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Entropy Ratio and Entropy Concentration Coefficient, with Application to the COVID-19 Pandemic
1Institute of Mathematics, University of Greifswald, 17487 Greifswald, Germany.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study introduces an entropy concentration coefficient to measure infection uniformity across regions over time. For COVID-19, it reveals homogeneous infection spread, suggesting targeted local interventions are effective.
Area of Science:
- Epidemiology
- Statistical Physics
- Data Science
Background:
- Understanding epidemic spread requires metrics for infection distribution.
- Existing coefficients may not capture multi-level variations effectively.
- Entropy-based measures offer a novel approach to assess uniformity.
Purpose of the Study:
- Introduce a new entropy ratio (U) and concentration coefficient (C) for epidemic spread analysis.
- Evaluate C as an alternative to Gini's coefficient for multi-level data.
- Apply the method to COVID-19 time series data.
Main Methods:
- Defined an entropy ratio (U) and concentration coefficient (C = 1-U).
- Established C as a multiplicative Kullback-Leibler distance variant (0-1 range).
- Utilized Markov chains for time series analysis of epidemic data.
Main Results:
- The entropy concentration coefficient (C) is invariant to measurement level for self-similar phenomena.
- C serves as an alternative to Gini's coefficient for hierarchical data.
- COVID-19 analysis showed homogeneous infection distribution, supporting localized control strategies.
Conclusions:
- The entropy concentration coefficient provides a robust measure of infection uniformity.
- Homogeneous spread patterns identified in COVID-19 suggest the efficacy of local public health actions.
- This metric aids in optimizing epidemic response strategies at regional levels.
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