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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
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.
Received 06.06.2018, Published 18.09.2018
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
Linking options:
https://www.mathnet.ru/eng/mbb366 https://www.mathnet.ru/eng/mbb/v13/i3/p104
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Abstract page: | 211 | Full-text PDF : | 71 | References: | 35 |
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