Wave Patterns of Cumulative Dynamics for the Parameters of Covid-19 in the Russian Federation from March 25 to December 31, 2020
Mazurkin PM
Published on: 2021-01-25
Abstract
Using the identification method based on statistical daily data on four Covid-19 indicators of the dynamics of the sum of values, quanta of pandemic behavior and responses from the health care system in the Russian Federation from March 25 to December 31, 2020 were identified. The general wavelet equation is presented in the form of a solitary wave equation, which, with an infinite period of oscillation, turns into a biotechnical law proposed by the author of the article. It is shown that the sums of the values of the pandemic parameters as "infected", "cured", "died" and "cases = infected + cured + died" from March 23 to December 31 in Russia received two superimposed bulges as in the amplitude of oscillations with infinite , that is, a much larger measurement time interval of 282 days, a period. That being said, the big bulge will continue into 2021. According to the computational capabilities of the CurveExpert-1.40 software environment, the general trigonometric model contains up to 4-5 components with a general correlation coefficient above 0.99. It has been proven that the nature of the spread of the virus has the form of a set of finite-dimensional wavelets with variable amplitude according to the biotechnical law and, as a rule, with a decreasing oscillation period. In these features, the dynamics of a pandemic differs from the behavior of natural and natural-anthropogenic objects of study, which also have infinite-dimensional wavelets with an amplitude in the form of Laplace's law (in mathematics), Mandelbrot's law (in physics), Zipf-Perl (in biology), Pareto (in econometrics). By modeling the standard deviation depending on the ordinal number in the list of wavelets, and without taking into account the constant term, it has been proven that the parameters of the Covid-19 pandemic also have a fractal distribution of wave equations. But their dynamics depends entirely on the behavior of the epidemiological system of each country. As a result, the Russian healthcare system has been at the proper height to counter the pandemic since May 3, 2020.
Keywords
Covid-19 parameters; cumulates; dynamics by day; wavelet analysis; patternsIntroduction
As reported by the World Health Organization, on January 7, 2020, the Chinese authorities have identified a new coronavirus. For the first three months of 2020, according to statistical data, a dynamic epidemiological model was proposed to recognize the initial stage of COVID-19 infection among countries in the modern world [7].
Such models are used not only in epidemiology. For example, to study the dynamics of the distribution of investment schemes in a given population, an epidemiological model was created in which the rate is included in the model as an exponentially distributed random variable that gives distribution of losses [1].
In the article [8] some interesting trigonometric sums are given. By us, asymmetric wavelets with variable amplitude and oscillation period also together form trigonometric sums. However, it turned out to be more convenient to use the cosine function due to the fact that for the zero value of the beginning of the positive semiaxis, the cosine also gives zero along the positive semiaxis of ordinates.
Based on the concept of vibrational adaptation in nature and the use of trigonometric cosine sums, a method was proposed for identifying [2] stable wave patterns from tables of quantitative data, especially from tables of statistical data [4]. Then each component of the trigonometric sum is a wavelet signal, and each wavelet itself in the CurveExpert-1.40 software environment is constructed from the so-called Hilbert bricks [3].
As a result, from such general invariants in the form of wavelets, a composite algebraic equation is constructed, sometimes containing more than 200 wavelets. Thus, we have proved the possibility of forming one single algebraic equation according to Descartes directly without solving differential and integral equations.
The wavelet analysis method made it possible to directly resolve more than 100 thousand examples of statistical modeling without constructing unsolvable differential and integral equations. For example, the wavelet analysis of the maximum temperature in Central England was brought to a measurement error [5]. Maybe someone will dare to obtain integral and differential equations from the trigonometric sums of wavelet signals given in this article.
Gradually, we realized that each component of the trigonometric sum is a quantized signal about the behavior of the object of study, for example, in the article [6] in the quantum meteorology of the behavior of the temperature of the surface air layer.
The purpose of the article is to use the example of time series from March 25 to December 31, 2020 to conduct a wavelet analysis and identify quanta of behavior of the "Covid-19 + healthcare system of Russia" system by cumulates (sums of consecutive values) for four pandemic parameters (infected, cured, died, cases = infected + cured + died).