A singular perturbation theorem for evolution equations and time-scale arguments for structured population models

Abstract

In this paper we present a generalization of a finite dimensional singular perturbation theorem to Banach spaces. From this we obtain sufficient conditions under which a faithful simplification by a time-scale argument is justified for age-structured models of slowly growing populations. An explicit formulation for the approximating, ordinary differential equation, model is obtained. Finally, we describe the precise class of structured population models for which we conjecture that a similar result holds.