A reaction-diffusion system modeling the spread of resistance to an antimalarial drug
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1.
Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedex
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2.
Laboratoire de Paludologie, Institut de Recherche pour le Développement, B.P. 1386, Dakar
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Received:
01 July 2004
Accepted:
29 June 2018
Published:
01 March 2005
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MSC :
92D30, 35K57.
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A mathematical model representing the diffusion of resistance to
an antimalarial drug is developed. Resistance can spread only when
the basic reproduction number of the resistant parasites is bigger
than the basic reproduction number of the sensitive parasites
(which depends on the fraction of infected people treated with the
antimalarial drug). Based on a linearization study and on numerical simulations,
an expression for the speed at which resistance
spreads is conjectured. It depends
on the ratio of the two basic reproduction numbers,
on a coefficient representing the diffusion of mosquitoes,
on the death rate of mosquitoes infected by resistant parasites,
and on the recovery rate of nonimmune humans infected by resistant parasites.
Citation: Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug[J]. Mathematical Biosciences and Engineering, 2005, 2(2): 227-238. doi: 10.3934/mbe.2005.2.227
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Abstract
A mathematical model representing the diffusion of resistance to
an antimalarial drug is developed. Resistance can spread only when
the basic reproduction number of the resistant parasites is bigger
than the basic reproduction number of the sensitive parasites
(which depends on the fraction of infected people treated with the
antimalarial drug). Based on a linearization study and on numerical simulations,
an expression for the speed at which resistance
spreads is conjectured. It depends
on the ratio of the two basic reproduction numbers,
on a coefficient representing the diffusion of mosquitoes,
on the death rate of mosquitoes infected by resistant parasites,
and on the recovery rate of nonimmune humans infected by resistant parasites.
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