Інформаційна технологія аналізу та прогнозування багатохвильової кількості нових випадків захворювань на коронавірус COVID-19 на основі моделі Prophet

Abstract

The article is devoted to the improvement of the information technology previously developed by the authors for the analysis and forecasting of the number of new confirmed cases of the disease for the coronavirus COVID-19 caused by the SARS-CoV-2 infection, using the example of the daily total data of the current "wave" in Ukraine, taking into account various holidays and pseudo-holydays, which may have an abnormal effect. The previously created technology was operable only for the area of continuous growth of the values of one wave, and the improved one can already be used to analyze and predict data throughout the entire period, since it takes into account the multi-wave nature of this phenomenon. An algorithm for identifying the parameters of each wave is proposed. A number of mathematical relationships have been developed that allow, in a first approximation, to estimate the start, end and period of each wave, even in the case when one wave passes into another. A new empirical relationships is proposed to estimate the order of the Fourier series for describing the time process of each wave for only 10 % of its values at the top, since, as a rule, such data are available in an explicit form, otherwise the data will not be recognized as a separate wave. The ratios are derived separately for the case of only positive coefficients, when the peak is located to the left of the middle of the half-period, and separately — for the case of an alternating series, when the peak is located to the right of it. However, these approximate estimates are recommended to be refined within a certain range of possible values, since in the general case of different variants of the harmonic amplitude values, the pro-posed ratios can give underestimates. It is proposed to apply the model identified by this technology to predict the most pessimistic and most optimistic scenar-ios for the development of the phenomenon, that is, changes in the number of new confirmed cases of the disease for the coronavirus COVID-19 in the future in a given country. Python software was created based on the Kaggle platform, which is used both for Ukraine and for 69 other countries. Using the identified models, a number of important conclusions were obtained regarding understanding the patterns of the spread of coronavirus both in Ukraine and in other 69 countries of the world. The results were submitted to the Working Group on Mathematical Modeling of Problems Associated with the SARS-CoV-2 Coronavirus Epidemic in Ukraine.