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Optimal Control of Malaria Transmission in Two Regions Using Treatment and Spraying

Dwilaras Athina, Toni Bakhtiar, Jaharuddin

Abstract



In 1890, Sir Ronald Ross demonstrated the life-cycle of the malaria parasite in mosquito, and he developed a simple model, that is the Ross Model. The model has been developed by many researchers, some of them are Johansson and Leander (2010). In this study, a model of the transmission of malaria in two regions, which was developed by Johansson and Leander, is equipped with two control variables. First, the treatment to reduce the number
of susceptible humans who become infected by infectious mosquitoes bites. Second, the effort of reducing mosquito population through spraying. Same rate of movement. The 4th-order Runge Kutta method is 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. When controls are applied to both regions, integrated control is most optimal to minimize the control performance in the two regions.

Keywords


malaria, optimum control model, Pontryagin maximum principle, Runge-Kutta method.

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