American Institute of Mathematical Sciences

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2005, 2(2): 227-238. doi: 10.3934/mbe.2005.2.227

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

Nicolas Bacaër 1, and  Cheikh Sokhna 2,

1. 

Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedex, France
2. 

Laboratoire de Paludologie, Institut de Recherche pour le Développement, B.P. 1386, Dakar, Senegal

Received  July 2004 Revised  February 2005 Published  March 2005

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.
Keywords: propagation speed., malaria, reaction-diffusion, resistance.
Mathematics Subject Classification: 92D30, 35K5.
Citation: Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227-238. doi: 10.3934/mbe.2005.2.227
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