Mathematical Model for the Control of Unemployment in Nigeria Incorporating Vocational Education and Apprenticeship

Background: Youth unemployment presents a significant threat to Nigeria’s socioeconomic stability, resulting in widespread issues such as poverty, insecurity, banditry, inequality, and robbery. Objective: In this paper, mathematical modelling for the control of unemployment in Nigeria incorporating vocational education and apprenticeship was formulated. The model equilibrium points were obtained and the local stability analysis was carried out. Methods: The basic reproduction number Re was computed using the Next Generation Matrix technique and used to determine whether unemployment will persist or be eradicated in Nigeria. Sensitivity analysis was carried out to determine the most sensitive parameters. Results: Numerical simulations were presented in a graphical form to show the effects of sensitive parameters on the reproduction number. The stability analysis shows that unemployment will be eradicated in Nigeria if Re ≤ 1. It was revealed from the sensitivity analysis that the theoretical education graduate employment rate, γ is the most sensitive parameter with −0.9883 and the rate of transition of becoming highly skilled due to vocational education, β is the least sensitive parameter with −0.0409. Conclusions: It was shown from the sensitivity analysis and the graphical presentation that the theoretical education graduate employment rate, γ is the most sensitive negative parameter which will decrease the reproduction number. This implies that when employment is created for the graduates from the higher institutions the unemployment rate will reduce drastically from the society. It is recommended that the government and the private sector owners should create more job for the graduates. Optimal control analysis is recommended for future research to determine the minimal cost for the increase graduate employment rate and motivation of vocational education.