Stability analysis of an unemployment model with time delay

Abstract

In this paper, we have developed and analyzed an unemployment model of differential equations with time delay, taking into consideration the role of government for the support of vacancies creation. We investigated the dynamic behavior of the model system and carried out a stability analysis. Conditions for the nonexistence of delay induced instability and the local asymptotic stability of the positive equilibrium points are derived. Moreover, sufficient conditions for global asymptotic stability of the positive equilibrium points are obtained. Numerical results have been given to show the effectiveness of the theoretical results.