In this paper, we propose and analyze a nonlinear mathematical model to study the effect of skill development on unemployment. We assume that government promulgates different levels of skill development programs for unemployed persons through which two different categories of skilled persons, namely, the low-skilled and the highly-skilled persons, are coming out and the highly-skilled persons are able to create vacancies. The model is studied using stability theory of nonlinear differential equations. We find analytically that there exists a unique positive equilibrium point of the proposed model system under some conditions. Also, the resulting equilibrium is locally as well as globally stable under certain conditions. The effective use of implemented policies to control unemployment by providing skills to unemployed persons and the new vacancies created by highly-skilled persons are identified by using optimal control analysis. Finally, numerical simulation is carried out to support analytical findings.
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