Clearance of young parasite forms following treatment of falciparum malaria in humans: comparison of three simple mathematical models.
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.
Davis
T M
TM
University of Western Australia, Department of Medicine, Fremantle Hospital, Australia.
Martin
R B
RB
D000293:Adolescent; D000328:Adult; D000962:Antimalarials / Q000494:pharmacology*; D037621:Artemisinins; D004359:Drug Therapy, Combination; D006801:Humans; D007700:Kinetics; D007783:Lactones / Q000494:pharmacology; D016014:Linear Models; D016778:Malaria, Falciparum / Q000097:blood / Q000188:drug therapy*; D015767:Mefloquine / Q000494:pharmacology; D008875:Middle Aged; D008954:Models, Biological; D011739:Pyrimethamine / Q000494:pharmacology; D012717:Sesquiterpenes / Q000494:pharmacology; D013413:Sulfadoxine / Q000494:pharmacology
D000962:Antimalarials; D037621:Artemisinins; D007783:Lactones; D012717:Sesquiterpenes; D013413:Sulfadoxine; D015767:Mefloquine; C075875:artemisin; D011739:Pyrimethamine