Analysis of "big data" and mathematical modeling of the covid-19 epidemic in Europe - Kulyk, Daria; Kurkchi, Yelizavieta; Kizilova, Nataliya (Bulletin of V.N. Karazin Kharkiv National University, series «Mathematical modeling. Information technology. Automated control systems», 2021)
The regularities of the dynamics of the covid-19 pandemic in Ukraine and other European countries are studied by using the methods of analyzing "big data" in the form of time series and related information from open online sources. Statistical analysis of smoothed curves of new cases I (t), dead D (t), recovered R (t) and other time series has shown different types of dynamics: wave (i), quasi-wave with time shift (ii), stepwise (iii), with abnormally high or low amplitudes of local oscillations. The appropriate similarity trees have been constructed by using the nearest neighbor method. It is shown that the countries with different types of dynamics (i, ii, iii) are located in separate branches of the trees. The stability of zero and nonzero stationary points have been investigated on the basis of the popular mathematical model SIRS. The solutions of the linearized system have been obtained and the influence of the model parameters on the eigenvalues of the system matrix has been investigated. The presence of different types of dynamics is shown: with three negative real (a), one positive real (b), one real and a pair of complex conjugate(c) eigenvalues. The phase portraits have been constructed and the connection of the types of time series (i, ii, iii) and solutions (a, b, c) of the SIRS equations is shown. The obtained results allow us to estimate the dynamic behavior of the system, its stability or instability with the possibility of chaotic dynamics on the basis of the analysis of time series on any current day.