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Mitigation strategies for pandemic influenza
in the United States
Timothy C. Germann*
†
, Kai Kadau*, Ira M. Longini, Jr.
‡
, and Catherine A. Macken*
*Los Alamos National Laboratory, Los Alamos, NM 87545; and
‡
Program of Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center and
Department of Biostatistics, School of Public Health and Community Medicine, University of Washington, Seattle, WA 98109
Communicated by G. Balakrish Nair, International Centre for Diarrhoeal Disease Research Bangladesh, Dhaka, Bangladesh, February 16, 2006
(received for review January 10, 2006)
Recent human deaths due to infection by highly pathogenic (H5N1)
avian influenza A virus have raised the specter of a devastating
pandemic like that of 1917–1918, should this avian virus evolve to
become readily transmissible among humans. We introduce and
use a large-scale stochastic simulation model to investigate the
spread of a pandemic strain of influenza virus through the U.S.
population of 281 million individuals for R
0
(the basic reproductive
number) from 1.6 to 2.4. We model the impact that a variety of
levels and combinations of influenza antiviral agents, vaccines, and
modified social mobility (including school closure and travel re-
strictions) have on the timing and magnitude of this spread. Our
simulations demonstrate that, in a highly mobile population,
restricting travel after an outbreak is detected is likely to delay
slightly the time course of the outbreak without impacting the
eventual number ill. For R
0
< 1.9, our model suggests that the rapid
production and distribution of vaccines, even if poorly matched to
circulating strains, could significantly slow disease spread and limit
the number ill to <10% of the population, particularly if children
are preferentially vaccinated. Alternatively, the aggressive deploy-
ment of several million courses of influenza antiviral agents in a
targeted prophylaxis strategy may contain a nascent outbreak
with low R
0
, provided adequate contact tracing and distribution
capacities exist. For higher R
0
, we predict that multiple strategies
in combination (involving both social and medical interventions)
will be required to achieve similar limits on illness rates.
antiviral agents 兩 infectious diseases 兩 simulation modeling 兩
social network dynamics 兩 vaccines
I
t is inevitable that another influenza pandemic will occur, and
recent events sugge st that this might happen sooner rather than
later (1). A highly pathogenic H5N1 influenza A virus appears to
have become endemic in avian hosts in Asia, and it is now spreading
in migratory birds westward across eastern Europe. Human infec-
tions caused by this virus have a high case fatality rate; together with
recent genetic data that implicate direct transmission of avian-
adapted influenza virus to humans as the cause of the 1918
influenza pandemic (2), these conditions raise the specter of
another devastating pandemic. To date, H5N1 viruse s cannot
transmit readily from human to human, thus providing a window to
plan for the pandemic that will occur should the virus evolve to be
readily transmissible among humans. If the nascent pandemic is not
contained by timely intervention at its source (3, 4), international
travel could carry pandemic viruses around the globe within weeks
to months of the initiation of the outbreak, causing a worldwide
public health emergency.
Intensive pandemic planning is occurring at the national [U.S.
Department of Health and Human Services (HHS) Pandemic
Inf luenza Plan, www.hhs.gov兾pandemicflu兾plan) and interna-
tional [World Health Organization (WHO) Global Inf luenza
P reparedness Plan, www.who.int兾csr兾resources兾publications兾
influenza兾WHO㛭CDS㛭CSR㛭GIP㛭2005㛭5兾en兾index.html] levels.
The most pressing public health questions are: what might be the
time c ourse and geographic spread of the outbreak, and what is
the most effective utilization of available therapeutic and social
resources to min imize the impact of the outbreak? Precise
plann ing is hampered by several unknowns, most critically the
eventual human-to-human transmissibility of the human-
adapted avian strain (characterized by the basic reproductive
number R
0
, the average number of secondary infections caused
by a single typical infected individual among a completely
susceptible population), and the supply of therapeutic agents.
Manufacturers of neuraminidase inhibitors, such as oselt amivir,
have committed to considerable increases in production over the
next 3–4 years. However, the production of vaccine, the tradi-
tional first line of defense against influenza vir us infections, is
hampered by the inability to predict the antigenic details of the
evolved vir us at the time that it becomes a pandemic strain and
the consequent inability to prepare a highly effective vaccine in
advance of a pandemic outbreak. Given these uncertainties, it is
import ant to develop multiple mitigation strategies, involving
vac cination, prophylaxis with antiviral drugs, and both voluntary
and imposed changes in social patterns such as school closures
and travel restrictions.
The course of an influenza outbreak is sensitive to many factors,
particularly population mobility and the susceptibility of individuals
to the virus. Traditional mathematical models of epidemics often
take the form of deterministic SIR differential equations for the
population dynamics of susceptible (S), infectious (I), and re-
moved兾recovered (R) individuals (5, 6). Such models have also
been extended to model the geographic spread of infectious dis-
eases (7, 8). However, the population-based nature of this class of
models best describes the dynamics of an epidemic when large
numbers of individuals are infected, rather than the initial or final
stage s of an outbreak, when small numbers of individuals are
involved and stochastic person-to-person transmission processes
dominate. To satisfactorily model the initial seeding and final
quenching of small community-level outbreaks requires a funda-
mentally different approach. To capture this crucial effect of
uncertainty in transmission on epidemic predictions, we develop
and use a stochastic agent-based discrete-time simulation model.
This class of model has been used to assess vaccination and antiviral
prophylaxis strategies on a local level (9–11); larger-scale versions
have recently been used to investigate strategie s at a regional level
for containing an emerging pandemic influenza strain at its source
(3, 4). Our national-level model combines an individual-level
description of influenza viral infection and transmission dynamics
with high-fidelity U.S. Census Bureau and Department of Trans-
portation data on population demographics and mobility, yielding
a massive-scale simulation model of the spatiotemporal dynamics of
spread of a pandemic strain of influenza virus among an artificial
U.S. population of 281 million people. Such an endeavor is only now
practical with modern parallel supercomputing platforms and pro-
gramming technique s.
Conflict of interest statement: No conflicts declared.
Abbreviations: TAP, targeted antiviral prophylaxis; NAI, neuraminidase inhibitor.
†
To whom correspondence should be addressed. E-mail: tcg@lanl.gov.
© 2006 by The National Academy of Sciences of the USA
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Results and Discussion
Simulation Model Design. The model population of 281 million
individuals is distributed among 65,334 census tracts to closely
represent the actual population distribution according to publicly
available 2000 U.S. Census data (www.census.gov兾main兾www兾
cen2000.html). Each tract is in turn organized into 2,000-person
communities. The model runs in cycles of two 12-hour periods
(‘‘day’’ and ‘‘night’’), during which we identify seven contexts
(‘‘mixing groups’’) within which individuals can associate. In five of
these contexts (households, household clusters, preschools, play-
groups, schools, and work groups), relatively close person-to-person
association regularly occurs. Additionally, ‘‘neighborhoods’’ and
‘‘communities’’ provide unspecified contexts (e.g., shopping malls)
within which occasional casual person-to-person association occurs.
Because each individual may interact with any member of his or her
mixing group, the group sizes determine the numbers of people who
would be considered for antiviral prophylaxis in our socially tar-
geted strategy of mitigation (below). Daytime contacts occur in
neighborhoods and communities as well as in the age-appropriate
setting, and nighttime contacts occur only in households, household
clusters, neighborhoods, and communities. U.S. Census data on
tract-to-tract worker flow is used to model the commute of working
adults to their workplace, thus accurately capturing the short- to
medium-distance population mobility important for disease spread.
In addition, each individual takes occasional long-distance trips
(three per year on average), lasting between 1 day and 3 weeks (4.1
days on average), matching Bureau of Transportation Statistics
data (www.bts.gov兾publications兾national㛭transportation㛭statistics).
Our simple model of long-range travel could be extended to
account for different types of travel (e.g., business or leisure) or
groups of travelers (such as a family) or to explicitly incorporate the
airline network structure, as in ref. 8.
The disease transmission and natural history models are briefly
described in Materials and Methods, with further details provided in
Supporting Text, Figs. 3–5, and Tables 3–5, which are published as
supporting information on the PNAS web site. To model the
introduction of pandemic influenza into the U.S., we assume that
impenetrable borders are either prohibitively expensive or impos-
sible to create, and that international air travel is the dominant
mode of influenza introduction from outside the U.S. Conse-
quently, a small random number of incubating individuals, equiv-
alent to 0.04% of arriving international passengers, is introduced
each day at each of 14 major international airports in the conti-
nental U.S. (see Table 6, which is published as supporting infor-
mation on the PNAS web site). The simulation covers 180 days,
roughly the length of a U.S. influenza season. We assume that,
because of the uncertainty in diagnosis of influenza infections and
the sporadic nature of the early stages of an outbreak, a cumulative
number of 10,000 symptomatic individuals nationwide is required
to trigger a nationwide pandemic alert (see Supporting Text for a
sensitivity analysis of various response delays, for selected inter-
vention strategies).
Intervention Strategies. A variety of intervention strategies com-
posed of one or more of the following four actions is considered: (i)
socially targeted antiviral prophylaxis (TAP), in which symptomatic
individuals and most of their close contacts receive treatment or
prophylaxis, respectively, with antiviral drugs; (ii) dynamic mass
vaccination, either of a random selection of individuals from the
entire population or with preference for children, and with various
production and distribution rate s and starting dates; (iii) closure of
schools, including preschools and play groups; and (iv) social
distancing, as a result of legally mandated travel restriction or
quarantine programs, or voluntary changes in social behavior.
TAP (11) is triggered by the first symptomatic person to be
ascertained within a household (the index case). Because symp-
tomatic diagnosis of influenza viral infection is inaccurate, leading
either to delays in accurate diagnosis by biological assay or to
excessive use of antivirals due to false positives, we simulate several
scenarios. For the majority of our simulations, we assume that there
are 0% false positive s, and 60% of index cases are ascertained (the
rest omitted because of, for example, misdiagnosis or lack of acce ss
to health care). When an index case is ascertained, he or she is
treated, and all remaining people in this person’s household and
household cluster are offered prophylaxis. If an ascertained index
case belongs to a daycare, preschool, school, or workplace, then
100% of the people in that daycare or preschool are offered
prophylaxis, or 60% of the people in that school or workplace.
(Results for other ascertainment percentages, diagnosis delays,
false positives, or prophylaxis strategies are presented in Supporting
Text.) Due to its labor-intensive nature, TAP is likely to be feasible
only during the earliest stages of an outbreak in any particular
community, before the community health system is overwhelmed.
The dose and duration for effective treatment and prophylaxis
using neuraminidase inhibitors (NAIs) against currently circulating
strains of human influenza virus are well known (12), although a
recent study suggests that an increased dose and duration of
treatment may be needed to counteract H5N1 viral infections (13).
On the other hand, these viruses may not retain their current
unusually high growth rates if they evolve to be readily human-to-
human transmissible. In light of this uncertainty, we use the current
manufacturer’s recommended dose (10 tablets of oseltamivir for 5
days of treatment or 10 days of prophylaxis) and current estimate s
of oseltamivir efficacy in reducing infectiousne ss and susceptibility
(see Supporting Text) (3, 14). Administration of a single course of
NAI is initiated the day after the index case is ascertained,
providing therapy for the index case and prophylaxis for others. A
susceptible individual may receive subsequent courses of NAIs if
another index case occurs later in a mixing group of which he or she
is a member. We assume that 5% of people who start taking
influenza antiviral agents will stop taking them after 1 day of
treatment or prophylaxis.
Interventions involving vaccination suffer from uncertainty
about the future identity of a pandemic strain, making it impossible
to stockpile well matched pandemic vaccine s. However, prevacci-
nation based on a killed avian virus precursor to the pandemic
strain is possible, providing a perhaps poorly matched but poten-
tially efficacious vaccine. Vaccination can also be based on killed or
live attenuated emergent pandemic virus, providing a close match
to the subsequent circulating strains but available with a lag of a few
months from emergence (in nonpandemic years, vaccine manufac-
ture take s between 6 and 9 months). A ‘‘dynamic vaccination’’
scenario, in which vaccine becomes available incrementally, starting
from as early as 2 months before, to as late as 2 months after, the
first individual in the U.S. is infected, is inve stigated, with different
production rates, total production amounts, and distribution poli-
cies (either uniformly throughout the population or preferentially
to children). We compare the administration of the recommended
two doses conferring best protection levels to a strategy in which
twice as many people are given a single dose, assuming that a single
dose of vaccine confers about half the protection of two doses (15).
§
Much uncertainty exists about the societal acceptability of op-
tions for creating social distance and thereby reduction in trans-
mission. Given the importance of children in the transmission of
influenza (16), school closure is likely to be an effective (albeit
burdensome) social distancing policy. Although formally imposed
quarantine or travel restriction policies are possible, voluntary
§
In fact, efficacy of experimental vaccines against a novel pandemic strain cannot be
ascertained in the absence of actual viral challenge; immunogenicity alone can be deter-
mined. Experimental vaccines based on avian influenza virus have required much greater
amounts of antigen for acceptable levels of immunogenicity than standard human
vaccines. This discrepancy does not enter into our calculations of required doses of vaccine.
We assume that pandemic vaccines will have the same relationship between efficacy and
immunogenicity as that for standard vaccines against human influenza virus.
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changes in hygienic and social behavior (including travel plans) will
undoubtedly occur. Indeed, the spontaneous public re sponse to
news of an approaching pandemic will affect social behavior in
unpredictable ways, so the social distancing strategies explored here
are hopefully realistic approximations to voluntary or imposed
distancing at three different scales: at the levels of schools, local
communities, and nationwide travel. At the local scale, this social
distancing is assumed to manife st itself in a concentration of
interactions within households and household clusters, and at
longer scales we consider uniform reductions in the amount of
long-range travel to as little as 1% of the normal frequency. (See
Supporting Text for details of implementation.) Although the social
distancing measures studied here form a necessary first step in
modeling such effects on disease transmission, further investigation
is needed into variations in contact structure that are not considered
in our model (e.g., classroom size variations with geographic region
and grade level, parents staying at home with sick children, and
other venues and mechanisms for transmission).
Simulation Results. Independent realizations of our simulations for
a given set of parameter values lead to very similar epidemic curves
(see Supporting Text, Table 7, and Figs. 6 and 7, which are published
as supporting information on the PNAS web site, for details
including the estimation of R
0
). In the absence of intervention, for
R
0
⫽ 1.9, our simulated pandemic begins with sporadic outbreaks
occurring across the country in areas of dense population for 24
days before the outbreak is recognized (Table 1 and Movie 1, which
is published as supporting information on the PNAS web site). The
pandemic peaks after 85 days, with a final illne ss attack rate of 43%
(Table 2). The greatest nationwide activity is concentrated in a
2-month period when ⬎100,000 people become ill each day,
although local areas differ in the timing and duration of their highly
active periods. This coincide s quite well with waves of past pan-
demics; the 1957–1958 influenza A (H2N2) ‘‘Asian’’ virus initially
appeared in June and July 1957, as sporadic cases in Iowa, Loui-
siana, and the West Coast, developing into local outbreaks during
August 1957 before peaking in a 60-day period covering September
and October 1957 (17). Similarly, the 1968–1969 influenza A
(H3N2) ‘‘Hong Kong’’ virus first appeared as sporadic cases along
the West Coast in July 1968, developing into local outbreaks 3
months later in October and peaking in December 1968 and
January 1969, before finally ending in March 1969 (7).
Although the dynamics of the pandemic in the absence of
mitigation are clearly sensitive to R
0
, interestingly, this sensitivity is
modest when R
0
increases beyond 1.9 compared with the effect of
increasing R
0
from 1.6 to 1.9 (Table 1). We use as our guideline for
adequate mitigation a reduction in the overall rate of illness to no
greater than that of a typical influenza epidemic, ⬇10%. The results
presented in Fig. 2 and Table 2 suggest that as R
0
increases from 1.6
to 1.9, a transition occurs from an outbreak that can be mitigated
with moderate efforts, to one that can be mitigated only with
vigorous application of multiple strategie s. For example, several of
the single interventions that we simulated are successful for R
0
⫽
1.6, with TAP the most effective single intervention for our model
of social mobility and transmission, provided adequate antiviral
supplies exist and close contacts can be rapidly identified (see Fig.
1 and Movie 2, which is published as supporting information on the
PNAS web site). In contrast, for R
0
⫽ 1.7, 10.0 million courses are
Table 1. Characteristics of simulated pandemic influenza in the
U.S. in the absence of interventions
Basic reproductive number, R
0
1.6 1.9 2.1 2.4
Rate of spread: 1,000th ill person* 14 13 12 11
10,000th ill person* 29 24 22 19
100,000th ill person* 48 37 34 29
1,000,000th ill person* 70 52 46 39
Peak of epidemic* 117 85 75 64
Daily number of new cases at peak
activity
2.3 M 4.5 M 6.0 M 7.9 M
Number of days with ⬎100,000
new cases
86 68 60 52
Cumulative number of ill persons 92 M 122 M 136 M 151 M
M, million.
*Days after initial introduction.
Table 2. Simulated mean number of ill people (cumulative incidence per 100) and for TAP, the number
of antiviral courses required for various interventions and R
0
Intervention R
0
⫽ 1.6 R
0
⫽ 1.9 R
0
⫽ 2.1 R
0
⫽ 2.4
Baseline (no intervention) 32.6 43.5 48.5 53.7
Unlimited TAP (no. of courses)* 0.06 (2.8 M) 4.3 (182 M) 12.2 (418 M) 19.3 (530 M)
Dynamic vaccination (one-dose regimen)
†‡
0.7 17.7 30.1 41.1
Dynamic child-first vaccination
†‡
0.04 2.8 16.3 35.3
Dynamic vaccination (two-dose regimen)
‡§
3.2 33.8 41.1 48.5
Dynamic child-first vaccination
‡§
0.9 25.1 37.2 47.3
School closure
¶
1.0 29.3 37.9 46.4
Local social distancing
¶
25.1 39.2 44.6 50.3
Travel restrictions during entire simulation
㛳
32.8 44.0 48.9 54.1
Local social distancing and travel restictions
¶㛳
19.6 39.3 44.7 50.5
TAP,* school closure,** and social distancing** 0.02 (0.6 M) 0.07 (1.6 M) 0.14 (3.3 M) 2.8
††
(20 M)
Dynamic vaccination,
†‡
social distancing,
¶
travel
restrictions,
¶㛳
and school closure**
0.04 0.2 0.6 4.5
TAP,* dynamic vaccination,
†‡
social distancing,
¶
travel restrictions,
¶㛳
and school closure**
0.02 (0.3 M) 0.03 (0.7 M) 0.06 (1.4 M) 0.1 (3.0 M)
Dynamic child-first vaccination,
†‡
social distancing,
¶
travel restrictions,
¶㛳
and school closure**
0.02 0.2 0.9 7.7
M, million.
*60% TAP, 7 days after pandemic alert, antiviral supply of 20 M courses unless stated.
†
10 million doses of a low-efficacy vaccine (single-dose regimen) per week.
‡
Intervention continues for 25 weeks, beginning such that the first individuals treated develop an immune response on the date of the
first U.S. introduction.
§
10 million doses of a high-efficacy vaccine (two-dose regimen) per week.
¶
Intervention starting 7 days after pandemic alert.
㛳
Reduction in long-distance travel, to 10% of normal frequency.
**Intervention starting 14 days after pandemic alert.
††
Exhausted the available supply of 20 M antiviral courses.
Germann et al. PNAS
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MEDICAL SCIENCES
predicted to limit the national illness attack rate to 0.2%, but for
R
0
⫽ 1.8, a prohibitively large 51 million courses would be required.
Fewer courses do not control the pandemic, and an overall attack
rate in excess of 10% ensues. An aggressive vaccine production and
distribution plan may also be succe ssful for R
0
⬍ 1.9 (see Movie 3,
which is published as supporting information on the PNAS web
site), particularly if initially targeted at children (18). With the
exception of school closures for R
0
⫽ 1.6, social distancing policie s
alone appear only to slow the pandemic without reducing its impact
as measured by morbidity (see Movie 4, which is published as
supporting information on the PNAS web site). Regardless of R
0
,
unless drastic travel restrictions are imposed, the extent or duration
of the pandemic is insensitive to details of the amount and
location(s) of introductions of pandemic influenza virus in our
simulations (see Figs. 8 and 9, which are published as supporting
information on the PNAS web site). Due to the highly mobile U.S.
population, the details of the introduction of the pandemic virus
only affect the precise geographic spread and timing of the epi-
demic peak.
For R
0
⬎ 1.9, no single policy is predicted to be sufficient to
mitigate an outbreak. For such highly transmissible strains, a
combination of behavioral changes (to slow the spread) and ther-
apeutic and prophylactic measures is essential. Throughout the
range of R
0
tested, antivirals, provided they are available in suffi-
cient quantities and can be rapidly distributed, are a powerful tool
for management. On the other hand, combinations of behavioral
changes, together with a steady production of a low-efficacy vaccine
throughout the pandemic (dynamic vaccination), can also success-
fully control pandemics of viruses with all except the highest level
of transmissibility (Table 2 and Fig. 2). It is also important to note
that the e stimated benefits of preferentially vaccinating children are
offset by the closing of schools, so that although one measure or the
other is highly recommended, both together seem to offer no
additional protection. Based on this result, the high societal cost of
an extended closing of schools, requiring parents or grandparents
to remain home with young children, may be avoidable through
such a focused vaccination strategy. Similarly, our model suggests
that the combination of TAP, school closure, and social distanc-
ing can be succe ssful up to R
0
⫽ 2.4, without any vaccination (see
Tables 8–10 and Figs. 10 and 11, which are published as supporting
information on the PNAS web site, for additional combinations of
intervention policies).
These projected major efforts necessary to mitigate pandemic
influenza in the U.S. make it obvious that, for the U.S. and other
c ountries, it would be optimal to control a potential pandemic
strain of influenza at the source. In the event that a pandemic
influenza virus does reach the U.S., according to our results, the
U.S. population could begin to experience a nation-wide pan-
demic within 1 month of the earliest introductions. Our simu-
lations indicate that the rapid imposition of a 90% reduction in
domestic travel would slow the vir us spread by only a few days
to weeks (depending on R
0
), without reducing the eventual size
Fig. 1. Two simulated pandemic influenza outbreaks
with R
0
⫽ 1.9, initiated by the daily entry of a small
number of infected individuals through 14 major in-
ternational airports in the continental U.S. (beginning
on day 0). The tract-level prevalence of symptomatic
cases at any point in time is indicated on a logarithmic
color scale, from 0.03% (green) to 3% (red) of the
population. No mitigation strategies are used in the
baseline simulation (Left), resulting in a 43.5% attack
rate. (Right) A 60% TAP intervention begins at day 31,
or 7 days after the pandemic alert. At day 99, the
nationwide supply of 20 million antiviral courses is
exhausted, leading to a nationwide pandemic.
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of the outbreak, unless other behavioral or medical responses are
introduced.
Conclusions
In this study, we regard strategies for mitigating pandemic
influenza in the U.S. as successful when they limit the national
att ack rate to that of annual influenza epidemics, ⬇10% of the
U.S. population. All of our c onclusions about the suc cess of
mitigation strategies are based on a simplified model of disease
transmission and social contacts. Alternative models producing
the same R
0
may differ in quantitative details, but we expect the
following conclusions to hold qualit atively. To achieve the target
level of mitigation with antiviral agents alone, a very large
stockpile is likely to be required (10 million courses of oselti-
mavir for R
0
⫽ 1.7, or 51 million courses for R
0
⫽ 1.8, in our
simulations). For larger values of R
0
, the stockpile would have to
be prohibitively large, e.g., 182 million courses for R
0
⫽ 1.9. Only
for R
0
ⱕ 1.6 is reasonable control predicted to be achievable with
the small currently available stockpile of 5 million courses. Our
articulated TAP strategy t argets sites of transmission for pro-
phylactic drug use (3, 11), consequently using much less drug
than if geographic regions or large groups, such as entire schools,
were targeted (3, 4). However, this TAP strategy requires the
identification of the effective sizes of the close-c ontact mixing
groups, which is much more difficult in practice than in our
assumed contact structure model. Consequently, the implemen-
t ation of TAP would require c onsiderable up-front preparation
or on-the-spot decision making, and its ef fectiveness may be
reduced by unforeseen sites or mechanisms of transmission that
are not included in our model. Nevertheless, we believe that,
even when antiviral stockpiles are small, the TAP strategy could
be quite effective in slowing virus spread until vaccination could
be implemented. (Of course, the potential emergence of an
antiviral-resistant strain should also be considered in any pan-
demic planning.)
When vaccine supplies are limited, our simulations indicate that,
at a population level, vaccinating n people with the recommended
two doses providing maximal protection is less effective at reducing
attack rates than vaccinating 2n people with single dose s, assuming
that a single dose confers roughly half the protection of a two-dose
regimen (which may or may not be an option, depending on the
particular vaccine). The relative benefits of single-dose vaccination
of 2n people and two-dose vaccination of n people are expected to
hold for prevaccination using poorly matched avian virus seed
stock, although benefits are expected to be less than those presented
here. The most effective single mitigation strategy would be a rapid
dynamic vaccination of the population, initiated within 2 weeks of
the pandemic alert, with a single dose of vaccine from the pandemic
virus. Specifically, for R
0
ⱕ 1.6, spread could potentially be con-
trolled if vaccine could be distributed nationally at the rate of 10
million doses per week for 25 weeks. For 1.9 ⱕ R
0
ⱕ 2.4, single-dose
vaccination would likely require augmentation with some combi-
nation of TAP, social distancing measures, and travel restrictions to
be effective. Assuming that children remain major spreaders during
the early stages of a pandemic outbreak, as they are for interpan-
demic influenza (16), the preferential vaccination of school children
should be much more effective than random vaccination unless
schools are closed. If vaccination in advance of a pandemic were
possible using an avian seed virus, use of this poorly matched
vaccine could slow virus spread as much as possible until a well
matched vaccine based on the emergent human pandemic virus
could be deployed.
Based on the pre sent work, with the assumptions inherent in our
model and its parameters, we believe that a large stockpile of
avian-based vaccine with potential pandemic influenza antigens,
coupled with the capacity to rapidly make a better-matched vaccine
based on human strains, would be the be st strategy to mitigate
pandemic influenza. This effort needs to be coupled with a rapid
vaccine distribution system capable of distributing at least 10 million
vaccine doses per week to affected regions of the U.S.. For highly
transmissible strains (i.e., having R
0
ⱖ 1.9), social distancing
policies, including school closure and兾or travel restrictions, may
also be required to slow the epidemic spread sufficiently to enable
production and distribution of sufficient quantitie s of vaccine. If
Fig. 2. Epidemic curves (note the
logarithmic scale) demonstrating
the effectiveness of several differ-
ent mitigation strategies, as com-
pared to the baseline scenario with-
out any intervention, for different
values of R
0
. See Table 2 for details
of each intervention. In the case of
vaccination, results shown here are
for a uniform coverage of the en-
tire population with a single-dose
regimen.
Germann et al. PNAS
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April 11, 2006
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vol. 103
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no. 15
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MEDICAL SCIENCES
antivirals were the preferred therapeutic defense, a stockpile of 20
million courses could be sufficient to effectively reduce national
spread of a virus with R
0
up to 1.7, provided extensive planning
and兾or on-the-spot decision making to distribute antivirals in a
timely fashion was carried out. If implemented for pandemic
planning, such infrastructure for stockpiling and rapid deployment
of therapeutics would lead to the more effective use of vaccine s (18)
and antiviral agents in annual influenza epidemics. On the other
hand, travel restrictions alone do not appear to be an effective
control strategy, due to the implausibly early and drastic measures
required to significantly reduce the large number of local outbreaks
that are likely to emerge around the country.
Although our simulation model was specifically designed for the
U.S., we believe that the qualitative conclusions reached here will
hold for other countries or regions with highly mobile populations.
However, for quantitative predictions to hold in settings other than
those explicitly studied here, it will be important to demonstrate a
robustness to various assumptions inherent in the model and its
parameters. (In the event of an actual pandemic, use of a model to
make quantitative predictions will require a rapid characterization
of the transmission dynamics, disease natural history, and vaccine
and antiviral efficacie s to e stimate these key model parameters.)
Then the computational tool introduced here, capturing both the
stochastic transmission proce sse s that dominate the initial stages
and final extinction of an outbreak and the detailed spatiotemporal
dynamics of infectious disease spread, can be applied to public
health que stions that cannot be effectively addressed with tradi-
tional mathematical models (5, 6). In particular, should avian
influenza continue to spread throughout the world, it will be
important to develop containment strategies, analogous to those
proposed for Southeast Asia (3, 4), that anticipate the possibility of
a human-to-human transmissible strain of H5N1 influenza emerg-
ing first in a highly mobile population such as Europe or the U.S.
Materials and Methods
Disease Transmission Model. Each class of mixing group is charac-
terized by its own set of age-dependent probabilities of person-to-
person contact of sufficient closeness and duration for transmission
of normal human influenza virus to plausibly occur within a 12-hour
period. Each of these contact probabilities is multiplied by the
probability of transmission given contact, a single multiplicative
constant that can be varied to model different R
0
values.
¶
As
described in Tables 3 and 4, the contact probabilities were cali-
brated against total and age-specific illness attack rates of data in
past pandemics (3, 9, 17), although the se attack rate data alone do
not uniquely determine parameter estimate s. Infection of suscep-
tible individuals is modulated by the antiviral and vaccination
statuse s of both the infectious and susceptible persons. A suscep-
tible individual has a daily probability of becoming infected, accu-
mulated over his兾her contacts within each of the mixing groups to
which he兾she belongs (see Supporting Text for details). Age-
dependent distributions are used to determine individual disease
progression, whether an infected person becomes ill or remains
asymptomatic and, if symptomatic, when (if ever) the person
withdraws to household-only contacts.
Disease Natural History Model. Predictions of the model are sensitive
to the assumed disease course, but we can refer to past pandemics
for guidance. The disease course for infection with the 1957 and
1968 pandemic influenza viruse s and with post-1968 influenza A
viruses (17) has been fairly consistent, with an estimated mean
latent period of around 1.9 days and mean infectious period of
around 4.1 days in several modeling studies (7, 9, 11, 20). The mean
serial interval or generation time (i.e., average time between new
infection and transmission to another susceptible) is thus ⬇4 days.
However, a recent reanalysis of incubation period and household
transmission data suggests a significantly shorter serial interval of
only 2.6 days, also consistent with viral shedding data from exper-
imental infection studies (4). On the other hand, H5N1 virus is quite
different from viruse s causing past pandemics (including the 1918
pandemic), bearing the distinctive molecular signature of highly
pathogenic avian influenza viruses, with possible implications for
the resulting disease course in humans. The limited clinical infor-
mation available to date on the disease course in individuals
infected with H5N1 virus suggests a longer time course (13).
Because H5N1 has not yet adapted for ready transmission among
humans, and disease presentation may change in conjunction with
this evolution, we focus on the midrange distributions in our model
(see Fig. 3b), with a generation time of 3.5 days (3).
Model Limitations. No seasonal or environmental effects or viral
evolution are modeled (although it would certainly be possible to
do so); we assume constant contact, transmission, and disease
course parameters throughout the U.S. for the entire duration of an
influenza season. Disease-related mortality was also neglected,
under the assumption that deaths would occur at the latter stages
of the infectious period and thus not significantly affect the spread
of disease. It is important to realize that, although we attempt to
make realistic estimates of model parameters, model validation in
the traditional sense is not possible due to the unpredictability of
viral evolution and the impossibility of documenting all cases of
influenza in any influenza season.
We are indebted to Norman Johnson, Peter Lomdahl, and Tim McPher-
son for several key contributions in the early stages of this work, and to
Mike Brown, Neil Ferguson, Brad Holian, Ed MacKerrow, Jef f Newman,
Gary Resnick, Tom Wehner, and Shufu Xu for their enc ouragement and
suggestions. We also thank Tony Redondo, Andy White, and the
Institutional Computing Prog ram at Los Alamos National L aboratory
for providing access to the necessary superc omputing resources. This
work was supported by the Department of Homeland Security through
program CBLA11MP (to T.C.G., K.K., and C.A.M.) and by National
Institute of General Medical Sciences MIDAS Grant U01-GM070749
(to I.M.L.). Los A lamos National Laboratory is operated by the Uni-
versity of California for the U.S. Department of Energy under Contract
W-7405-ENG-36.
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¶
R
0
is a difficult quantity to estimate during an actual epidemic, because it depends critically
upon the disease serial interval (or generation time) and to a somewhat lesser extent on the
relative durations of the latent and infectious periods (19, 20). Because our model assumes
particular values for these quantities, R
0
is a useful measure of transmissibility, but care needs
to be taken when comparing results for different models or epidemiological data.
5940
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www.pnas.org兾cgi兾doi兾10.1073兾pnas.0601266103 Germann et al.
