Figure 2

Geometrical definition of the adjusted bed net coverage. (a) Geometric definition of the ABC statistic. Populations i characterized by bed net coverage c _i and malaria endemicity e _i are projected onto a vector $\overrightarrow{a}$. This vector is to be chosen such that projection A B C _i of region i is higher for lower values of c _i and lower for higher values of e _i . By parameterizing the vector using angle θ and e _{m a x} the correspondence with external statistics of protection can be optimized. In this paper, θ is chosen such that A B C _i corresponds with the reduction of malaria endemicity for a given endemicity and bed net coverage as predicted by the model of Smith et al. [7]. (b) Figure altered from Smith et al. [7]. For a set of benchmark parameters, the resulting malaria endemicity as a function of baseline endemicity and bed net coverage. The colours represent different endemicity levels (dark red, >40%; red, 5%-40%; pink, 1%-5%; and gray, <1%). In this paper, θ was choosen such that the $\overrightarrow{a}$ is orthogonal to the boundary of the area for which the final malaria endemicity is lower than 1%. (c) Results of fitting a linear model to data of Smith et al. [7]. The blue dots represent the predicted final malaria endemicity for a program that scaled-up the bed net coverage from 0 to a specific target level at the end of five years. The grid represents the result of a linear fit of the data. A linear model could fit the data very well (R²=0.97). The regression function was E _{s t a b l e} =−0.0163−0.1971×C+1.0047×E. Although the fitted data is not the data displayed in Figure 2 and used to parameterize the ABC for the purpose of the current paper, it shows that the predictions of Smith et al. [7] can fitted adequately using a linear model.