Optimal Control Strategies and Cost Effectiveness Analysis of a Malaria Transmission Model

Abstract

In this paper, a non-linear model with three control parameters for household of malaria has been study. The disease free equilibrium is obtained and the basic reproduction number is computed using the next generation matrix. We carry out cost evaluation of the model to optimize the cost of the intervention in the objective functional using Pontryagins’s Maximum Principle (PMP). We apply the optimal control strategy to investigate and analyze the optimal cost for controlling the transmission of malaria using treated bednets, treatment and indoor residual spray as parameters. Numerical simulation has been carry out using Runge-Kutta of order four to calculate the incremental cost effectiveness ratio () for the implementation of various combinations of the parameters to determine the most cost effective strategy that check the spread of the disease. Our findings show that the most cost-effective strategy to check the spread of malaria is strategy F (the combination of treatment of infected individuals and indoor residual spray parameters).

Keywords: Optimal Control, Malaria Transmission, Cost-Effectiveness, Treated Bednets, Treatment, Indoor Spray