Complexity of COVID-19 Dynamics

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.

Higher-Order Phase-Space Reconstruction for Detection of Epileptic Electroencephalogram

In this paper, the authors propose a new technique for the classification of seizures, non-seizures, and seizure-free EEG signals based on non-linear trajectories of EEG signals. The EEG signals are decomposed using the EMD technique to obtain intrinsic mode functions (IMFs). The phase space of these IMFs is then reconstructed using a novel technique of higher-order dimensions (3D, 4D, 5D, 6D, 7D, 8D, 9D, and 10D). The existing techniques of seizure detection have deployed 2D & 3D phase–space reconstruction only. The Euclidean distance of all higher-order PSR is used as a feature to classify seizures, non-seizures, and seizure-free EEG signals. The performance of the proposed method is analyzed on the Bonn University database in which 7D reconstructed phase space classification accuracy of 99.9% has been achieved both using Random Forest classifier and J48 decision tree.