The development of malaria due to Plasmodium falciparum is a complex, multi-stage process. It is usually characterized by an exponential growth in the number of parasite-infected erythrocytes, followed by marked oscillations in this number with a period of 48 h, which are eventually dampened. This course of events has been the subject of various mathematical models. In this paper we propose a new mathematical model for the in-host asexual erythrocytic development of P. falciparum malaria. Synchronicity of the infection is shown to be an inherent feature of infection, irrespective of the duration of merozoite release from the liver. It will, therefore, cause periodic symptoms, as known in malaria patients. We also simulate the effects of an induced host immune response and show how the level of immunity affects the development of disease. The simulations fit well with the clinical observations. We show how infection can become asynchronous and discuss the effect of desynchronization on the circulating and total parasitaemia and demonstrate that synchronized broods will show parasitaemia fluctuations.