Complexity of COVID-19 Dynamics

Abstract

With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.

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

“…To choose the optimal embedding dimension, we use the lowest value for the false nearest neighbors [3, 18, 19]. The concept of false nearest neighbors is about topology and dimensionality, if the embedding dimension is too low with respect to the attractor’s dimensionality, then, one is obtaining a lower dimensional projection of a higher dimensional geometrical structure, in this case, points that are not neighbors will be projected onto a close neighborhood in the lower dimensional embedding, which will lead to problems, especially when dealing with topological data analysis, one of these problems is that what may seem to be noise-like signatures are associated not with noise but with the attempt to embed a higher dimensional object in a lower dimensional space.…”

“…Recent research into the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has uncovered evidence of low dimensional attractors and markers of chaos in the pandemics' dynamics for different countries and regions [1][2][3][4]. Taking into account this evidence, in the current work, we apply chaos theory's main empirical methods including both chaos metrics such as embedding dimension and Lyapunov spectra estimation along with spectral analysis and expand on these empirical methods by employing state-of-the-art topological data analysis methods including: recurrence analysis metrics, persistent homology analysis, predictability metrics from nearest neighbors machine learning algorithms incorporated into adaptive artificial intelligences (A.I.…”

Bibliometric Analysis of Literature on Physical Activity and COVID-19

“…A large proportion of non-research articles were published in the form of expert excerpts. Although these pieces of literature raised valuable knowledge, the knowledge of and perspectives toward COVID-19 were dynamic, especially in the early phase of the outbreak [ 30 , 31 ]. Therefore, these publications should be carefully interpreted.…”

On the intrinsic dimensionality of Covid-19 data: a global perspective

“…However, there has been little work done to explore the latent dynamics of the pandemic spread across continents and countries. Sivakumar and Deepthi (2021) examine the temporal dynamics of Covid-19 daily cases and deaths in 40 countries, using a False Nearest Neighbour method to identify the relevant embedding dimension (ED) for each country. The authors recognise that new Covid-19 cases and deaths exhibit a low-to medium-level ED.…”