Although artesunate, one of the potent derivatives of the qinghaosu family of drugs for treating falciparum malaria, is already in use in the field, its therapeutic protocol has only been developed empirically by hit-or-miss. A pharmacokinetic–pharmacodynamic (PK–PD) model, required for creating such a protocol, is not straightforward. Artesunate presents extremely fast pharmacokinetics. As a result the stage specificity of its action must be treated explicitly. Also, use of standard PK–PD modelling fails to explain the clinical results. Our PK–PD modelling of its activity leads us to the postulation of the existence of a novel effect: a small fraction of the parasites, as a result of chemotherapeutic pressure, become cytostatic, or ‘dormant’. At this stage, the parasite cycle is halted, making them unsusceptible to further dosing until wakening. This slows down the antimalarial activity of the drug, entailing either many frequent doses or an extended period of treatment and surveillance. Based on our modelling, we suggest a method for deciding on rational models of chemotherapy against falciparum malaria.