Mathematical Model of the Effect of Out-of-School Children on the Development of Northern Nigeria

Samenvatting

Out-of-school children represent a significant developmental challenge in Northern Nigeria, where low enrollment and high dropout rates perpetuate cycles of poverty and underdevelopment. This paper presents a deterministic compartmental model that captures the dynamic relationship between educational attainment and socioeconomic development. The model stratifies the population into six compartments: school-age children not yet enrolled, in-school children, out-of-school children, skilled individuals, economic productivity index, and development index. The positivity and boundedness of solutions are established to ensure biological feasibility. We obtain the out-of-school-free equilibrium and endemic equilibrium, and calculate the basic reproduction number $\mathcal{R}_0$ using the next-generation matrix approach. Stability analysis reveals that the out-of-school-free equilibrium is locally asymptotically stable if $\mathcal{R}_0 < 1$ and unstable if $\mathcal{R}_0 > 1$. Sensitivity analysis identifies key parameters driving the persistence of out-of-school children. The model reveals critical policy insights, including threshold conditions for intervention effectiveness and development self-sustainability. Numerical simulations illustrate the effects of key parameters on system dynamics, highlighting the importance of integrated interventions combining enrollment enhancement, re-enrollment programs, and direct development investment