Investigation of the dynamics of four waves covid-19 in European countries

Abstract

The peculiarities of the dynamics of successive waves of the covid-19 pandemic in Ukraine and other European countries have been considered by the methods of time series analyses. Both the oscillatory harmonic and growing non-harmonic dynamics have been detected. The curves of daily new cases of infected I(t), deceased D(t) and recovered R(t) individuals have been obtained from open sources and the mean and oscillating components have been identified. For the most countries the mean components of the curves I(t) and D(t) exhibit a small shift in 1-3 weeks that corresponds to the incubation period of the disease. The analysis of the spectrum of the oscillating components has showed that all countries have a fundamental harmonic with a period of T = 7 days, associated with the specifics of the working week of medical and statistical institutions. The rest of the harmonics in most countries turns out to have been close to zero, which corresponds to random errors in the collection of statistical data for the country's institutions. In a number of countries, signs of chaotic dynamics in the form of large amplitudes of neighboring harmonics and significant unexpected changes in the phase shifts between them have been revealed. Statistically reliable exponential approximations of the I(t) and D(t) curves at the stages of the fast and slow growth as well as fast and slow decrease in the number of cases for each of the four covid-19 waves in European countries have been obtained. The obtained approximations have been used for validation of the SEIRS mathematical model of the epidemic spread for a given country. The resulting country-specific models in the form of the systems of ordinary differential equations can be used for studying the dynamics of each wave in detail, and for predicting the further dynamics of covid-19 in the country.