Estimated efficacy against infection as a function of the average proportion of parasites killed for pre-erythrocytic (green) and blood-stage vaccines (red). (a) The number of successfully developing sporozoites is assumed to follow a Negative Binomial distribution with mean n and shape parameter r = 0.5. With a mean of n = 30 sporozoites, a pre-erythrocytic vaccine that eliminates 85% of sporozoites will prevent 20% of infections. Combining two vaccines that eliminate 85% of sporozoites via independent mechanisms will result in a multicomponent vaccine that prevents 60% of infections. The curve is convex such that incremental increases in the proportion of sporozoites eliminated translate to greater increases in efficacy against infection. (b) Blood-stage parasites are assumed to increase in number every two-day cycle by a factor equal to the parasite multiplication rate (PMR), which varies among individuals according to a Log-Normal distribution with coefficient of variation C
= 0.5. With a mean PMR = 8, a blood-stage vaccine that eliminates 75% of parasites will prevent only 10% of infections. Combining two vaccines that eliminate 75% of parasites through independent mechanisms will result in a multi-component vaccine preventing 95% of infections. The point of inflection in the curve corresponds to the proportion of BS parasites that must be eliminated to reduce the PMR below the threshold of 1.