Geodesic
Asymptotic properties of solutions in a model of antibacterial immune response
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1198-1215

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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.
Keywords: antibacterial immune response, delay differential equations, asymptotic stability, estimates of solutions, attraction set, modified \linebreak Lyapunov–Krasovskii functional. 
@article{SEMR_2018_15_a101,
     author = {M. A. Skvortsova},
     title = {Asymptotic properties of solutions in a model of antibacterial immune response},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1198--1215},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a101/}
}
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M. A. Skvortsova. Asymptotic properties of solutions in a model of antibacterial immune response. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1198-1215. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a101/