Optimal Control of Malaria Transmission: Analysis of Mosquito’s Bias

It is well-known that mosquitoes like specific smell or odor from the human so that some people is likely to be bitten more than other people. In recent years, it was investigated that mosquitoes like people more who has malaria parasite, especially gametocyte. This effect is called a mosquito-bias effect. As the dynamics of vector-borne disease is highly related to vector’s behavior, it is worth studying this feeding behavior of mosquitoes. The aim of this paper is to study necessity of a mosquito-bias effect when estabilshing control strategy. For this, we used Chamchod’s model to investigate a control problem. To show which parameter has high influences to change R0, sensitivity analysis was implemented. This says that prevention is most important policy to reduce malaria endemic. Next, time-dependent optimal control problem was studied. We used Pontryagin’s maximal principle to derive necessary conditions of the problem. Especially, we paid attention to cost-effectiveness of control intervention. It shows that a mosquito-bias effect doesn’t influence to change control policy, but serious errors are occurred as a view of a control effectiveness if we do not consider a mosquito-bias effect.