Estimates of solutions for one biological model

In the paper we consider a model of immune response in plants described by nonlinear system of delay differential equations. The delay parameter is responsible for the ripening time of plant tissue. Asymptotic properties of solutions to this system in the case of infection are studied. Conditions for the asymptotic stability of the equilibrium point corresponding to the infected plant are obtained, estimates for the attraction set of this equilibrium point are indicated, and estimates of solutions characterizing the stabilization rate at infinity are established. All values present in the estimates are expressed explicitly in terms of the coefficients of the system. The results are obtained using Lyapunov–Krasovskii functionals.