Asymptotic properties of solutions to a system describing the spread of avian influenza

In the present paper we consider a system of delay differential equations describing the spread of avian influenza between birds migrating between two territories. We study the asymptotic stability of the zero solution and the periodic solution corresponding to healthy birds. We establish estimates of solutions characterizing the rate of convergence to the zero solution, and also attraction domains and estimates of solutions characterizing the rate of convergence to the periodic solution. The results are obtained by the use of a solution to the special boundary value problem for the Lyapunov differential equation.