A Compartmental Mathematical Model for the Control of Financial Debt Dynamics in Nigeria Using Leadership Intelligence Quotient (LIQ)

Abstract

The rapid expansion of public debt in developing economies requires mathematical frameworks capable of explaining the dynamic mechanisms underlying debt accumulation and identifying effective control strategies. This study develops a deterministic compartmental mathematical model to investigate the transmission dynamics of Nigeria's public debt by explicitly integrating Leadership Intelligence Quotient (LIQ) as institutional control variables. The model partitions the system into four interacting compartments representing the people, economic productivity, debt accumulation, and leadership quality, and using a system of nonlinear ordinary differential equations to describe their interactions. Fundamental qualitative properties of the model, including positivity, boundedness, and the existence of feasible equilibrium solutions, were established. The Next Generation Matrix approach was employed to derive the basic reproduction number, while local stability analysis, sensitivity analysis, and numerical simulations were conducted to evaluate the influence of model parameters on public debt dynamics. The analysis yielded a basic reproduction number of R₀ = 0.0667, indicating that the public debt system remains asymptotically stable under the prevailing control conditions. Sensitivity analysis identified debt transmission, governance inefficiency, and low leadership intelligence as the principal drivers of debt persistence, whereas improvements in governance effectiveness and leadership quality significantly reduced debt propagation and accelerated convergence toward equilibrium. Numerical simulations further confirmed that strengthening institutional quality suppresses debt accumulation and promotes long-term fiscal stability. The proposed compartmental framework provides a novel mathematical approach for analysing sovereign debt dynamics by explicitly integrating Leadership Intelligence Quotient (LIQ) into a deterministic nonlinear model. The findings demonstrate that improvements in governance quality and leadership capacity are critical to achieving long-term public debt sustainability in Nigeria. Accordingly, the study recommends sustained governance reforms, leadership capacity development, and institutional strengthening as essential strategies for maintaining long-term fiscal stability.