Problems with continuous-time malaria models in describing gametocytogenesis

Most mathematical models of malaria infection represent parasites as replicating continuously at a constant rate whereas in reality, malaria parasites replicate at a fixed age. The behaviour of continuous-time models when gametocytogenesis is included, in comparison to a more realistic discrete-time model that incorporates a fixed replication age was evaluated. Both the infection dynamics under gametocytogenesis and implications for predicting the amount parasites should invest into gametocytes (level of investment favoured by natural selection) are considered. It is shown that the many malaria models with constant replication rates can be represented by just 3 basic types. For these 3 types, it is then shown that under gametocytogenesis (i) in 2 cases, parasite multiplication and gametocyte production is mostly much too low, (ii) in the third, parasite multiplication and gametocyte production is mostly much too high, (iii) the effect of gametocyte investment on parasite multiplication is mostly too high, (iv) the effect of gametocyte investment on gametocyte production is nearly always too low and (v) with a simple approximation of fitness, the predicted level of gametocyte investment is mostly much too low. However, a continuous model with 48 age-compartments compares well to the discrete model. These findings are a further argument for modelling malaria infections in discrete time.