A malaria model with controls on mass treatment and insecticide
a Department of Mathematics, Faculty of Science and Technology, Universitas
Airlangga Kampus C Unair, Jl. Mulyorejo Surabaya 60115, Indonesia
b Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Indonesia Kampus UI Depok, Depok 16424, Indonesia
b Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Indonesia Kampus UI Depok, Depok 16424, Indonesia
Abstract
In this
paper we derive a mathematical model for malaria transmis-sion in population.
We use controls on mass treatment and insecticide to reduce the number of
infected hosts and infected vectors. The model considers human, larvae and
mosquito populations. The host popula- tion is assumed constant, but the larvae
and vector populations vary. First, we investigated the existence and stability
of equilibria of the model without control based on the basic reproduction
ratio. Then, the Pontryagins maximum principle is used to characterize the
optimal control. The optimality system is derived and solved numerically for
several scenarios. © 2013 Fatmawati and Hengki Tasman.
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