Low Dimensional Chaotic Attractors in Daily Hospital Occupancy from COVID-19 in the USA and Canada (preprint)

Epidemiological application of chaos theory methods have uncovered the existence of chaotic markers in SARS-CoV-2's epidemiological data, including low dimensional attractors with positive Lyapunov exponents, and evidence markers of a dynamics that is close to the onset of chaos for different regions. We expand on these previous works, performing a comparative study of United States of America (USA) and Canada's COVID-19 daily hospital occupancy cases, applying a combination of chaos theory, machine learning and topological data analysis methods. Both countries show markers of low dimensional chaos for the COVID-19 hospitalization data, with a high predictability for adaptive artificial intelligence systems exploiting the recurrence structure of these attractors, with more than 95% R2 scores for up to 42 days ahead prediction. The evidence is favorable to the USA's hospitalizations being closer to the onset of chaos and more predictable than Canada, the reasons for this higher predictability are accounted for by using topological data analysis methods.

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

Background: Recent studies applying chaos theory methods have found the existence of chaotic markers in SARS-CoV-2's 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 Methods: We 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 theory's 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. Results: The 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.