Optimal Control of Malaria Transmission using Insecticide Treated Nets and Spraying

3rd International Seminar On Sciences "Sciences On Precision And Sustainable Agriculture"

Athina, D.^1 ; Bakhtiar, T.^1 ; Jaharuddin^1

Department of Mathematics, Faculty of Mathematics and Natural Science, Bogor Agricultural University, Indonesia^1

关键词: Control variable;    Differential equation systems;    Human being;    Malaria transmission;    Numerical results;    Optimal controls;    Optimality conditions;    Optimization problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/58/1/012027/pdf
DOI  :  10.1088/1755-1315/58/1/012027

来源: IOP

【 摘 要 】

In this paper, we consider a model of the transmission of malaria which was developed by Silva and Torres equipped with two control variables, namely the use of insecticide treated nets (ITN) to reduce the number of human beings infected and spraying to reduce the number of mosquitoes. Pontryagin maximum principle was applied to derive the differential equation system as optimality conditions which must be satisfied by optimal control variables. The Mangasarian sufficiency theorem shows that Pontryagin maximum principle is necessary as well as sufficient conditions for optimization problem. The 4th-order Runge Kutta method was then performed to solve the differential equations system. The numerical results show that both controls given at once can reduce the number of infected individuals as well as the number of mosquitoes which reduce the impact of malaria transmission.