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Matematicheskie Trudy, 2023, Volume 26, Number 1, Pages 150–175
DOI: https://doi.org/10.33048/mattrudy.2023.26.108 (Mi mt693) 		 
Estimates of solutions in a model of antiviral immune response

M. A. Skvortsovaab

a Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/mattrudy.2023.26.108
Abstract: We consider a model of antiviral immune response suggested by G.I. Marchuk. The model is described by a system of differential equations with several delays. We study asymptotic stability for a stationary solution of the system that corresponds to a completely healthy organism. We estimate the attraction set of this stationary solution. We also find estimates of solutions characterizing the stabilization rate at infinity. A Lyapunov–Krasovskii functional is used in the proof.
Key words: antiviral immune response model, delay differential equations, asymptotic stability, estimates of solutions, attraction set, Lyapunov–Krasovskii functional
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0008
The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).
Received: 20.04.2023
Revised: 15.05.2023
Accepted: 17.05.2023
English version:
Siberian Advances in Mathematics, 2023, Volume 33, Issue 4, Pages 353–368
DOI: https://doi.org/10.1134/S1055134423040089
Bibliographic databases:
Document Type: Article
UDC: 517.929.4
Language: Russian
Citation: M. A. Skvortsova, “Estimates of solutions in a model of antiviral immune response”, Mat. Tr., 26:1 (2023), 150–175; Siberian Adv. Math., 33:4 (2023), 353–368
Citation in format AMSBIB
\Bibitem{Skv23}
\by M.~A.~Skvortsova
\paper Estimates of solutions in a model of antiviral immune response
\jour Mat. Tr.
\yr 2023
\vol 26
\issue 1
\pages 150--175
\mathnet{http://mi.mathnet.ru/mt693}
\elib{https://elibrary.ru/item.asp?id=54901444}
\transl
\jour Siberian Adv. Math.
\yr 2023
\vol 33
\issue 4
\pages 353--368
\crossref{https://doi.org/10.1134/S1055134423040089}
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