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.
- Antibacterial immune response
- Asymptotic stability
- Attraction set
- Delay differential equations
- Estimates of solutions
- Modified Lyapunov-Krasovskii functional