Stochastically Perturbed Epidemic Model with Time Delays

We investigate a stochastic epidemic model with time delays. By using Liapunov functionals, we obtain stability conditions for the stochastic stability of endemic equilibrium.

GLOBAL STABILITY OF A NONLINEAR DISCRETE POPULATION MODEL WITH TIME DELAYS

The global stability of a nonlinear discrete population model of Volterra type is studied. The model incorporates time delays. By linearization of the model at positive solutions and construction of Liapunov functionals, sufficient conditions are obtained to ensure that a positive solution of the model is stable and attracts all positive solutions. An example shows the feasibility of our main results.

Global Attractivity of Positive Periodic Solutions of Delay Differential Equations with Feedback Control

By constructing suitable Liapunov functionals and estimating uniform upper and lower bounds of solutions, sufficient conditions are obtained for the global attractivity of positive periodic solutions of the delay differential system with feedback controldy/dt=y(t)F(t,y(t−τ1(t)),…,y(t−τn(t)),u(t−δ(t))),du/dt=−η(t)u(t)+a(t)y(t−σ(t)). When these results are applied to the periodic logistic equation with several delays and feedback control, some new results are obtained.