Russian version English version
Volume 13   Issue 1   Year 2018
Application of M-Matrices for the Study of Mathematical Models of Living Systems

Nikolay V. Pertsev, Boris Yu. Pichugin, Anna N. Pichugina

Sobolev Institute of Mathematics SB RAS, Omsk Branch
Omsk F.M. Dostoevsky State University

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.
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2018.13.208
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)
References Translation into English
Math. Biol. Bioinf.
doi: 10.17537/2018.13.t104

Full text (eng., pdf)


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