Dynamic Relationship Between Informal Sector and Unemployment: A Mathematical Model

Shortage of formal jobs, lack of skills in workforce and increasing human population proliferate the informal sector. This sector provides an opportunity to unskilled workers to gain skills along with earnings. In this paper, a deterministic nonlinear mathematical model is developed to study the effects of informal skill learning and job generation on unemployment. For the formulated system, feasibility of equilibria and their stability properties are discussed. A pertinent quantity (${{ℛ}}_0$), known as the reproduction number, is calculated and it is shown that the formulated system undergoes transcritical, saddle-node, Hopf and Bogdanov–Takens bifurcations on the variation of ${{ℛ}}_0$. The analytically obtained results are validated through numerical simulations. The results obtained from this study indicate that a substantial rate of job generation by self-employed individuals has a stabilizing effect on the system. Moreover, self-employment along with informal skill acquisition through engaging in informal work proves to be an effective measure in curbing the issue of unemployment in society.