The dynamics of Plasmodium falciparum blood-stage infection

We develop a system of ordinary differential equations to model the dynamics of the blood-stages of the malaria parasite, Plasmodium falciparum. Variants of the model allow the study of a set of hypotheses about the interaction of the parasite with the host immune system, in particular with regard to the stimulation of the immune response and the regulation of the rate of conversion from the pathogenic, asexual to the transmissible, sexual blood stage. The values of several parameters of our models can be estimated from previous empirical work. Although the dynamics of the variants differ somewhat, in each variant some set of values of the three unconstrained parameters, different from one variant to the next, produces a range of behaviours quantitatively consistent with those reported from clinical studies. Some parameter values produce infections which quickly terminate, while others approach a chronic equilibrium level or produce oscillations, with repeated severe peaks separated by periods of undetectable parasitemia. We examine these and several other distinctions that might be used to assess model variants and focus further empirical research.