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2009, 6(3): 649-661. doi: 10.3934/mbe.2009.6.649

A model for transmission of partial resistance to anti-malarial drugs

Hengki Tasman 1, , Edy Soewono 1, , Kuntjoro Adji Sidarto 1, , Din Syafruddin 2, and  William Oscar Rogers 3,

1. 

Industrial and Financial Mathematics Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia, Indonesia, Indonesia
2. 

Eijkman Institute for Molecular Biology, Jl. Diponegoro 69, Jakarta 10430, Indonesia
3. 

United States Naval Medical Research Unit 2, Jl. Percetakan Negara 29, Jakarta 10560, Indonesia

Received  November 2008 Revised  February 2009 Published  June 2009

Anti-malarial drug resistance has been identified in many regions for a long time. In this paper we formulate a mathematical model of the spread of anti-malarial drug resistance in the population. The model is suitable for malarial situations in developing countries. We consider the sensitive and resistant strains of malaria. There are two basic reproduction ratios corresponding to the strains. If the ratios corresponding to the infections of the sensitive and resistant strains are not equal and they are greater than one, then there exist two endemic non-coexistent equilibria. In the case where the two ratios are equal and they are greater than one, the coexistence of the sensitive and resistant strains exist in the population. It is shown here that the recovery rates of the infected host and the proportion of anti-malarial drug treatment play important roles in the spread of anti-malarial drug resistance. The interesting phenomena of ''long-time" coexistence, which may explain the real situation in the field, could occur for long period of time when those parameters satisfy certain conditions. In regards to control strategy in the field, these results could give a good understanding of means of slowing down the spread of anti-malarial drug resistance.
Keywords: dynamical system., basic reproduction ratio, anti-malarial drug resistance, mathematical epidemiology, treatment proportion.
Mathematics Subject Classification: 92D3.
Citation: Hengki Tasman, Edy Soewono, Kuntjoro Adji Sidarto, Din Syafruddin, William Oscar Rogers. A model for transmission of partial resistance to anti-malarial drugs. Mathematical Biosciences & Engineering, 2009, 6 (3) : 649-661. doi: 10.3934/mbe.2009.6.649
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