Nonlinear Dynamics, Stability and Control Strategies: Mathematical Modeling on the Big Data Analyses of Covid-19 in Poland

Detailed numerical data on covid-19 epidemic have been collected since February 2020, and now >200 countries and regions are presented in online databases. A brief review of the data analyses and mathematical modelling for different countries is given. The time series on four “waves” of pandemic in 16 provinces of Poland are analyzed. Statistical regularities, self- and cross-correlations, common and different features in the regions are revealed. Spectral analysis of oscillating components and phase curves demonstrated non-linear quasi-regular and chaotic dynamics. Based on the comparative analyses of the 7-day averaged curves, the non-linear SEIDQRV model with time delay was estimated as the most proper mathematical model. Material parameters of the model for each “wave” and region have been used for stability analysis and controllability of the pandemic. The reproduction number for each region/wave have been obtained as the stability criterion for the systems of equations of the SIR, SIRS, SEIR, SEIRS, SEIDQR models with and without time delay. Sensitivity of the models to different control functions (social restrictions, lockdown measures, availability/quality of medical treatment, vaccination level) revealed different sets of the most influencing parameters in different provinces and waves. The results are compared for similar data for Poland and other European countries. It is shown; the nonlinear dynamics and best control strategies differ at the level of the country and its regions that needs more complex local governmental measures against further development of the pandemic.