Global dynamics of Nicholson-type delay systems with applications

Abstract

Models of marine protected areas and B-cell chronic lymphocytic leukemia dynamics that belong to the Nicholson-type delay differential systems are proposed. To study the global stability of the Nicholson-type models we construct an exponentially stable linear system such that its solution is a solution of the nonlinear model. Explicit conditions of the existence of positive global solutions, lower and upper estimations of solutions, and the existence and uniqueness of a positive equilibrium were obtained. New results, obtained for the global stability and instability of equilibria solutions, extend known results for the scalar Nicholson models. The conditions for the stability test are quite practical, and the methods developed are applicable to the modeling of a broad spectrum of biological processes. To illustrate our finding, we study the dynamics of the fish populations in Marine Protected Areas.