Malaria's Missing Number: Calculating the Human Component of R0 by a Within-Host Mechanistic Model of Plasmodium falciparum Infection and Transmission
Figure 4
Comparison of model and malaria therapy cumulative distributions for two indices.
(A) These line curves show the cumulative distributions of the durations of infection for the malaria therapy data, as well as those of our mechanistic model and the compartmental models of Lawpoolsri et al. [29] and Okell et al. [12]. The distribution from the malaria therapy data comes from fitting a Gompertz probability distribution to the durations of infection from 54 patients, as reported by Sama et al. [33]. The cumulative distribution function of the best-fit Gompertz distribution is plotted in red. The mechanistic model cumulative distribution was generated by calculating the durations of infection for 1,000 runs and plotting their empirical cumulative distribution function. The distributions from Lawpoolsri et al. and Okell et al. were generated by running those compartmental models according to their mathematical assumptions. The malaria therapy and mechanistic model distributions show relatively tight fits throughout the distribution. The durations of infections for the malaria therapy data and our mechanistic model are defined as the last observable day by smear minus the first observable day; the durations for the compartmental models are defined as the durations of time in infectious compartments. (B) We reviewed a total of 262 malaria therapy charts and recorded the maximum observed gametocytemia from each patient (data were recorded as log10 values to the nearest tenth) [24], [65]. We then recorded the maximum gametocytemias from 1,000 runs of our model. Because the malaria therapy data only include individuals who recorded at least four positive gametocyte observations, we censored out model runs in which gametocyte levels never exceeded 10 per µL (N = 988) [24]. Illustrated are the empirical cumulative distributions for the two data sets after log-transformation, i.e., the proportion of data that are less than or equal to a given level of log10 gametocytemia.