A model for transmission of partial resistance to anti-malarial drugs
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1.
Industrial and Financial Mathematics Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132
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2.
Eijkman Institute for Molecular Biology, Jl. Diponegoro 69, Jakarta 10430
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3.
United States Naval Medical Research Unit 2, Jl. Percetakan Negara 29, Jakarta 10560
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Received:
01 November 2008
Accepted:
29 June 2018
Published:
01 June 2009
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MSC :
92D30.
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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.
Citation: Hengki Tasman, Edy Soewono, Kuntjoro Adji Sidarto, Din Syafruddin, William Oscar Rogers. A model for transmission of partial resistance to anti-malarial drugs[J]. Mathematical Biosciences and Engineering, 2009, 6(3): 649-661. doi: 10.3934/mbe.2009.6.649
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Abstract
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.
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