Plasmodium falciparum malaria is one of mankind's main killers. Part of the parasite's life-cycle is spent in human blood, mainly as asexual stages. A fraction of the asexual parasites develops into gametocytes (gamete precursors) while sequestered in deep tissues. After re-entering the circulation, gametocytes can be picked up by a mosquito to continue the parasite's life-cycle. We present estimates of the conversion probability from asexual parasites to circulating gametocytes and of the gametocytes' sequestration and circulation times, obtained for the first time by fitting a dynamic model to individual patients' histories (daily records of 113 neurosyphilitic patients undergoing malariatherapy). The model assumes that the conversion probability can vary among the successive waves of asexual parasitaemia of a patient, and that gametocytes die at an age-dependent rate which increases under high asexual parasite densities. On average, 1 gametocyte per 156 asexual parasites (range 7.4-3700) is produced. The most remarkable findings are the large individual variation of conversion probabilities and circulation times, the average gametocyte circulation time of 6.4 days (range 1.3-22.2 days) which is more than twice the currently accepted value, and the large variation of conversion probabilities among successive waves of asexual parasitaemia without any particular time pattern. The latter finding could be explained by an association between conversion probability and variation of PfEMP1.