Models can be used to plan the best use of pandemic vaccines. This research addresses 2 key aspects of pandemic vaccines under current scrutiny: 1) the use of antigen-sparing vaccines and 2) the effect of timing on the use of matched vaccine. Antigen-sparing vaccines are a means of increasing population coverage at the price of reduced efficacy. Our approach of estimating efficacy by fitting linear models to trial data provides a simple means of comparing vaccines on the basis of their population impact, taking into account both efficacy and coverage.

This process was illustrated by calculating the effect on

*R*_{0} and attack rates, both of which were minimized by the lowest tested dose when based on existing adjuvanted trial data ( and ). This result is consistent with that of Riley et al. (

14), who also found that the lowest tested dose was optimal for reducing attack rates for prepandemic vaccination. An exception is when supply is sufficient to provide 100% coverage at a higher dose. Their analysis focused on an

*R* value of 1.8 and a small stockpile sufficient to vaccinate 10% of the population with the maximum tested dose in a multitype-vaccinated population with uniform mixing. They also examined semistructured populations including the case of a subpopulation with elevated transmission. Under most circumstances, these results supported their main conclusion.

Our analysis took a different approach to estimating vaccine efficacy, adding the element of delays due to seroconversion and delivery, enabling comparison of 1- and 2-dose vaccine programs. We fitted linear models to trial data, enabling simple characterization of the optimal dose for reducing

*R* and the attack rate. Estimates of vaccine efficacy were applied to infection hazards, which is more appropriate than a relative risk measure when modeling partially protective vaccines. We showed how vaccines that also reduce infectivity of breakthrough vaccinated cases can alter the expression for the optimal dose and the expected magnitude of the reduction in

*R* and the attack rate. This assumption is supported by evidence of greatly reduced viral loads and symptoms in challenge trials in the closest animal models (

16), although the size of the reduction is unclear. The effect of a vaccine on transmission is greater if infectivity of breakthrough cases is also reduced (, panels D and F compared with panels C and E; and , panels B and D compared with panels A and C). If true, this finding would further support the use of low-antigen vaccines.

The time delay to vaccination has a critical effect on the impact of a vaccine matched to the pandemic strain. Campaigns based on matched vaccines are expected to occur during pandemic phase 6, when local transmission is well established. Our results showed that, even under the optimistic assumption of matched vaccination occurring at cumulative attack rates of 0.01% or 1% of the population, the effect of vaccination was substantially reduced ().

When we varied *R*_{0} and the delay to vaccination in the ranges of 1.5–2.5 months and 2–6 months, respectively, most simulations showed a modest reduction in attack rates, even with high vaccine effectiveness and coverage (, panels A and C). We compared 1- and 2-dose programs based on immunogenicity data from the GlaxoSmithKline Biologicals 3.8-μg adjuvanted vaccine. Our assumption of being able to obtain twice the coverage with the 1-dose vaccine, combined with a relatively high estimate for vaccine efficacy and seroconversion occurring just once, meant that a 1-dose program was favored in our analysis. This preference could change if the 1-dose program had a substantially lower vaccine efficacy. We also found that the benefit of a 1-dose program over a 2-dose program was greatest when the vaccine was delivered while prevalence was above 0.1% but prior to its peak.

If the delay to vaccination were known in advance, then one could in principle assess whether a 1- or 2-dose program would be better while case numbers were small, since prevalence at this time point can be estimated on the basis of the epidemic growth rate. Currently, 2 doses of vaccine are required for high immunogenicity, even when the vaccine involves a novel adjuvant. However, our results show that a 1-dose program can lead to a lower attack rate by trading off lower immunogenicity against higher coverage.

Further benefits can be derived by increasing vaccine coverage through reducing the antigen required per dose. Efficacy of a single dose of vaccine could be aided either by priming individuals with a stockpiled H5N1 vaccine during pandemic phase 5/6 or by incorporating a H5N1 component in seasonal vaccines.

Our analysis focused on strategies designed to protect an entire population, and calculations of the optimal dose apply only when supply is constrained. The analysis does not apply to vaccination strategies aimed at protecting subsets of the population, where individual protection is the paramount concern and vaccine supply is adequate.

Limitations to our model include uniform seroconversion 21 days after each vaccination and the assumption of uniform mixing in a homogenous population. Titers rise continuously after vaccination, potentially more rapidly after the second dose, implying that our model may be biased slightly in favor of 1-dose programs. Subgroups, such as children, have been identified that display increased influenza transmission, and targeting transmitters has been shown to be an efficient use of influenza vaccine (

17–

19). In these circumstances, the optimal strategy may differ from that indicated by a homogenous mixing model, with higher dose, low-coverage strategies becoming more favorable. We did not account for stochastic behavior or importations of cases, both of which are influential during the early stages of an outbreak. Our estimates of optimal doses were based on a small number of data points for antigen volume and an assumed perfect correlation between infection rates in historic challenge trials and in a new pandemic as a function of titers of hemagglutination inhibition. This correlation is unlikely to be the case but reflects the unavoidable difficulty of estimating efficacy for H5N1 vaccines. Vaccination could also assume a staged form based on perceived disease or transmission risks (

8,

20), and correlations between this order and transmission between different subgroups of the population cannot be assessed in a homogeneously mixed model. Also note that a focus on attack rates can sometimes be misleading in terms of prevention of severe disease and death (

20).

The many limitations do suggest a role for carefully designed studies to improve estimates of model parameters. The infectivity of breakthrough-vaccinated cases seems particularly amenable, given that similar estimation studies have been performed with antiviral prophylaxis to prevent influenza (

21). A household-based design in a moderately to highly vaccinated population, with recruitment based on a positive rapid test during the influenza season, might be a good start to addressing this question.

In conclusion, our results suggest that population benefits can accrue from low-antigen vaccination strategies that provide greater herd immunity but reduced individual protection. These benefits increase if the vaccine reduces both infectivity and susceptibility, as supported by studies performed on animal models of influenza. However, the effectiveness of a matched vaccine during pandemic phase 6 falls with both increasing *R*_{0} and the delay to vaccine distribution. Once prevalence is greater than about 1%, the benefit of a matched vaccine falls away. If other control measures can slow the increase in prevalence, antigen-sparing vaccination strategies including a 1-dose vaccination campaign can reduce the overall attack rate.