COST-EFFECTIVENESS ANALYSIS OF PUBLIC HEALTH INTERVENTIONS USING LINEAR AND NONLINEAR PROGRAMMING

In resource-constrained health systems like Ghana, the ability to optimize public health interventions can determine whether thousands of lives are saved or lost. This study applied linear and nonlinear programming models to assess the cost-effectiveness of health interventions across 105 district-level cases from 2020 to 2024, addressing how mathematical programming influences efficiency, budget utilization, and marginal health gains under real-world constraints. Using secondary data from the Ghana Health Service, WHO, and WAHO, the study employed descriptive statistics, Pearson correlation, and multiple linear regression to analyze objective function construction, quadratic cost modeling, and time-resource trade-offs, while controlling for funding and infrastructure. Regression results revealed low explanatory power (R² = 0.022), with the strongest correlation being r = -0.123 for objective function design. Despite limited statistical significance, descriptive results confirmed that linear programming reduced vaccine wastage by 27% and improved efficiency indices by up to 48%, while nonlinear models achieved a 33% improvement in forecasting costs under dynamic scenarios. The study concludes that mathematical programming enhances policy implementation when aligned with local capacity and real-time data. It recommends scaling hybrid optimization models, integrating algorithmic tools into national health systems, and investing in computational infrastructure and staff training to institutionalize data-driven planning.