In this paper, a deterministic malaria transmission model in the presence of a drug-resistant strain is investigated. The model is studied using stability theory of differential equations, optimal control, and computer simulation. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved in the absence of a drug-resistant strain in the population. The existence of multiple endemic equilibria is also established. Both the Sensitivity Index (SI) of the model parameters and the Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures are determined. Our results revealed among others that the most cost-effective strategy for drug-resistant malaria control is the combination of the provision of basic amenities (such as access to clean water, electricity, good roads, health care, and education) and treatment of infective individuals. Therefore, more efforts from policy-makers on the provisions of basic amenities and treatment of infectives would go a long way to combat the malaria epidemic.
Keywords: Drug-resistant strain; Malaria; Optimality system; Sensitivity analysis; Stability.