Optimal control strategies and cost-effectiveness analysis of a malaria model

The aim of this paper is to investigate the effectiveness and cost-effectiveness of three malaria preventive measures (use of treated bednets, spray of insecticides and a possible treatment of infective humans that blocks transmission to mosquitoes). For this, we consider a mathematical model for the transmission dynamics of the disease that includes these measures. We first consider the constant control parameters’ case, we calculate the basic reproduction number and investigate the existence and stability of equilibria; the model is found to exhibit backward bifurcation. We then assess the relative impact of each of the constant control parameters measures by calculating the sensitivity index of the basic reproductive number to the model's parameters. In the time-dependent constant control case, we use Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. We also calculate the Infection Averted Ratio (IAR) and the Incremental Cost-Effectiveness Ratio (ICER) to investigate the cost-effectiveness of all possible combinations of the three control measures. One of our findings is that the most cost-effective strategy for malaria control, is the combination of the spray of insecticides and treatment of infective individuals. This strategy requires a 100% effort in both treatment (for 20 days) and spray of insecticides (for 57 days). In practice, this will be extremely difficult, if not impossible to achieve. The second most cost-effective strategy which consists of a 100% use of treated bednets and 87% treatment of infective individuals for 42 and 100 days, respectively, is sustainable and therefore preferable.