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Matematicheskaya Biologiya i Bioinformatika, 2018, Volume 13, Issue Suppl., Pages t104–t131
DOI: https://doi.org/10.17537/2018.13.t104 (Mi mbb366) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Translations of Published Articles

Application of M-matrices for the study of mathematical models of living systems

N. V. Pertseva, B. Yu. Pichugina, A. N. Pichuginab

a Sobolev Institute of Mathematics SB RAS, Omsk Branch, Omsk, Russia
b Dostoevsky Omsk State University, Omsk, Russia
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DOI: https://doi.org/10.17537/2018.13.t104
Abstract: We present some results of the application of M-matrices to the study the stability problem of the equilibriums of differential equations used in models of living systems. The models of living systems are described by differential equations with several delays, including distributed delay, and by high-dimensional systems of differential equations. To study the stability of the equilibriums the linearization method is used. Emerging systems of linear differential equations have a specific structure of the right-hand parts, which allows to effectively use the properties of M-matrices. As examples, the results of studies of models arising in immunology, epidemiology and ecology are presented.
Key words: mathematical models for living systems, mathematical models in immunology, epidemiology and ecology, basic reproductive number, delay differential equations, high-dimensional differential systems, stability, М-matrix.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I.1.1., Project № 0314-2016-0009
The research was funded by the Program of Fundamental Scientific Research, SB RAS № I.1.1., Project № 0314-2016-0009.
Received 06.06.2018, Published 18.09.2018
Document Type: Article
UDC: 517.958:57
Language: English
Citation: N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Application of M-matrices for the study of mathematical models of living systems”, Mat. Biolog. Bioinform., 13, Suppl. (2018), t104–t131
Citation in format AMSBIB
\Bibitem{PerPicPic18}
\by N.~V.~Pertsev, B.~Yu.~Pichugin, A.~N.~Pichugina
\paper Application of M-matrices for the study of mathematical models of living systems
\jour Mat. Biolog. Bioinform.
\yr 2018
\vol 13
\pages t104--t131
\issueinfo Suppl.
\mathnet{http://mi.mathnet.ru/mbb366}
\crossref{https://doi.org/10.17537/2018.13.t104}
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  • https://www.mathnet.ru/eng/mbb366
  • https://www.mathnet.ru/eng/mbb/v13/i3/p104
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    This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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