A delayed model of unemployment with a general nonlinear recruitment rate

Abstract

This article examines unemployment phenomenon using delay differential equations. Our objective consists in evaluating the influence of the delay and recruitment function on the stability of the equilibrium. We propose a nonlinear function of general type. The dynamics of this model is analyzed by constructing a Lyapunov function. First, we prove the existence and uniqueness of positive equilibrium. Next, we demonstrate the overall stability of this equilibrium. Finally, we present some numerical examples (bilinear function, with separate variables and general) to illustrate and compare our results in different situations.