A Mathematical Model to Analyze the Effects of Nigeria’s Deregulated Economy on Healthcare Funding

Abstract

Background: Nigeria’s deregulated economy, initiated in 2023 through fuel subsidy removal and exchange rate unification, has fundamentally altered the fiscal environment with significant implications for healthcare financing. This study develops a mathematical model to quantify the relationship between deregulation‑induced macroeconomic changes and healthcare funding outcomes.
Methods: A system dynamics model incorporating macroeconomic and fiscal variables was constructed using ordinary differential equations. The model integrates oil revenue, non‑oil revenue, exchange rate, inflation, fiscal deficit, and healthcare allocation. Data from 2020–2025 were used for parameter estimation. Sensitivity analysis and scenario modeling assessed policy impacts.
Results: The model reveals a structural break in healthcare funding dynamics post‑deregulation. The derived equation H = αR_total + βΔER + γπ + δFD demonstrates that a 10% naira depreciation reduces real healthcare spending by 6.2% (p<0.001). Under moderate shock scenarios, projected healthcare funding shortfalls range from ₦380–620 billion annually. The model identifies an optimal fiscal rule: allocating 15% of oil windfall revenues to a Health Stabilization Fund would reduce funding volatility by 42% (95% CI: 35–49%). Sensitivity analysis shows health outcomes are most responsive to primary healthcare funding (elasticity 0.68) compared to tertiary care (0.31). The post‑deregulation coefficient for health share of oil revenue decreased from 0.038 to 0.032 (p=0.02), reflecting competing expenditure priorities.
Conclusion: Mathematical modeling demonstrates that deregulation creates competing fiscal pressures on healthcare funding through exchange rate effects, inflationary erosion, and competing expenditure priorities. The findings support establishment of a Health Stabilization Fund linked to oil windfall revenues and constitutional guarantees for primary healthcare funding.