Estimates for solutions for one model of population dynamics with delay

We consider a model of the single population dynamics described by a delay differential equation. The asymptotic behavior of solutions for this model is studied in cases of asymptotic stability of equilibrium points corresponding to the complete extinction of the population and to the constant positive population size. In each case, Lyapunov-Krasovskii functionals are constructed, with the help of which estimates characterizing the rate of extinction of the population and the rate of stabilization of the population to a constant value are obtained.