A Delay Mathematical Model for the Control of Unemployment

Abstract

In this paper, we have proposed and analyzed a nonlinear mathematical model for control of unemployment in the developing countries by incorporating time delay in creating new vacancies. In the modeling process, three dynamic variables have been considered, namely, (i) number of unemployed persons, (ii) number of employed persons, and (iii) number of newly created vacancies. The model is studied using stability theory of differential equations. It is found that the model has only one equilibrium, which is stable in absence of delay. It is further shown that this stable equilibrium becomes unstable as delay crosses some critical value. This critical value of delay has been obtained analytically. Further, direction of Hopf bifurcation and stability of the bifurcating periodic solutions are studied by applying the normal form theory and the center manifold theorem. Numerical simulation of the model has been carried out to illustrate the analytical results.