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.
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
\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
}
This publication is cited in the following 5 articles:
T. L. Sabatulina, V. V. Malygina, “Exponential stability and estimates of solutions to systems of functional differential equations”, Siberian Adv. Math., 33:3 (2023), 230–241
T. S. Mikhakhanova, O. F. Voropaeva, “Triggernaya model dinamiki ostrogo i khronicheskogo asepticheskogo vospaleniya”, Matem. biologiya i bioinform., 17:2 (2022), 266–288
Pertsev N., Loginov K., Bocharov G., “Nonlinear Effects in the Dynamics of Hiv-1 Infection Predicted By Mathematical Model With Multiple Delays”, Discret. Contin. Dyn. Syst.-Ser. S, 13:9, SI (2020), 2365–2384
N. V. Pertsev, “Stability of linear delay differential equations arising in models of living systems”, Siberian Adv. Math., 30:1 (2020), 43–54
N. V. Pertsev, “Matrix Stability and Instability Criteria For Some Systems of Linear Delay Differential Equations”, Sib. Electron. Math. Rep., 16 (2019), 876–885
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