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The objective of the present study was to show that the spread of the COVID-19 pandemic around the world shows complex system properties such as lognormal laws, temporal fluctuation scaling, and time correlation. First, the daily cumulative number of confirmed cases and deaths is distributed among countries as lognormals such that the time series exhibit a temporal fluctuation scaling. Second, the daily return time series of cases and deaths per day have associated Levy stable distributions and they have time correlation. The idea was to draw attention to the fact that the spread of the COVID-19 pandemic can be seen as a complex system, and, thus, contribute to the identification of the structural properties of this system, which is relevant as it is expected that future stochastic models describing the spread of the COVID-19 pandemic from a microscopic dynamics perspective should be able to explain the emergence of the structural properties identified here.

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The Taylor power law (or temporal fluctuation scaling), is a scaling relationship of the form σ ~ (P)λ where !! is the standard deviation and hPi the mean value of a sample of a time series has been observed for power output data sampled at 5 min and 1 s and from five wind farms and a single wind turbine, located at different places. Furthermore, an analogy with the turbulence field is performed, consequently allowing the establishment of a scaling relationship between the turbulent production IP and the mean value (P).

Taylor's law of temporal fluctuation scaling, variance , is ubiquitous in natural and social sciences. We report for the first time convincing evidence of a solid temporal fluctuation scaling law in stock illiquidity by investigating the mean-variance relationship of the high-frequency illiquidity of almost all stocks traded on the Shanghai Stock Exchange (SHSE) and the Shenzhen Stock Exchange (SZSE) during the period from 1999 to 2011. Taylor's law holds for A-share markets (SZSE Main Board, SZSE Small & Mediate Enterprise Board, SZSE Second Board, and SHSE Main Board) and B-share markets (SZSE B-share and SHSE B-share). We find that the scaling exponent is greater than 2 for the A-share markets and less than 2 for the B-share markets. We further unveil that Taylor's law holds for stocks in 17 industry categories, in 28 industrial sectors and in 31 provinces and direct-controlled municipalities with the majority of scaling exponents . We also investigate the -min illiquidity and find that the scaling exponent increases logarithmically for small values and decreases fast to a stable level. [ABSTRACT FROM AUTHOR]