Vaccine allocation in a declining
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
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 .
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,
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 . 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
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 (email@example.com).
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
Published online 6 July 2012
Received 18 May 2012
Accepted 14 June 2012
This journal is q 2012 The Royal Society
April–July 2009. Clin. Infect. Dis. 52(Suppl. 1) S60–S68.
2 Louie, J. K. et al. 2009 Factors associated with death or
hospitalization due to pandemic 2009 influenza A
(H1N1) infection in California. J. Am. Med. Assoc. 302,
3 Flu.Gov. 2010 U.S. sees increase in H1N1 flu activity,
29 March. See http://www.flu.gov/news/blogs/increase-
4 Pleis, J. R., Lucas, J. W. & Ward, B. W. 2009 Summary
health statistics for U.S. adults: National health interview
survey, 2008. Vital Health Stat. 10, 1–157.
Chaudhuri, A. R. & Zalutsky, R. 2007 How common are the
‘common’ neurologic disorders? Neurology 68, 326–337.
6 Zimmerman, R. K., Lauderdale, D. S., Tan, S. M. &
Wagener, D. K. 2010 Prevalence of high-risk indications for
influenza vaccine varies by age, race, and income. Vaccine
28, 6470–6477. (doi:10.1016/j.vaccine.2010.07.037)
7 Flegal, K. M., Carroll, M. D., Ogden, C. L. & Curtin, L. R.
2010 Prevalence and trends in obesity among US adults,
1999–2008. J. Am. Med. Assoc. 303, 235–241. (doi:10.
8 Wallinga, J., van Boven, M. & Lipsitch, M. 2010 Optimiz-
ing infectious disease interventions during an emerging
epidemic. Proc. Natl Acad. Sci. USA 107, 923–928.
2008 Optimal allocation of pandemic influenza vaccine
depends on age, risk and timing. Vaccine 26, 3742–3749.
10 Matrajt Jr, L. & Longini, I. M. 2010 Optimizing vaccine
allocation at different points in time during an epidemic.
PLoS ONE 5, e13767. (doi:10.1371/journal.pone.0013767)
11 Shaman, J., Pitzer, V. E., Viboud, C., Grenfell, B. T. &
Lipsitch, M. 2010 Absolute humidity and the seasonal
onset of influenza in the continental United States. PLoS
Biol. 8, e1000316. (doi:10.1371/journal.pbio.1000316)
12 US Centers for Disease Control and Prevention. 2009
ACIP vaccination recommendations for the 2009 H1N1
influenza epidemic. See http://www.cdc.gov/media/press-
13 US Centers for Disease Control and Prevention. FluView,
US CDC Influenza Division. See http://www.cdc.gov/flu/
14 US Centers for Disease Control and Prevention. United
States surveillance data. See http://www.cdc.gov/flu/
15 Donnelly, C. A. et al. 2011 Serial intervals and the temporal
distribution of secondary infections within households
of 2009 pandemic influenza A (H1N1): implications for
influenza control recommendations. Clin. Infect. Dis.
52(Suppl. 1), S123–S130. (doi:10.1093/cid/ciq028)
16 Cauchemez, S., Donnelly, C. A., Reed, C., Ghani, A. C.,
Fraser, C., Kent, C. K., Finelli, L. & Ferguson, N. M.
2009 Household transmission of 2009 pandemic influenza
A (H1N1) virus in the United States. N. Engl. J. Med.
361, 2619–2627. (doi:10.1056/NEJMoa0905498)
17 Yang, Y., Sugimoto, J. D., Halloran, M. E., Basta, N. E.,
Chao, D. L., Matrajt, L., Potter, G., Kenah, E. & Longini,
I. M. 2009 The transmissibility and control of pandemic
influenza A (H1N1)virus. Science 326, 729–733.
18 Cowling, B. J., Fang, V. J., Riley, S., Malik Peiris, J. S. &
Leung, G. M. 2009 Estimation of the serial interval of
influenza. Epidemiology 20, 344–347. (doi:10.1097/EDE.
19 Goldstein, E., Cobey, S., Takahashi, S., Miller, J. &
Lipsitch, M. 2011 Predicting the epidemic sizes of influenza
A/H1N1, A/H3N2 and B: a statistical method. PLoS Med.
8, e1001051. (doi:10.1371/journal.pmed.1001051)
20 US Centers for Disease Control and Prevention. United
States census estimates.
Recommendations for the use of influenza A (H1N1)
2009 monovalent vaccine. See http://www.neias.org/pdf/
tribution response plan. See http://www.ct.gov/ctfluwatch/
Chen, C. H., Shen, D., Wang, J. R. & Sung, J. M. 2012 Poor
immune response to a standard single dose non-adjuvenated
vaccination against 2009 pandemic H1N1 influenza virus A
in the adult and elder hemodialysis patients. Vaccine 30,
24 Andrews, N., Waight, P., Yung, C. F. & Miller, E. 2011
Age-specific effectiveness of an oil-in-water adjuvanted
pandemic (H1N1) 2009 vaccine against confirmed infec-
tion in high risk groups in England. J. Infect. Dis. 203,
25 Emborg, H. D., Krause, T. G., Hviid, A., Simonsen, J. &
Molbak, K. 2012 Effectiveness of vaccine against pandemic
influenza A/H1N1 among people with underlying chronic
diseases: cohort study, Denmark, 2009–10. Br. Med. J.
344, d7901. (doi:10.1136/bmj.d7901)
26 Simpson, C. R., Ritchie, L. D., Robertson, C., Sheikh, A. &
McMenamin, J. 2010 Vaccine effectiveness in pandemic
influenza—primary care reporting (VIPER): an observa-
tional study to assess the effectiveness of the pandemic
influenza A (H1N1)v vaccine. Health Technol. Assess. 14,
son, L. A. 2007 Mortality benefits of influenza vaccination in
elderly people: an ongoing controversy. Lancet Infect. Dis. 7,
28 UK Health Protection Agency. Swine flu vaccination:
what you need to know. See http://www.direct.gov.uk/
29 Kettler, B. 2009 Focus of H1N1 vaccination effort shifts.
Mail Tribune, 14 November 2009. See http://www.mailtri-
30 Zimmer, S. et al. 2010 Seroprevalence following the second
wave of pandemic 2009 H1N1 influenza in Pittsburgh,
PA, USA. PLoS ONE 5, e11601. (doi:10.1371/journal.
31 Wu, J. T. et al. 2011 Estimating infection attack rates and
severity in real time during an influenza pandemic: analysis
of serial cross-sectional serologic surveillance data. PLoS
Med. 8, e1001103. (doi:10.1371/journal.pmed.1001103)
32 Goldstein, E., Cowling, B. J., Aiello, A. E., Takahashi, S.,
King, G., Lu, Y., Lipsitch, M. & Yates, A. 2011 Estimating
incidence curves of several infections using symptom
surveillance data. PLoS ONE 6, e23380. (doi:10.1371/
33 Lipsitch, M., Finelli, L., Heffernan, R. T., Leung, G. M. &
Redd, S. C. 2011 Improving the evidence base for decision
making during a pandemic: the example of 2009 influenza
A/H1N1. Biosecur. Bioterror. 9, 89–115.
173, 127–135. (doi:10.1093/aje/kwq347)
ofPublic Health. 2009
Vaccination in a declining epidemic
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J. R. Soc. Interface (2012)