Asymptotic properties of solutions in a model of antibacterial immune response. (Russian. English summary) Zbl 1402.34083
Summary: 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.
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K21 | Stationary solutions of functional-differential equations |
Keywords:
antibacterial immune response; delay differential equations; asymptotic stability; estimates of solutions; attraction set; modified Lyapunov-Krasovskii functionalReferences:
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