspondence should be addressed.
Entropy 2026, 28(1), 82; https://doi.org/10.3390/e28010082 (registering DOI)
Submission received: 11 December 2025 / Revised: 4 January 2026 / Accepted: 8 January 2026 / Published: 10 January 2026
(This article belongs to the Section Multidisciplinary Applications)
Versions Notes

Abstract

We present several remarks on the spread of the COVID-19 epidemics in Bulgaria. The remarks are based on the hypothesis that the spread of the infection exhibits scaling properties similar to the scaling in urban dynamics. The corresponding mathematical theory leads us to a relationship for a power-law dependence of the number of infected in a certain region on the corresponding homochrony number. We prove the correctness of the mathematical theory on the basis of data for several Bulgarian regions for the first large COVID-19 wave in 2020. We observe a collapse of the real data along a single straight line.
Keywords: self-similarity; allometric urban scaling; dynamic scaling; power law; SARS-CoV-2; COVID-19; homocrony number; Bulgaria self-similarity; allometric urban scaling; dynamic scaling; power law; SARS-CoV-2; COVID-19; homocrony number; Bulgaria

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MDPI and ACS Style

Kartalov, S.; Vitanov, N.K. Remarks on a Scaling Theory of Spread of COVID-19 with an Application to the Case of Bulgaria. Entropy 2026, 28, 82. https://doi.org/10.3390/e28010082

AMA Style

Kartalov S, Vitanov NK. Remarks on a Scaling Theory of Spread of COVID-19 with an Application to the Case of Bulgaria. Entropy. 2026; 28(1):82. https://doi.org/10.3390/e28010082

Chicago/Turabian Style

Kartalov, Svetlan, and Nikolay K. Vitanov. 2026. "Remarks on a Scaling Theory of Spread of COVID-19 with an Application to the Case of Bulgaria" Entropy 28, no. 1: 82. https://doi.org/10.3390/e28010082

APA Style

Kartalov, S., & Vitanov, N. K. (2026). Remarks on a Scaling Theory of Spread of COVID-19 with an Application to the Case of Bulgaria. Entropy, 28(1), 82. https://doi.org/10.3390/e28010082

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