A within-vector mathematical model of Plasmodium falciparum and implications of incomplete fertilization on optimal gametocyte sex ratio.

A mathematical model that simulates the within-vector dynamics of Plasmodium falciparum in an Anopheles mosquito is developed, based on experimental data. The model takes a mosquito's blood meal as input and computes the salivary gland sporozoite load as the final output, a probable measure of mosquito infectivity. Computational model results are consistent with observed results in nature. Sensitivity analysis of the model parameters suggests that reducing the gametocyte density in the blood meal most significantly lowers sporozoite load in the salivary glands and hence mosquito infectivity, and is thus an attractive target for malaria control. The model is used to investigate the implication of incomplete fertilization on optimal gametocyte sex ratio. For a single strain, the transition from complete fertilization to increasingly incomplete fertilization shifts that ratio from 1 to N, where N is the number of viable male gametes produced by a single male gametocyte, towards 1 to 1, which is demonstrated to be the limiting ratio analytically. This ratio is then shown to be an evolutionarily stable strategy as well in the limiting case.