A malaria model with controls on mass treatment and insecticide

Fatmawati^a ,

Tasman, H.^b 

^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 

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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