Partition Markov Model for Covid-19 Virus

Abstract

In this paper, we investigate a specific structure within the theoretical framework of Partition Markov Models (PMM) [see García Jesús and González-López, Entropy 19, 160 (2017)]. The structure of interest lies in the formulation of the underlying partition, which defines the process, in which, in addition to a finite memory o associated with the process, a parameter G is introduced, allowing an extra dependence on the past complementing the dependence given by the usual memory o. We show, by simulations, how algorithms designed for the classic version of the PMM can have difficulties in recovering the structure investigated here. This specific structure is efficient for modeling a complete genome sequence, coming from the newly decoded Coronavirus Covid-19 in humans [see Wu et al., Nature 579, 265–269 (2020)]. The sequence profile is represented by 13 units (parts of the state space’s partition), for each of the 13 units, their respective transition probabilities are computed for any element of the genetic alphabet. Also, the structure proposed here allows us to develop a comparison study with other genomic sequences of Coronavirus, collected in the last 25 years, through which we conclude that Covid-19 is shown next to SARS-like Coronaviruses (SL-CoVs) from bats specimens in Zhoushan [see Hu et al., Emerg Microb Infect 7, 1–10 (2018)].

An Efficient Coding Technique for Stochastic Processes

“…Specifically in this article, we use three genetic sequences, in the Fasta format—one from China and the other two collected in Brazil. Our selection is based on the discoveries made in [ 3 , 4 ] that have allowed us to know the stochastic behavior of these sequences. The sequence MN908947.3, coming from a patient of Central Hospital in Wuhan (Hubei, China), can be obtained from the free base NCBI.…”

“…It is the first SARS-CoV-2 complete genome sequence registered in the literature, see [ 15 ]. In [ 3 ], we model this sequence (using its Fasta format), and the resulting model is a PMM model with interstice on the alphabet As introduced in [ 3 ], the model was selected using the BIC criterion. This model is very natural for genetic behavior.…”

“…To the usual parameter o (see Definition 8), we add a new parameter which means that a piece of extra information about the behavior of the sample further in the past needs to be incorporated into the model to better catch the stochastic behavior of the sequence. In this case, (since we deal with the genomic alphabet, which is organized in triples), and (see table 6 (right) in [ 3 ]). Then, in the compression process, we need to report two parameters and We have a continuous past of size and a gap between positions 4 and 8 in the past, the value in the position being used to define the states of the state space, as illustrated in Figure 1 .…”

“…In [ 3 ], this model is widely investigated within the framework of the sequence MN908947.3 of SARS-CoV-2. It results in a model made up of 13 parts, where each part gathers states with the constitution described above.…”

“…A message, a DNA sequence, among other data structures, can be seen as a realization of a stochastic process, subject to a certain alphabet and with a certain memory. For example, in [ 3 , 4 ], it is shown that the genetic structures of SARS-CoV-2, in FASTA format, can be modeled as a Markovian process. In this case, a model of partitions with interstice was used, which is a variant of the model initially proposed in [ 5 ] (and investigated in [ 6 ]).…”