Abstract
One of the major macroeconomic issues that plagues any economy and impedes its evolution is unemployment. To address this major macroeconomic concern, we have developed and investigated a delayed mathematical model of unemployment with four dynamic variables. The three dynamic variables represent the segregation of the population into three classes: the unemployed class, the employed class, and the retired class. Also, an additional variable for new vacancies available for recruitment is considered in the model as the fourth dynamic variable. The development of skills and the creation of jobs for the unemployed segment of society are two key factors that greatly aid in the treatment of this important macroeconomic issue. Since these procedures require time, we have included time delays in skill development and vacancy creation. The existence of a unique employment equilibrium point has been established, and the stability of the non-delayed system around the equilibrium point has been analysed. Also, the system dynamics for various delay combination scenarios have been examined. It has been proven in each scenario that when the respective time delay exceeds a certain threshold value, the considered model experiences a Hopf bifurcation around the employment equilibrium point. Additionally, an examination of the Lyapunov stability and Hopf bifurcation properties has been carried out. Lastly, numerical simulations are performed to confirm the analytical results. Our analysis shows that it is not possible to take large values for both the time delays without causing system instability. Our work emphasizes the necessity of including time delays in the unemployment model to better understand the system dynamics, which will help devise and adopt the necessary strategies to reduce the unemployment rate. It is deduced from the quantitative observations that one of the key strategies for reducing unemployment can be to encourage and raise public awareness about skill development. Additionally, it is advised that policymakers ensure that policies for vacancy creation are designed by considering that the rate of vacancy creation is commensurate with the number of unemployed individuals.
Published Version
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