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

Abstract

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.

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

“…In the case of COVID-19, the proximity of the epidemiological dynamics to a bifurcation point opens up the possibility of bifurcations occurring in the system's dynamics with the loss of attractor stability, this occurred specifically in Oceania, as stated above, and was linked to the emergence of new variants [5].…”

“…Epidemiological applications of chaos theory methods to the SARS-CoV-2/COVID-19 pandemic [1][2][3][4][5] have uncovered evidence of chaotic markers in the pandemics' dynamics.…”

“…In [5] we found evidence of stochastic chaos with emergent low dimensional attractors for the COVID-19 regional data at the level of the number of new positive cases per million and the number of new deaths per million, in particular, the type of dynamics identified was a power law chaos dynamics also called color chaos [5][6][7], characterized by power law signatures in the frequency spectrum, this dynamics occurred for Asia, Africa and Europe, while in North and South America, for the new cases per million, the decay in the frequency spectrum of the signal was faster than power law, except for the number of new deaths per million in the case of South America [5]. For Oceania we found the occurrence of a bifurcation in both series' dynamics [5].…”

“…Another major finding was that all regions except Oceania showed evidence of being near a bifurcation point between a periodic window and a chaotic dynamics, also called onset of chaos [5]. Near the onset of chaos, chaotic attractors are characterized by low maximum Lyapunov exponents and can exhibit recurrences associated with close proximity to periodic or even quasiperiodic orbits, which become like "ghost trails" that are recurrently visited [5], leading to long evenly or unevenly spaced diagonals in recurrence matrices with 100% recurrence that only show up for a sufficiently high radius, diagonals that are intermixed with broken diagonals and isolated points which are characteristic of chaotic dynamics [5,8].…”

“…In the present work, we expand on the work we developed in [5], combining chaos theory, machine learning and topological data analysis to address the daily hospital occupancy from COVID-19, the study compares USA with Canada, using the dataset available from Our Word in Data for the country-specific daily hospital occupancies from COVID-19 from the first available datapoint up until 2022-09-30. The methodologies applied are easily extensible to any other country.…”