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A reaction-diffusion system modeling the spread of resistance to an antimalarial drug

1. Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedex
2. Laboratoire de Paludologie, Institut de Recherche pour le Développement, B.P. 1386, Dakar

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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Keywords propagation speed.; malaria; reaction-diffusion; resistance

Citation: Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences and Engineering, 2005, 2(2): 227-238. doi: 10.3934/mbe.2005.2.227

 

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Copyright Info: 2005, Nicolas Bacaër, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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