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A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. (English) Zbl 1070.92034
Summary: 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.

92C60 Medical epidemiology
35K57 Reaction-diffusion equations
92D30 Epidemiology
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