The k-statistics approach to epidemiology

Abstract

A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced $\kappa$-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of $\kappa$-statistics in fitting empirical data. In this paper, we use $\kappa$-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived $\kappa$-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the $\kappa$-Weibull model has universal features.

15 pages, 1 table, 5 figures

References in corpus (28)

• Power-law distributions in empirical data
• Power laws, Pareto distributions and Zipf's law
• Statistical mechanics in the context of special relativity
• Deformed exponentials and logarithms in generalized thermostatistics
• Coevolutionary success-driven multigames
• Maximum entropy principle and power-law tailed distributions
• Group entropies, correlation laws and zeta functions
• Non-gaussian statistics and stellar rotational velocities of main sequence field stars
• Tsallis and Kaniadakis statistics from a point of view of the holographic equipartition law
• Power-law statistics and stellar rotational velocities in the Pleiades
• A Novel Methodology for Epidemic Risk Assessment of COVID-19 outbreak
• Jeans instability criterion from the viewpoint of non-gaussian statistics
• Preliminary analysis of COVID-19 spread in Italy with an adaptive SEIRD model
• Entropic Forms and Related Algebras
• The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis
• Tsallis and Kaniadakis statistics from the viewpoint of entropic gravity formalism
• Loop Quantum Gravity Immirzi parameter and the Kaniadakis statistics
• A method to deconvolve stellar rotational velocities
• Exploiting the flexibility of a family of models for taxation and redistribution
• Composition law of $\kappa$-entropy for statistically independent systems
• Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems
• k-Deformed Fourier Transform
• Bi-stability of SUDR+K model of epidemics and test kits applied to COVID-19
• A k-deformed Model of Growing Complex Networks with Fitness
• Non-Gaussian thermostatistical considerations upon the Saha equation
• Common Origin of Power-law Tails in Income Distributions and Relativistic Gases
• Analysis on hadron spectra in heavy-ion collisions with a new non-extensive approach
• A new $\kappa$-deformed parametric model for the size distribution of wealth

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• Generalized pair-wise logit dynamic and its connection to a mean field game: theoretical and computational investigations focusing on resource management
• Decomposition of waves in time series of data related to Covid-19
• Universal behavior of the Covid-19 tails: Inverse power-law distribution
• An outlier-resistant $\kappa$-generalized approach for robust physical parameter estimation