Plasmodium falciparum parasitaemia described by a new mathematical model

L.  MOLINEAUX  a1, H. H.  DIEBNER  a2 a3, M.  EICHNER  a2, W. E.  COLLINS  a4, G. M.  JEFFERY  a5 and K.  DIETZ  a2 c1
a1 World Health Organization (Retired )
a2 Department of Medical Biometry, University of Tübingen, Westbahnhofstrasse 55, D-72070 Tübingen, Germany
a3 Center for Art and Media, Lorenzstrasse 19, D-76135 Karlsruhe, Germany
a4 Centers for Disease Control and Prevention, US Public Health Service, Department of Health and Human Services, Atlanta, GA, USA
a5 U.S. Public Health Service (Retired )


A new mathematical model of Plasmodium falciparum asexual parasitaemia is formulated and fitted to 35 malaria therapy cases making a spontaneous recovery after primary inoculation. Observed and simulated case-histories are compared with respect to 9 descriptive statistics. The simulated courses of parasitaemia are more realistic than any previously published. The model uses a discrete time-step of 2 days. Its realistic behaviour was achieved by the following combination of features (i) intra-clonal antigenic variation, (ii) large variations of the variants' baseline growth rate, depending on both variant and case, (iii) innate autoregulation of the asexual parasite density, variable among cases, (iv) acquired variant-specific immunity and (v) acquired variant-transcending immunity, variable among cases. Aspects of the model's internal behaviour, concerning variant dynamics, as well as the respective contributions of the three control mechanisms (iii) – (v), are displayed. Some implications for pathogenesis and control are discussed.

(Received April 27 2000)
(Revised October 13 2000)
(Accepted October 15 2000)

Key Words: Plasmodium falciparum; mathematical model; malaria therapy; PfEMP1.

c1 Corresponding author: Department of Medical Biometry, University of Tübingen, Westbahnhofstrasse 55, D-72070, Tübingen, Germany. Tel: +49 7071 29 72112. Fax: +49 7071 29 5075. E-mail: