Waves of the dynamics of the rate of increase in the parameters of Covid-19 in Russia for 03/25/2020-12/31/2020 and the forecast of all cases until 08/31/2021 - Mazurkin PM (Annals of Mathematics and Physics - Peertechz Publications, 2021)
In applied mathematics and statistics, only linear equations are still used. The article proposes the sum of asymmetric wavelets with variable amplitudes and periods of oscillation. As a result, the behavior of any object or subject is given by the sum of vibrations. Using the identification method based on statistical daily data on four indicators of the dynamics of the rate of Covid-19, quanta of the pandemic behavior in the territory of the Russian Federation from March 25 to December 31, 2020 were identified. It is shown that the rates are infected, cured, died, and "all cases = infected + cured + died" in Russia got two superimposed bulges. Based on the computational capabilities of CurveExpert-1.40, 4-5 components were jointly identified with an overall correlation coefficient above 0.86 for infected and over 0.99 for all cases. It has been proven that the spread of the virus has the form of a set of finite-dimensional wavelets with variable amplitudes and, as a rule, with a decreasing oscillation period. By modeling the standard deviation by the serial numbers of the wavelets, it was proved that the parameters of the Covid-19 pandemic have fractal distributions. For the velocity parameter "died", the main bulge does not reach its maximum. And the second member of the trend peaked at 164 deaths on 06/18/2020, and it will leave the scene from 03/23/2021. The third member of the model, aimed at countering mortality, at the beginning of the time series on 03/25/2020 received a fluctuation period of 355 days. By the date of December 31, 2020, the fluctuation period became equal to 278 days. More often with constant half-periods of 3.5 and 16.1 days, fluctuations occurred. In this case, the 70th term gives a constant oscillation period, even 1.88 days. The average relative modeling error in modulus is equal for speeds: 1) died - 2.09; all cases - 3.22; cured - 17.17 and infected 29.91%. In this case, the range of error values changes in the following intervals: 1) died from -18.93 to 11.95%; all cases from -31.37 to 20.20%; cured from -248.8 to 396.0%; infected from -1934.0 to 779.7%. According to the distributions of the relative error after 1%, the following rating was obtained: 1) the correlation coefficient of 0.9807 for the speed died; 2) at 0.9768 the rate of all cases; 3) 0.8640 has been cured; 4) 0.8174 - infected. The fractality coefficient is equal to the ratio of the standard deviations of the linear model to the last component: for infected 3572.76 / 310.97 = 11.5; cured 5.8; died 24.3 and all cases 9.6. Further, due to the high range of relative error, the rates of cured and infected are excluded from forecasting. The forecast for the rate of deaths was carried out until 02/14/2021. The right border at the forecast horizon was adopted due to the fact that negative values appear from 15.02.2021. For a longer time interval from 01.01.2021 to 31.08.2021 the model allows predicting the rate of change of all cases. To reduce the relative modeling error, it is recommended to re-identify the model of the dynamics of the parameters died and all cases every three weeks. The identification method is applicable to any statistical series, and not only to dynamic ones.