Abstract
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused the global pandemic, coronavirus disease-2019 (COVID-19) which has resulted in 60.4 million infections and 1.42 million deaths worldwide. Mathematical models as an integral part of artificial intelligence are designed for contact tracing, genetic network analysis for uncovering the biological evolution of the virus, understanding the underlying mechanisms of the observed disease dynamics, evaluating mitigation strategies, and predicting the COVID-19 pandemic dynamics. This paper describes mathematical techniques to exploit and understand the progression of the pandemic through a topological characterization of underlying graphs. We have obtained several topological indices for various graphs of biological interest such as pandemic trees, Cayley trees, Christmas trees, and the corona product of Christmas trees and paths. We have also obtained an analytical expression for the thermodynamic entropies of pandemic trees as a function of R0, the reproduction number, and the level of spread, using the nested wreath product groups. Our plots of entropy and logarithms of topological indices of pandemic trees accentuate the underlying severity of COVID-19 over the 1918 Spanish flu pandemic.
Highlights
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), commonly called the novel coronavirus (COVID-19), has resulted in 1.42 million deaths worldwide up to now [1,2]
Recursive trees constructed from phylogenetics have provided graphical representation of microbiomes and have been proven to be powerful in the perturbations induced to genomes and proteomes by environment or toxins [10,11,12,13], and graph techniques are especially suited to understand the dynamics of the COVID-19 epidemic
We have obtained the eccentricity-related indices for the pandemic tree network, Cayley tree network, Christmas trees, and the corona
Summary
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), commonly called the novel coronavirus (COVID-19), has resulted in 1.42 million deaths worldwide up to now [1,2]. Recursive trees constructed from phylogenetics have provided graphical representation of microbiomes and have been proven to be powerful in the perturbations induced to genomes and proteomes by environment or toxins [10,11,12,13], and graph techniques are especially suited to understand the dynamics of the COVID-19 epidemic. A pandemic tree provides a pictorial representation of the epidemic dynamics where each node is connected to k other nodes, where k is an integer rounded from the R0 value, an epidemiological measure of the degree of infection, suggesting that an infected individual in turn infects R0 others in a susceptible population pool. We consider several trees of biological and phylogenetic interests and corona products of graphs in order to obtain the topological measures of the associated networks.
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