Mathematical approach to optimal and cost-effective strategies for malaria control in Ghana

Malaria continues to pose a serious public health burden across many tropical regions, with the greatest impact in sub-Saharan Africa, where it causes significant morbidity and mortality despite extensive control efforts. The persistence of the disease underscores the need for effective data-driven strategies that optimize limited resources. This study develops and evaluates a deterministic compartmental model to describe the transmission dynamics of malaria between humans and mosquitoes, explicitly accounting for the developmental stages of the mosquito population. The model is calibrated using malaria data from Ghana spanning 2011 to 2022, yielding a good fit with a mean squared error of 0.0004 and an estimated basic reproduction number of R0=2.632606, confirming sustained endemic transmission. The positivity, boundedness, and global stability of the model are established. Both local and global sensitivity analyses were conducted using the normalized forward sensitivity index and Latin Hypercube Sampling combined with Partial Rank Correlation Coefficients, revealing that the transmission parameters ρ1, ρ2, ρ3, and the mosquito mortality rate α2 play dominant roles in driving disease transmission. Informed by these findings, three time-dependent control variables, namely preventive measures (u1), vector control (u2), and treatment (u3), were incorporated to assess optimal intervention strategies using Pontryagin’s Maximum Principle. The results show that applying these interventions simultaneously can significantly reduce infection levels and mosquito populations. The cost-effectiveness analysis, based on the Average Cost-Effectiveness Ratio (ACER) and the Incremental Cost-Effectiveness Ratio (ICER), identified vector control strategies such as larviciding, habitat modification, and the Sterile Insect Technique (SIT) as the most cost-effective approach. Based on these findings, it is recommended that public health programs in Ghana and similar endemic settings prioritize vector control interventions, particularly larviciding, habitat modification, and the Sterile Insect Technique (SIT), as the most cost-effective strategy for reducing malaria transmission. While combining all three interventions yields the greatest reduction in infections, vector control alone offers the best health benefit per unit cost, making it the preferred strategy under resource-constrained conditions.