Low Dimensional Chaotic Attractors in SARS-CoV-2's Regional Epidemiological Data

BackgroundRecent studies applying chaos theory methods have found the existence of chaotic markers in SARS-CoV-2s epidemiological data, evidence that has implications on the prediction, modeling and epidemiological analysis of the SARS-CoV-2/COVID-19 pandemic with implications for healthcare management. Aim and MethodsWe study the aggregate data for the new cases per million and the new deaths per million from COVID-19 in Africa, Asia, Europe, North and South America and Oceania, applying chaos theorys empirical methods including embedding dimension estimation, Lyapunov spectra estimation, spectral analysis and state-of-the-art topological data analysis methods combining persistent homology, recurrence analysis and machine learning with the aim of characterizing the nature of the dynamics and its predictability. ResultsThe results show that for all regions except Oceania there is evidence of low dimensional noisy chaotic attractors that are near the onset of chaos, with a recurrence structure that can be used by adaptive artificial intelligence solutions equipped with nearest neighbors machine learning modules to predict with a very high performance the future values of the two target series for each region. The persistent homology analysis uncovers a division into two groups, the first group comprised of Africa and Asia and the second of Europe, North and South America. For Oceania, we found evidence of the occurrence of a bifurcation which we characterize in detail applying a combination of machine learning and topological analysis methods, we find that the bifurcation in the region is related to the emergence of new variants.