Page 1

Vaccine allocation in a declining

epidemic

E. Goldstein1,*, J. Wallinga3and M. Lipsitch1,2

1Center for Communicable Disease Dynamics, Department of Epidemiology, and

2Department of Immunology and Infectious Diseases, Harvard School of Public Health,

Boston, MA 02115, USA

3Centre for Infectious Disease Control, National Institute of Public Health and the

Environment (RIVM), 3720 BA Bilthoven, The Netherlands

Sizeable quantities of 2009 pandemic influenza A/H1N1 (H1N1pdm) vaccine in the USA

became available at the end of 2009 when the autumn wave of the epidemic was declining.

At that point, risk factors for H1N1-related mortality for some of the high-risk groups,

particularly adults with underlying health conditions, could be estimated. Although those

high-risk groups are natural candidates for being in the top priority tier for vaccine allocation,

another candidate group is school-aged children through their role as vectors for transmission

affecting the whole community. In this paper, we investigate the question of prioritization for

vaccine allocation in a declining epidemic between two groups—a group with a high risk of

mortality versus a ‘core’ group with a relatively low risk of mortality but fuelling transmission

in the community. We show that epidemic data can be used, under certain assumptions on

future decline, seasonality and vaccine efficacy in different population groups, to give a cri-

terion when initial prioritization of a population group with a sufficiently high risk of

epidemic-associated mortality is advisable over the policy of prioritizing the core group.

Keywords: influenza pandemic; vaccination; high risk; mortality

1. INTRODUCTION

Approximately 62–65% of fatalities among hospitalized

H1N1pdm patients were in adults with underlying

health conditions other than pregnancy [1,2]. These

statistics were obtained during the early stages of an

epidemic, when most children were still susceptible to

infection; as the epidemic progressed, the proportion

of infections among adults (and thus among high-risk

adults) would probably increase [3].

Suchestimatesofthefractionofdeathsassociatedwith

particular high-risk conditions, combined with estimates

of the prevalence of such conditions [1,4–7], permit esti-

mation of the relative risks for mortality among persons

with these conditions. Among the groups at the highest

risk of dying of pandemic influenza in 2009 were those

with renal disease, neurological disorders and perhaps

immunosuppression. Providing vaccine to individuals in

such groups has a large immediate benefit in preventing

mortality, assuming that the vaccine is effective in

such groups. On the other hand, vaccination of healthy

school-aged children, who are not at high risk of dying,

hasabenefitintermsofreducingtransmissioninthecom-

munity and decreasing the rate of transmission, which

would in turn benefit the whole community, including

high-risk adults, who form the majority of fatalities.

This benefit is particularly pronounced during the early

stages of an epidemic; later on its effect is dampened

because fewer children are susceptible, hence children

play a lesser role in transmission [8]. Prior studies [9,10]

have suggested that vaccination of children is optimal, in

various senses, when vaccine is available in substantial

quantities relatively early in an epidemic, while vacci-

nation of higher risk groups may be more beneficial if

vaccine supplies are limited and become available late

in an epidemic. These considerations lead to a natural

quantitative question: Under what conditions is direct

vaccination of the high-risk group members superior as a

strategytovaccinationofchildrentoreducetransmission?

The question we consider here is as follows: suppose

that small, initial quantities of a vaccine are becoming

available during a declining epidemic. Should we give

them to the population stratum whose relative risk of

fatality is high, or should we give them to the stratum

whose relative risk of fatality is low (below average), but

which has a strong impact on the epidemic’s dynamics

in the whole population? The measure of the benefit in

both scenarios is the total number of lives that are to

be saved throughout the remainder of the epidemic.

We propose to answer this question using a more

flexible approach than that adopted in prior studies

[9,10]. First, we do not assume knowledge of contact

and transmission patterns in different population

groups; rather, prioritization is guided by the available

data on the epidemic’s decline rate. Second, we do not

assume that high-risk adults play the same role in the

transmission process as adults without underlying

*Author for correspondence (egoldste@hsph.harvard.edu).

Electronic supplementary material is available at http://dx.doi.org/

10.1098/rsif.2012.0404 or via http://rsif.royalsocietypublishing.org.

J. R. Soc. Interface (2012) 9, 2798–2803

doi:10.1098/rsif.2012.0404

Published online 6 July 2012

Received 18 May 2012

Accepted 14 June 2012

2798

This journal is q 2012 The Royal Society

Page 2

medical conditions. Certain high-risk adults may have

fewer contacts, particularly with children, and may

play a very limited role in transmission to others;

in this context, the benefit of allocating vaccine to

high-risk adults is only measured using data on their

share among the severe outcomes. Third, the approach

in both studies [9,10] assumes that a certain vaccine

quantity is delivered at once (with no further vac-

cine distribution) and compares the effect of that

allocation for high transmission versus high-risk individ-

uals. In practice, vaccine is produced and distributed

gradually during an epidemic. We make no assumption

on future vaccine availability in formulating the priori-

tization criterion. We assume only that the overall

transmissibility of the virus does not increase after the

point at which the vaccine allocation decision is made; if

changing weather or other seasonal factors increase trans-

mission opportunities [11], we assume that such increases

are offset by decreasing numbers of susceptible hosts.

Here, we consider this question specifically in the con-

text of a declining epidemic. We note that for the 2009

H1N1 influenza epidemic in the USA, sizeable vaccine

quantities became available during the epidemic’s declin-

ing stage, and, according to recommendations made by

the Advisory Committee on Immunization Practices

(ACIP) [12], healthy children aged 5–18 and adults

with underlying health conditions had the same priority

for vaccination. Surveillance data such as those collected

by the US Centers for Disease Control and Prevention

(CDC) [13] can be used to estimate the weekly decline

rate of epidemic incidence. Using this rate and several

assumptions, we formulate conditions under which initial

prioritization of the high-risk group over the core group is

advantageous. We calibrate those conditions against the

available data in the USA and assess their relevance for

the 2009 H1N1 pandemic, emphasizing several sources

of uncertainty, particularly with regard to vaccine

efficacy (VE) against fatal outcomes for high-risk adults.

2. METHOD AND RESULTS

2.1. Relative risk between population groups

Let X and Y be two population subgroups—for example,

morbidly obese persons and persons with cancer (note:

some individuals may be members of both groups). We

define the relative risk Rt(X,Y) for mortality in group

X compared with group Y at time t to be the ratio of

the risk of mortality in group X at time t and the corre-

sponding risk in group Y. Here, the risk of mortality in a

particular group at time t is the number of deaths in that

group at time t divided by the size of that group.

Data on the prevalence of various underlying con-

ditions among the fatal cases collected during the

early stages of an epidemic (e.g. [1,2]), combined with

prevalence data for different underlying medical con-

ditions in the population allow for an assessment of

Rearly(X,W)—the relative risk of mortality in the var-

ious high-risk groups X compared with the whole

population W during the early stages of the epidemic.

We assume that, even as the epidemic progresses,

the relative risk for any unvaccinated subgroup of the

high-risk group X is at least

RR ¼ RearlyðX;WÞ:

ð2:1Þ

That is, the relative risk of the high-risk group does not

decline during the epidemic, relative to the whole popu-

lation. Although we are not aware of data confirming

that assumption, depletion of susceptibles among children

and young adults suggests that their relative share among

the infected decreases (which could be seen in the decrease

of their share among the influenza-like illness (ILI) cases

during the H1N1 pandemic [14]), and the share of other

population groups (and correspondingly their relative risk

of fatality) should increase. The latter increase might not

beuniforminallpopulationgroups—seemoreonthatin§3.

Table 1 summarizes the prevalence of adults with cer-

tain underlying conditions among the fatal H1N1pdm

cases in Fowlkes et al. [1] and Louie et al. [2], and their

estimated relative risk of fatality.

2.2. Effect of vaccination

2.2.1. Targeted vaccination strategies for a limited

quantity of vaccines

Suppose that we have enough vaccine to give one dose

to a proportion q of the whole population—thus, q is

the number of vaccine doses divided by the number of

persons in the whole population W. We wish to com-

pare various vaccination strategies for this limited

Table 1. Prevalence among fatal cases from Fowlkes et al. [1] and Louie et al. [2] and relative risk (RR) for H1N1pdm fatality

for certain underlying health conditions in US adults. Ranges are the exact (Clopper and Pearson) confidence intervals for

each study. For prevalence of morbid obesity among the fatalities in Fowlkes et al. [1], limited body mass index (BMI) data are

available, and no absolute counts are reported.

underlying condition (adults)share among US fatalities

share among US

population (%) RR for fatality

renal disease12.3% (9–16.4%) [1]

15.3% (9.3–23%) [2]

9.9% (6.9–13.7%) [1]

11.9% (6.6–19.1%) [2]

17.6% (13.6–22.2%) [1]

8.9% [1]

31.5% (21.2–43.2%) [2]

13% (9.5–17.1%) [1]

1.2889.6 (7–12.8) [1]

11.9 (7.2–17.9) [2]

10.9 (7.5–15) [1]

13.0 (7.3–21) [2]

9.2 (7.2–11.7) [1]

2.0 [1]

7.1 (4.8–9.7) [2]

3.9 (2.9–5.1) [1]

neurological disorder/developmental delay 0.91

immunosuppressive condition

morbid obesity (BMI ?40)

1.9

4.47

chronic obstructive pulmonary disease 3.33

Vaccination in a declining epidemic

E. Goldstein et al. 2799

J. R. Soc. Interface (2012)

Page 3

quantity of vaccines and determine for which strategy

the number of subsequent deaths is lowest.

UnderstrategyHR,thisvaccinequantityisgiventothe

high-riskgroupX.UnderstrategyC,thisvaccinequantity

is given to the core group (children). The only difference

between strategy HR and strategy C is in the distribution

of this quantity q; we assume that the subsequent

distribution of vaccine doses beyond q is the same in

both strategies. A reference strategy, referred to as N,

leaves this vaccine quantity q unused, the subsequent

distribution being identical to the HR and C scenarios.

We denote the vaccine efficacy against infection in

some population group G by VEI

against death by VED

mating the ratio of the vaccine efficacy against death

VED

against infection VEI

G, and vaccine efficacy

G. We are mostly interested in esti-

HRfor the high-risk group and the vaccine efficacy

Gfor children:

ER ¼VED

VEI

HR

C

:

ð2:2Þ

Although we are not aware of data allowing for the

estimate of the efficacy ratio (ER), we note that vaccine

efficacy against death in any given group might be

higher than the efficacy against infection, based on

the idea that a limited antibody response to vacci-

nation, insufficient to prevent infection, might still

mitigate illness to prevent a fatal outcome.

2.2.2. Acomparisonresultbetweenvaccinationstrategies

To formulate our main result, we introduce some nota-

tion. Let w() be the serial interval distribution for

influenza (which we assume to be no longer than 7

days), and let m be its mean.

Let t0 be the day when vaccine quantity q takes

effect, and r0be the epidemic’s daily exponential decline

rate at that time.

Suppose that distributing quantity q to the core

group decreases the effective reproductive number of

the epidemic by a fraction Aq.

Finally, we assume that for the week beyond t0the

decline rate does not change much under scenario N.

Underthisassumption,wedemonstrate(seetheelectronic

supplementary material) that an initial campaign

prioritizing the high-risk group over the core group is

advantageousintermsofreducingcumulativemortalityif

?

VED

HR? RR ? A

1

emr0? 1þ

1

1 ? e?7r0

?

:

ð2:3Þ

2.2.3. Assessing the prioritization criterion for the 2009

H1N1pdm data in New England

There is some variability in estimates of the serial inter-

val distribution in the literature [15–18]. One can

estimate from those papers that the mean m of the

serial interval distribution is at least 2.5 days.

To estimate the epidemic’s decline rate r at different

time points, we use surveillance data such as those col-

lected by the CDC [13] following the approach in

Goldstein et al. [19]. The weekly incidence of influenza

IWtwfor week twis estimated to be the proportion of

ILI among doctor visits multiplied by the proportion

of collected specimens testing positive for influenza

during that week. The incidence estimate is given up to

(an unknown) multiplicative factor; however, the ratio

IWtw

IWtw?1, 1

can be thought of as the estimate of the decline rate in

incidence during week tw.

Let the daily exponential rate of change in incidence

during the week tw(assumed constant over that week)

be rw. It is estimated from

e?7rw¼

IWtw

IWtw?1:

Estimates of the decline rates of the epidemic at the

time when sizeable quantities of the vaccine appeared in

2009 varied significantly by different regions in the USA.

New England had robust decline rates of the epidemic by

the end of November/early December 2009, with the

decline subsequently sustained in the winter. Table 2

gives estimates of the daily decline rate between weeks 45

and48inNewEngland,onthebasisoftheILIandtheres-

piratoryspecimen testing data collected by the CDC [14].

A method to estimate A in equation (2.3) from the

epidemic data appears in

method suggests that

Wallinga et al. [8]. This

A ¼ VEI

C? Ap;

where Apq would be the reduction of the reproductive

number under the distribution of quantity q of a perfect

vaccine to children. Equation (2.3) suggests that a cri-

terion for prioritization of a high-risk group with the

epidemic’s daily decline rate being r is

?

We note that since 0–17 year olds constituted 24.3

per cent of the US population in 2009 [20], and since

giving perfect vaccine at random to a fraction q of the

population reduces the reproductive number by a frac-

tion q, one necessarily has that Ap? 1/0.243 ¼ 4.12

(the latter would be true if other population groups

had no impact on the epidemic). Estimation of Ap

based on the method in Wallinga et al. [8] applied to

the data from the 2009 H1N1 influenza epidemic in

the USA is described in the electronic supplementary

material. This method suggests a bound

RR ?Ap

ER

1

e2:5r? 1þ

1

1 ? e?7r

?

:

ð2:4Þ

Ap? 2:15:

ð2:5Þ

Figure 1 plots a range of values for the decline rate r

and the relative risk of a fatal outcome, for which our

criterion suggests the prioritization of the high-risk

group over children for Ap¼ 2.15 and 2.5, assuming

Table 2. Daily exponential decline rate between weeks 45

and 48 in New England.

week45–46 46–4747–48

daily decline rate r

0.0930.099 0.12

2800

Vaccination in a declining epidemic

E. Goldstein et al.

J. R. Soc. Interface (2012)

Page 4

that ER ? 1. We note that for the complementary

region, plotted in grey, our criterion is inconclusive,

andno prioritization recommendation

children or for the high-risk adults can be made.

Finally, applying the criterion in equation (2.4) with

Ap? 2.15 (as estimated from the epidemic data in

theelectronicsupplementarymaterial)undertheassump-

tion that ER?1 suggests that, by week 48 of 2009 in New

England, prioritization of adults with neuromuscular

disorders, renal disease and possibly immunosuppression

over healthy children was advisable. On the other hand,

if ER is significantly lower than 1, it might have been the

case that prioritizing school-aged children was advisable

owing to the effect of vaccinating children on the epidemic

dynamicsandmortalityinthewholecommunity.Wenote

that, in New England, adherence to the ACIP guidelines

[12] giving equal priority to healthy school-aged children

andadultswithunderlyinghealthconditionswasadopted

by the local health departments [21,22].

eitherfor

2.2.4. Practical considerations behind prioritization of

high-risk individuals

Our proposed strategy is that, when a small quantity of

vaccine becomes available during the declining phase of

an epidemic, prioritizing high-risk adults can reduce

overall mortality compared with prioritizing healthy

children, provided the adults in the priority group are

at high enough risk, as defined in equation (2.3).

When sizeable proportions of the population are already

vaccinated, or when the criterion in equation (2.3) is

not met, prioritizing high-risk adults might not be war-

ranted, and a larger impact can potentially be obtained

by prioritizing children rather than high-risk adults to

accelerate the epidemic’s decline.

Wealsonotethatourapproachassumesthefeasibility

of implementing a flexible vaccine distribution policy.

Such a policy would entail a switch from an initial,

short-term drive to vaccinate certain groups of high-risk

individuals to a campaign for vaccinating children.

Prior planning of resources to reach those high-risk indi-

viduals, which includes fostering their awareness about

the risks they are facing, and the ability to redirect the

targeting of the available vaccine on a timely basis are

necessary for the approach to be successful.

3. DISCUSSION

This paper examines prioritization for vaccine allo-

cation in a declining influenza epidemic. It formulates

conditions under which an initial campaign to vaccinate

individuals with a high risk of mortality from influenza

is preferable to vaccinating a core group, like children,

which has a relatively low risk of mortality but fuels

transmission in the community. It is shown how those

conditions can be validated in real time under a range

of uncertainties in the estimates of certain quantities

related to the epidemic’s progression and VE. We

note that, for an emerging epidemic, priority for vaccine

allocation with the goal of minimizing the overall mor-

tality burden may go to school-aged children rather

than adults with underlying health conditions [9,10].

Abasicsourceofuncertaintyinapplyingtheprioritiza-

tioncriterionistheneedforanestimateofvaccineefficacy

against fatal outcomes in various high-risk groups.

Althoughwearenotawareofdataassessingtheaboveeffi-

cacy, several studies estimating the immunogenicity and

efficacy against infection in different high-risk groups for

the vaccine against the 2009 A/H1N1 influenza have

been published. A case–control study has found poor

immuneresponsetovaccination in haemodialysispatients

[23].Someobservationaldataarenowavailableonvaccine

efficacy against infection among the high-risk groups for

the 2009 H1N1 influenza pandemic [24–26]. These data

suggest that vaccine efficacy against infection is lower in

high-risk individuals than in healthy children. However,

observational studies of influenza vaccine effectiveness

may be subject to significant residual confounding,

especiallyamonghigh-riskpersons[27].Moreover,vaccine

efficacy against fatal outcomes among high-risk adults

might be different, either affirming the rationale behind

their prioritization as indicated by our approach or

suggesting that low efficacy in direct protection of high-

risk adults makes prioritization of school-aged children

advisable because of the effect of vaccinating children on

20

RR for mortality

10

0.06 0.08 0.10 0.12

epidemic decline rate, r

epidemic decline rate, r

0.14

0.06 0.08 0.10 0.12 0.14

15

prioritization uncertain

prioritization to

high-risk group

(a)(b)

prioritization to

high-risk group

prioritization uncertain

25

20

15

10

Figure 1. Ranges for the epidemic decline rate r and the relative risk (RR) for mortality in a high-risk group (red) for which prior-

itization of the high-risk group is justifiable under equation (2.4) for different values of the parameter Ap, under the assumption

that ER ? 1. (a) Ap¼ 2.15 and (b) Ap¼ 2.5.

Vaccination in a declining epidemic

E. Goldstein et al. 2801

J. R. Soc. Interface (2012)

Page 5

the epidemic dynamics and mortality in the whole com-

munity. Another source of uncertainty related to the

impact of vaccination is the potential detrimental short-

term effect that vaccination might have on susceptibility.

Data from Emborg et al. [25] suggest a negative and

statistically significant vaccine efficacy against infection

occurring within a week from vaccination. Given that, in

adecliningepidemic,asizeablefractionoffutureinfections

are likely to occur within afairlyshorttime, such an effect

may take away from the benefit of vaccinating high-risk

individuals, although it may also have an impact on

vaccinating children.

Another potential source of uncertainty in priori-

tizing high-risk adults is the feasibility of a timely

implementation of a vaccination campaign for those

groups. For children, rapid administration of a vaccine

is possible through school-based vaccination drives.

High-risk adults might be a harder target group to

reach, with past efforts concentrated on their healthcare

providers [28,29]. A combination of risk awareness and a

speedy distribution framework is needed to ensure that

vaccine allocation to high-risk adults would not lag sig-

nificantly behind an alternative of administering the

corresponding vaccine quantity to children.

Besides vaccine efficacies in different population

groups, the key quantities needed to ascertain our prior-

itization criterion are the epidemic’s decline rate and the

impact of vaccinating the core group (children) on the

epidemic’s reproductive number. The decline rate can

be estimated from surveillance data, such as those col-

lected by the CDC [13], using a proxy for influenza

incidence described in Goldstein et al. [19]. The impact

of vaccinating the core group on the reproductive

number can be gauged following the method in Wallinga

et al. [8]. That method requires knowledge of the relative

susceptibility and infectivity in different population

groups, and the epidemic’s incidence curve stratified by

those groups. Data on relative susceptibility and infectiv-

ity in different age groups can be obtained from

household studies and may, in principle, become available

in real time; we have borrowed the estimates from

Cauchemez et al. [16], which was published at the end

of2009.Wedidnothaveagoodestimateoftheepidemic’s

incidence curve; instead, we have adapted the method in

Wallinga et al. [8] to give an upper bound on the impact

of vaccinating children using the final attack rates in

different age groups, extrapolated from Zimmer et al.

[30]. We want to point out that, in principle, it is possible

that better surveillance data for the epidemic’s pro-

gression can produce sharper, real-time estimates of the

impact of vaccinating children. Such surveillance data

can come from serial serological data [31], or from age-

stratified data on ILI and respiratory specimen testing,

combined with a real-time serological study, or possibly

from syndromic data [32]. The practical aspects of

obtaining such data in real time remain uncertain [33].

An assumption we make in our approach is that, as

time progresses, depletion of susceptibles owing to natural

infections in high-risk groups is slower than the depletion

of susceptibles in the whole population (particularly

among children and the young adults); thus, the relative

risk for the unvaccinated subgroup of a high-risk group

increases with time. The role of young individuals

during the early stages of an epidemic and their sub-

sequent depletion is known [8], and evidence for the

decline of the relative share of the young individuals

among the infected can be seen in the ILI data [14].

More evidence for the assumption on the increasing rela-

tive risk of severe outcomes in the high-risk groups

is provided by Flu.Gov [3]. However, those considerations

need not imply that relative risks in each high-risk group

increasewith time. Children and young adults represent a

small fraction of fatal cases, and adults in certain high-

risk groups might be more susceptible to infection than

other adults in the corresponding age groups, experien-

cing a larger initial depletion of susceptibles and

correspondingly lower relative risk of fatality in later

stages of an epidemic. To assess this issue, one can

measure the share of individuals with a particular under-

lying health condition for a certain recorded outcome, e.g.

hospitalization, in different age groups. Changes in their

relative share through time should give an indication

aboutthechangeintheirrelativeriskoffatalitycompared

with the early stages of the epidemic.

Yet another assumption in our approach is that the

impact of further vaccination and depletion of susceptible

individuals is stronger than the impact of seasonality or

genetic changes affecting the transmissibility of the virus.

For the 2009 H1N1pdm this assumption with regard to

seasonality was violated in southeastern USA owing to

little willingness in the population to get vaccinated

when vaccine was widely available. It is reasonable to

assume that for a more pathogenic strain this factor

would play a lesser role. At the same time, the decline

rate of the epidemic in the southeast was lowand awinter-

time resurgence owing to seasonal forcing could be

predicted [34]. Moreover, under the approach of this

paper, such a low decline rate would justify prioritization

of risk groups whose relative risks for fatal outcomes are

higher than those existing in the published data.

Some regions of the USA, such as New England, had

high H1N1pdm vaccination rates and a decline in the

epidemic which was sustained through the winter.

We assess our criterion for New England and specify

the high-risk groups which should have been initially

prioritized for vaccination over school-aged children,

under certain assumptions on vaccine efficacy against

mortality in those high-risk groups. We note that

there is a wide range of uncertainty in the available

data for the 2009 H1N1 pandemic with regard to the

estimates for the relative risk of mortality for individ-

uals with various underlying conditions, as well as for

the attack rates and the relative susceptibility and

infectivity in the different population groups. More

detailed epidemiological data would reduce the above

uncertainties, and correspondingly the uncertainty in

our conclusions for vaccine prioritization.

This work was supported in part by the US National Institutes

of Health Models of Infectious Disease Agent Study programme

through cooperative agreement 1 U54 GM088558.

REFERENCES

1 Fowlkes, A. L. et al. 2011 Epidemiology of 2009 pandemic

influenza A (H1N1) deaths in the United States,

2802

Vaccination in a declining epidemic

E. Goldstein et al.

J. R. Soc. Interface (2012)