Abstract
In developing countries, informal sector is the primary job provider for a significant portion of the workforce. This study aims to analyze how jobs in the informal sector affect the unemployment dynamics of developing nations. To achieve this goal, we formulate a nonlinear mathematical model by categorizing the considered workforce into three distinct classes: unemployed, employed, and self-employed, and include a separate dynamic variable to represent vacancies within the informal sector. The proposed model is analyzed using the qualitative theory of dynamical systems. A threshold quantity known as the reproduction number is derived and using this, one can compute the job generation rate necessary to stabilize the system. It is observed that variations in the reproduction number lead to qualitative changes, such as transcritical (forward or backward) and saddle-node bifurcations in the formulated system. Moreover, we propose an optimal control problem to determine an optimal strategy for government policy implementation in enhancing the employment rate of unemployed individuals and promoting the self-employment of informal employees inside the informal sector. Further, the analytical findings are validated numerically. The obtained results suggest that promoting the self-employment of informal employees for job generation effectively reduces unemployment.