Optimal control of malaria chemotherapy

We present an intra-host mathematical model of malaria that describes the interaction of the immune system with the blood stage malaria merozoites. The model is modified by incorporating the effects of malaria drugs that target blood stage parasites. The optimal control represents a percentage effect of the chemotherapy of chloroquine in combination with chlorpheniramine on the reproduction of merozoites in erythrocytes. First we maximize the benefit based on the immune cells, and minimize the systemic cost based on the percentage of chemotherapies given and the population of merozoites. An objective functional to minimize merozite reproduction and treatment systemic costs is then built. The existence and uniqueness results for the optimal control are established. The optimality system is derived and the Runge-Kutta fourth order scheme is used to numerically simulate different therapy efforts. Our results indicate that highly toxic drugs with the compensation of high infection suppression have the potential of yielding better treatment results than less toxic drugs with less infection suppression potential or high toxic drugs with less infection suppression potential. In addition, we also observed that a treatment protocol with drugs with high adverse effects and with a high potential of merozoite suppression can be beneficial to patients. However, an optimal control strategy that seeks to maximize immune cells has no potential to improve the treatment of blood stage malaria.