Modelling the Transition of Asexual Blood Stages of Plasmodium falciparum to Gametocytes

In this paper, we investigate the transition of asexual blood stages of P. falciparum to gametocytes. The study is based on daily data, collected from 262 individual courses of parasitaemia. We propose several mathematical models that follow biological reasoning. The models are fitted with maximum likelihood and are compared with each other. The models differ in the assumptions made about the mortality of circulating gametocytes and about the transition rate of the asexual parasites. Gametocyte mortality is modelled as being (i) constant over time, (ii) linearly increasing over time, (iii) linearly increasing over gametocyte age, and (iv) exponentially increasing over gametocyte age, respectively. The transition rate is either kept constant per patient or piecewise constant within intervals that correspond to waves of asexual parasitaemia which are assumed to be caused by different Pfemp1-variants. According to likelihood ratio tests, the models with age-dependent mortality rate and wave-dependent transition rates are superior to the models with constant transition rate and/or constant or time-dependent mortality rate. The best fits are reached for models with exponentially increasing (Gompertz-type) mortality. Furthermore, an impact of high asexual parasite densities on the survival of gametocytes, interpreted as a cytokine-mediated effect, is evident in some cases.