Modeling the Effect of Informal and Formal Jobs on the Dynamics of Unemployment

The limited availability of formal jobs in developing nations always heightens the challenge for unemployed individuals in securing regular employment. Temporary employment in the informal sector serves as a source to fulfill their basic needs and enhance their employable skills. In this paper, we introduce a nonlinear mathematical model to study the effect of informal and formal jobs on the dynamics of unemployment. For the model formulation, we categorize the labor force into three classes: unemployed, temporary employed, and regularly employed. A separate dynamical variable is used to represent the available temporary vacancies. It is assumed that temporarily employed individuals may transition into regular employment or self-employment. Furthermore, self-employed individuals contribute to generating temporary vacancies within the informal sector. The long-term behavior of the proposed system is analyzed using the qualitative theory of differential equations. A quantity known as the reproduction number of the system is derived, and it is found that the occurrence of multiple bifurcations for the proposed system is influenced by the value of this threshold quantity. Furthermore, we validate our analytical findings numerically. The findings of this study illustrate that an increase in the shifting rate of individuals from temporary to regular employment is not always effective in increasing the number of regularly employed individuals. Additionally, an increase in the transition of temporarily employed individuals into self-employment, coupled with their involvement in creating more temporary jobs, proves beneficial in reducing unemployment.