Multiple partition Markov model for B.1.1.7, B.1.351, B.1.617.2, and P.1 variants of SARS-CoV 2 virus

Abstract

With tools originating from Markov processes, we investigate the similarities and differences between genomic sequences in FASTA format coming from four variants of the SARS-CoV 2 virus, B.1.1.7 (UK), B.1.351 (South Africa), B.1.617.2 (India), and P.1 (Brazil). We treat the virus’ sequences as samples of finite memory Markov processes acting in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A=\{a,c,g,t\}.$$\end{document} We model each sequence, revealing some heterogeneity between sequences belonging to the same variant. We identified the five most representative sequences for each variant using a robust notion of classification, see Fernández et al. (Math Methods Appl Sci 43(13):7537–7549. 10.1002/mma.5705 ). Using a notion derived from a metric between processes, see García et al. (Appl Stoch Models Bus Ind 34(6):868–878. 10.1002/asmb.2346), we identify four groups, each group representing a variant. It is also detected, by this metric, global proximity between the variants B.1.351 and B.1.1.7. With the selected sequences, we assemble a multiple partition model, see Cordeiro et al. (Math Methods Appl Sci 43(13):7677–7691. 10.1002/mma.6079), revealing in which states of the state space the variants differ, concerning the mechanisms for choosing the next element in A. Through this model, we identify that the variants differ in their transition probabilities in eleven states out of a total of 256 states. For these eleven states, we reveal how the transition probabilities change from variant (group of variants) to variant (group of variants). In other words, we indicate precisely the stochastic reasons for the discrepancies.