doi: 10.1371/journal.ppat.1003849.
eCollection 2014 Mar.
A missing dimension in measures of vaccination impacts
Affiliations
- PMID: 24603721
- PMCID: PMC3946326
- DOI: 10.1371/journal.ppat.1003849
Item in Clipboard
A missing dimension in measures of vaccination impacts
PLoS Pathog.
.
No abstract available
Conflict of interest statement
The authors have declared that no competing interests exist.
Figures
(A) Equilibrium prevalence of infection under a pathogen transmission model in which an intervention (vaccine or symbiont) reduces host susceptibility to a factor that is distributed as specified. The model is formally represented by the rates of change in the proportions of the population that are susceptible and infected: 
, 
, 
, and 
, where S and I are nonintervention, while 
and 
are intervention groups with susceptibility x distributed as 
(right panels). Colored lines assume total intervention coverage (
), while the black line represents the scenario without intervention (
). (B) Dose-response curves expected from an experiment in which groups of naive (black) and intervention (colored) hosts are challenged with a range of pathogen doses, under a model in which the intervention reduces susceptibility to a factor that is distributed as in panels on the right. Models for infected proportions in nonintervention and intervention groups are formalized in a dose-response manner by 
and 
, respectively, where d is the number of pathogens the host is challenged by and p is the probability of infection for each pathogen. Colored lines assume susceptibility factors distributed with mean 0.5 in all cases and variance 0 (red), 0.05 (orange), 0.1 (green), 0.2 (cyan), and 0.25 (blue). Red and blue at the extremes are discrete, while the intermediate cases are continuous beta distributions, with shape parameters a and b such that the mean is fixed,
, and the variance, 
, spans the range, 
. Transmission models assume 
, and controlled infection models assume 
.
, , , and , where S and I are nonintervention, while and are intervention groups with susceptibility x distributed as (right panels). Colored lines assume total intervention coverage (), while the black line represents the scenario without intervention (). (B) Dose-response curves expected from an experiment in which groups of naive (black) and intervention (colored) hosts are challenged with a range of pathogen doses, under a model in which the intervention reduces susceptibility to a factor that is distributed as in panels on the right. Models for infected proportions in nonintervention and intervention groups are formalized in a dose-response manner by and , respectively, where d is the number of pathogens the host is challenged by and p is the probability of infection for each pathogen. Colored lines assume susceptibility factors distributed with mean 0.5 in all cases and variance 0 (red), 0.05 (orange), 0.1 (green), 0.2 (cyan), and 0.25 (blue). Red and blue at the extremes are discrete, while the intermediate cases are continuous beta distributions, with shape parameters a and b such that the mean is fixed,, and the variance, , spans the range, . Transmission models assume , and controlled infection models assume .
Beta distributions are classified as: polarized if 
; symmetric if 
(gray dashed line), as in Figure 1; homogeneous in the limit 
(red circle), as red in Figure 1; all-or-nothing in the limit 
(blue circle), as blue in Figure 1; and uniform if 
(gray square). The power to identify polarized distributions is analyzed in a neighborhood of the uniform distribution (Figure S1).
; symmetric if (gray dashed line), as in Figure 1; homogeneous in the limit (red circle), as red in Figure 1; all-or-nothing in the limit (blue circle), as blue in Figure 1; and uniform if (gray square). The power to identify polarized distributions is analyzed in a neighborhood of the uniform distribution (Figure S1).References
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