An optimal control strategy to reduce the spread of malaria resistance

• We model malaria transmission considering the resistance of malaria parasites to the anti-malarial drugs.
• We investigated the existence and stability of equilibrium of the model.
• We apply the mass treatment and insecticide as optimal control strategies.
• We perform the effectiveness of the optimal control to reduce the number of infected hosts and vectors.

This paper presents a mathematical model of malaria transmission considering the resistance of malaria parasites to the anti-malarial drugs. The model also incorporates mass treatment and insecticide as control strategies. We consider the sensitive and resistant strains of malaria parasites in human and mosquito populations. First, we investigated the existence and stability of equilibria of the model without control based on two basic reproduction ratios corresponding to the strains. Then, the Pontryagins Maximum Principle is applied to derive the necessary conditions for optimal control. Simulation results show the effectiveness of the optimal control to reduce the number of infected hosts and vectors.