Mathematical Model for Malaria Transmission with Optimal Control Strategies and Their Effects

Abstract

In this paper, we propose a SEIR-SEI optimal control model of malaria transmission with standard incidence rate. We present four control strategies to prevent the prevalence of infection in the society. In order to do this, we introduce an optimal control problem with an objective function, where the four control functions, prevention using Long-Lasting Insecticide Treated Net(LLITN) u1(t), the control effort on malaria treatment of infected individuals u2(t), the insecticide spray on the breeding grounds for the mosquito u3(t), the prevention using Indoor Residual Spraying u4(t); have been used as control measures for exposed and infected individuals. We show the existence of an optimal control pair for the optimal control problem and derive the optimality conditions. Our numerical simulation suggests that the two controls strategies u1(t)and u2(t) are more effective than the other control strategies in controlling (reducing) the number of exposed and infected individuals and also in increasing the number of recovered individuals.