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

摘要

In the present paper we consider a system of delay differentialequations describing the spread of avian influenza between birds migratingbetween two territories. We study the asymptotic stability of the zerosolution and the periodic solution corresponding to healthy birds. Weestablish estimates of solutions characterizing the rate of convergence tothe zero solution, and also attraction domains and estimates of solutionscharacterizing the rate of convergence to the periodic solution. The resultsare obtained by the use of a solution to the special boundary valueproblem for the Lyapunov differential equation.