Optimal Control and Economic Impact Analysis of Malaria Intervention Strategies Using a Mathematical Modeling Approach

Malaria remains a major public health challenge, particularly in sub-Saharan Africa, because of the complex interaction between human infection dynamics and mosquito vector transmission. In this study, we develop and analyze a deterministic host–vector malaria transmission model that incorporates vaccination, vaccine-induced protection, treatment of infected individuals, and mosquito control through insecticide-treated nets (ITNs). The model describes the coupled transmission dynamics between humans and mosquitoes while accounting for imperfect vaccine protection and the effects of control interventions. The model is calibrated using confirmed malaria case data from Ghana to enhance its biological relevance and practical applicability. We investigate key model properties, including the disease-free equilibrium, endemic equilibrium, control reproduction number, and stability conditions. The analysis demonstrates the presence of backward bifurcation, suggesting that malaria transmission may persist even when the control reproduction number is below unity. This finding emphasizes the importance of implementing sufficiently strong and sustained interventions to achieve effective disease control. We formulate the optimal control problem using Pontryagin’s maximum principle and solve it numerically using the forward–backward sweep method with fourth-order Runge–Kutta integration. The effectiveness of different intervention strategies is assessed based on infection reduction, measured by the area under the infected human and mosquito population curves. We evaluate the economic performance of these strategies using average cost-effectiveness ratios (ACERs) and incremental cost-effectiveness ratios (ICERs) derived from an implementation-cost objective function. Dominance elimination is applied to identify the most efficient intervention strategies. The results show that all considered interventions reduce malaria transmission compared with the uncontrolled scenario. The cost-effectiveness analysis reveals that the all-controls strategy achieves the lowest ACER, indicating the highest economic efficiency per infection averted. However, the combination of treatment and mosquito control provides a favorable balance between effectiveness, cost, and implementation feasibility. The findings demonstrate that integrated human and vector-based interventions, supported by data-driven modeling and an understanding of nonlinear transmission dynamics, are essential for sustainable malaria control in Ghana and other endemic regions.