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To characterize post-treatment clearance of young forms of Plasmodium falciparum from the blood, three differential equation models, a linear decline, a linear then logarithmic decline, and the Michaelis-Menten (MM) kinetic equation, were fitted to log-transformed serial parasite counts from 30 semi-immune patients with synchronous parasitaemias allocated one of six antimalarial drug regimens. The first two equations were solved analytically. The MM equation was solved numerically using a fifth-order Runge-Kutta method. For each equation, parasite clearance was assumed stochastic and log-transformed parasite counts were assumed to be normally distributed at each time-point. Comparisons between models were by Minimum Akaike Information Criterion Estimate. A constrained MM equation fitted the data at least as well as the other two models in 5 of 6 drug groups and also when pooled data were analysed, providing a single index which could be used in drug efficacy studies in similar situations or as part of more complex models that encompass asynchronous, complicated infections.

Clearance of young parasite forms following treatment of falciparum malaria in humans: comparison of three simple mathematical models