Generating Global Maps of PfEIR and PfRc

First, an algorithm was developed to predict PfEIR based on PfPR. Using an assembly of 123 pairs of co-measured PfPR and PfEIR (Protocol S6), we compared several candidate models and selected an empirical (log-linear) model with a correction term for the PfEIR estimation method (Protocol S7) [50,51,19]. Second, a malaria transmission model was utilized to describe the relationship between PfPR and PfRC [19,9,12]. The transmission model assumes that infections by different parasite types can accumulate in a single human host (super-infection), and that they clear independently. The model also assumes that exposure risk is distributed unevenly in the population (heterogeneous biting) but is well-characterized and described by a one-parameter family of Gamma distributions. The model ignores acquired immunity and its effects on incoming infections, which is adequately explained by heterogeneous biting [52]. The steady state assumption implies that a population has been exposed for some time, so it is consistent with and most suitable for describing malaria prevalence in older children, i.e. for PfPR2-10 [9]. The model can be written so that each of the three transmission metrics can be predicted as a function of the other two (Protocol S7). This, combined with the different candidate models linking PfPR with PfEIR, means numerous formulations can be defined for predicting PfRc [11,34,16]. Sampling issues mean that the reliability of estimates of PfPR and PfEIR, several transmission parameters, and the model itself are also expected, a priori, to vary with underlying transmission intensity. The various formulae for estimating PfRC either directly from PfPR or indirectly from PfPR after transforming it to the PfEIR are, therefore, useful at different points along the transmission intensity spectrum. An overarching algorithm was developed to estimate PfRC from PfPR that weighted each function along the spectrum by a priori considerations. All constituent functions and further details on parameter estimation and sampling variance are provided in Protocol S7. We used these final algorithms to convert the predicted probability distribution of PfPR2-10 at each pixel into equivalent distributions of PfEIR and PfRc. These distributions encapsulate uncertainty in both the underlying prevalence estimates and in the parameterisation of the malaria transmission model. Maps of PfEIR and PfRc were generated showing the central tendency of predictions (posterior median). Additional maps were made showing summaries of the posterior distribution to illustrate prediction uncertainty in different ways.