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The purpose of this paper is to develop and analyze a mathematical model that represents the problem of unemployment in poor countries with limited availability of jobs. We are interested in studying the effect of training programs on the model's dynamics. These training programs aim to improve the skills of unemployed people, contributing to a reduction of the unemployment rate. The model consists of a system of four ordinary differential equations; two equilibria of the model are found: one of which is the employment free equilibrium and the other corresponds to the presence of employment. The existence and stability analysis of both equilibria depend on the basic reproduction number which is found using the method of next generation matrix. However, this number depends on the model parameters which are usually unknown. Hence, we propose to estimate them using the modulating function-based method. Moreover, we study the existence of transcritical bifurcation with the rate of training as a bifurcation parameter. Finally, we support our qualitative results using numerical simulations. [ABSTRACT FROM AUTHOR]