^{1}

^{*}

^{2}

^{3}

^{4}

^{5}

^{6}

^{1}

The authors have declared that no competing interests exist.

We consider a minimal susceptible (

Vaccines that provide leaky protection against infection act by reducing susceptibility to a factor

(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:

This illustration indicates that the distribution of vaccine effects among individuals is a major determinant of population-level impact and should be considered in evaluation. Specifically, the more homogeneously a vaccine acts, the lower its impact on disease transmission. Measures based on multipopulation study designs, spanning a range of transmission intensities, enable the inference of such distributions.

Infection in a controlled experimental setting is modeled by describing infected proportions in terms of challenge dose. Adopting standard formulations

This model fails to fit many experimental data sets in which groups of hosts are exposed to varying doses of the pathogen, and the proportion infected in each group is calculated. In particular, the slope of the curve implied by this model is steeper than what is often observed. However, if individual hosts vary in their susceptibility to infection, a reduced slope arises. A simple model

We have adopted the same notation,

Experimental dose-infectivity curves provide information to infer the mode of action of interventions, such as vaccines. Given the lack of uniform convergence to all-or-nothing as the leaky mode becomes increasingly polarized, we have classified beta distribution shapes according to polarization (

Beta distributions are classified as: polarized if

Power analysis to identify polarized intervention effects. Simulated sets of dose-infectivity data were generated and used to estimate model parameters (

(TIFF)

Simulation and estimation experiment. A simulated set of dose-infectivity data was generated using models ^{4}, 10^{5}, 10^{6}, 10^{7}, 10^{8}, 10^{9}, and 10^{10}) and ^{−6}). The host susceptibility of the intervention group is described by a beta distribution,

(TIFF)

We thank the participants of the workshops on Heterogeneity in Host-Pathogen Systems and the members of the Collective Dynamics group at Instituto Gulbenkian de Ciência (IGC) for numerous discussions, particularly Erida Gjini, Joao Lopes, Caetano Souto-Maior, and Delphine Pessoa.