TY - JOUR

T1 - Asymptotic properties of solutions in a model of antibacterial immune response

AU - Skvortsova, Maria Aleksandrovna

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In the present paper we consider a model of antibacterial immune response proposed by G.I. Marchuk. The model is described by a system of differential equations with three delays. We study the asymptotic stability of the stationary solution corresponding to a healthy organism. We obtain estimates of the attraction set of this solution and establish estimates of solutions characterizing the stabilization rate at infinity. The results are obtained using a modified Lyapunov-Krasovskii functional.

AB - In the present paper we consider a model of antibacterial immune response proposed by G.I. Marchuk. The model is described by a system of differential equations with three delays. We study the asymptotic stability of the stationary solution corresponding to a healthy organism. We obtain estimates of the attraction set of this solution and establish estimates of solutions characterizing the stabilization rate at infinity. The results are obtained using a modified Lyapunov-Krasovskii functional.

KW - Antibacterial immune response

KW - Asymptotic stability

KW - Attraction set

KW - Delay differential equations

KW - Estimates of solutions

KW - Modified Lyapunov-Krasovskii functional

UR - http://www.scopus.com/inward/record.url?scp=85074907585&partnerID=8YFLogxK

U2 - 10.17377/semi.2018.15.097

DO - 10.17377/semi.2018.15.097

M3 - Article

AN - SCOPUS:85074907585

VL - 15

SP - 1198

EP - 1215

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -