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Matematicheskaya Biologiya i Bioinformatika, 2018, Volume 13, Issue 1, Pages 208–237
DOI: https://doi.org/10.17537/2018.13.208 (Mi mbb334) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Review 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
b Omsk F.M. Dostoevsky State University
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DOI: https://doi.org/10.17537/2018.13.208
Abstract: Some results are presented of application of M-matrices to the study the stability problem of the equilibriums of differential equations used in models of living systems. The models studied 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 of living systems, mathematical models in immunology, epidemiology, ecology, delay differential equations, high-dimensional systems of differential equations, stability of the equilibriums, M-matrix.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences I.1.1., проект № 0314-2016-0009
Received 06.06.2018, Published 28.06.2018
Document Type: Article
UDC: 517.958:57
Language: Russian
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., 13:1 (2018), 208–237
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
\issue 1
\pages 208--237
\mathnet{http://mi.mathnet.ru/mbb334}
\crossref{https://doi.org/10.17537/2018.13.208
}
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