uncertainties of pandemic influenza
TRANSCRIPT
Int. J. Risk Assessment and Management, Vol. 16, Nos. 1/2/3, 2012 1
Copyright © 2012 Inderscience Enterprises Ltd.
Measuring the uncertainties of pandemic influenza
Jeanne M. Fair* Biosecurity and Public Health, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Fax: 505-665-3866 E-mail: [email protected] *Corresponding author
Dennis R. Powell Risk Analysis and Decision Support Systems, Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: [email protected]
Rene J. LeClaire Energy and Infrastructure Analysis, Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: [email protected]
Leslie M. Moore Statistical Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: [email protected]
Michael L. Wilson Sandia National Laboratories New Mexico, Albuquerque, NM 87185, USA E-mail: [email protected]
Lori R. Dauelsberg Risk Analysis and Decision Support Systems, Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: [email protected]
2 J.M. Fair et al.
Michael E. Samsa Decision Support and Risk Management, Argonne National Laboratory, Argonne, IL 60439,USA E-mail: [email protected]
Sharon M. DeLand Sandia National Laboratories New Mexico, Albuquerque, NM 87185, USA E-mail: [email protected]
Gary Hirsch Creator of Learning Environments, Wayland, MA 01778, USA E-mail: [email protected]
Brian W. Bush Energy Analysis, National Renewable Energy Laboratory, Golden, CO 80401, USA E-mail: [email protected]
Abstract: It has become critical to assess the potential range of consequences of a pandemic influenza outbreak given the uncertainty about its disease characteristics while investigating risks and mitigation strategies of vaccines, antivirals, and social distancing measures. Here, we use a simulation model and rigorous experimental design with sensitivity analysis that incorporates uncertainty in the pathogen behaviour and epidemic response to show the extreme variation in the consequences of a potential pandemic outbreak in the USA. Using sensitivity analysis we found the most important disease characteristics are the fraction of the transmission that occur prior to symptoms, the reproductive number, and the length of each disease stage. Using data from the historical pandemics and for potential viral evolution, we show that response planning may underestimate the pandemic consequences by a factor of two or more.
Keywords: influenza; epidemics; public health epidemiology; pandemic; simulation; sensitivity analysis.
Reference to this paper should be made as follows: Fair, J.M., Powell, D.R., LeClaire, R.J., Moore, L.M., Wilson, M.L., Dauelsberg, L.R., Samsa, M.E., DeLand, S.M., Hirsch, G. and Bush, B.W. (2012) ‘Measuring the uncertainties of pandemic influenza’, Int. J. Risk Assessment and Management, Vol. 16, Nos. 1/2/3, pp.1–27.
Measuring the uncertainties of pandemic influenza 3
Biographical notes: Jeanne M. Fair is a Research Scientist at Los Alamos National Laboratory specialising in zoonotic infectious diseases. She received her PhD in Biology from the University of Missouri-St. Louis. Her current research includes risk assessment, epidemiology, disease modelling, and specifically, diseases in birds. She was the Lead Analyst for Critical Infrastructure Protection and Decision Support Systems team investigations for pandemic influenza.
Dennis R. Powell is a Mathematician with over 25 years of experience in developing simulations and using them for analysis. He has worked in diverse areas of study including underwater acoustics, artificial intelligence, ground combat modelling, manufacturing supply chain analysis, multi-polar nuclear warfare, critical infrastructure protection modelling and simulation, agent-based simulation, epidemiological simulation, risk assessment, decision analysis, and counter terrorism modelling. He is a Research Scientist at Los Alamos National Laboratory working with the National Infrastructure Simulation and Analysis Center (NISAC) to provide analysis insights for potential disruptions to critical infrastructure.
Rene J. LeClaire received his BS and MS in Nuclear and Energy Engineering from the University of Lowell in 1981 and ScD (Doctorate of Science) from the Massachusetts Institute of Technology in Fusion Technology in 1986. He is currently a Research Engineer IV in the Energy and Infrastructure Analysis Group at Los Alamos National Laboratory where he has been engaged in nuclear reactor safety modelling and assessment for the Nuclear Regulatory Commission, dispersion modelling and analysis for LANL dynamic experiments and LANL facilities and institutional analysis.
Leslie M. Moore is a Research Scientist in the Statistical Sciences group at Los Alamos National Laboratory. Her academic background includes a PhD in Mathematics with concentration in Statistics earned at the University of Texas at Austin under the direction of Professor Emeritus Peter John. She specialises in design and analysis for computer experiments and her research includes papers on minimax/maximin distance criteria for selecting space filling designs, projection-array-based Latin hypercube design and sensitivity analysis.
Michael L. Wilson is a technical-staff member at Sandia National Laboratories. He holds a PhD in Physics and has been involved in modelling, analysis and risk assessment in a variety of areas, including performance assessment (risk analysis) of radioactive-waste disposal, risk and vulnerability assessments for nuclear power plants and other nuclear facilities, modelling and analysis of critical infrastructures and their interdependencies, and validation of models for radiation damage to semiconductors.
Lori R. Dauelsberg is a Scientist at Los Alamos National Laboratory (LANL). She received her Master’s in Economics from Boston University and her undergraduate degree from the University of California, Riverside. Since joining LANL, she has worked on a variety of projects to estimate economic impacts to critical infrastructures due to terrorist events, disease outbreaks and natural disasters. Her general area of research interest is macroeconomics, with an emphasis on analysing the economics of modelled events such as infectious disease spread and events of national significance. Her work modelling and analysing H1N1 earned a team Distinguished Performance Award from LANL.
Michael E. Samsa is the Decision Support and Risk Management Group Leader, with the Decision and Information Sciences Division of Argonne National Laboratory in Chicago. His research interests include Bayesian decision analysis, judgment theory, and judgment and decision making in high uncertainty, high stakes and low base rate security environments.
4 J.M. Fair et al.
Sharon M. DeLand is a Principle Member of Technical Staff in the Global Security Program at Sandia National Laboratories. She received her PhD in Physics from the University of Illinois. Her research interests include technical policy analysis in diverse areas including arms control and modelling and simulation of critical infrastructure disruptions.
Gary Hirsch has consulted with organisations on management strategy and organisational change for the past 40 years in areas such as healthcare, human services, education and news media. His healthcare work has concentrated on population health, chronic illness and emergency preparedness. He specialises in system dynamics and systems thinking and uses these techniques to create simulation-based learning environments including simulations of community level healthcare systems. He received his SB and SM degrees from MIT and is the author of three books and numerous articles and presentations.
Brian W. Bush is a member of the Energy Forecasting and Modelling Group in the Strategic Energy Analysis Center at the National Renewable Energy Laboratory in Golden, Colorado. He received his PhD in Physics from Yale University and has expertise in high performance computing, software architecture, design, implementation and testing. His primary research interests include energy modelling methodologies, sensitivity analysis and uncertainty quantification for multidisciplinary models and simulations, including understanding the limits of predictability.
1 Introduction
Public healthcare policy makers are concerned with preparing for a potential pandemic influenza outbreak, even once a pandemic is underway as with H1N1 influenza in 2009. Response planning is challenging, given that rapidly changing infectious diseases, such as influenza, have strong elements of uncertainty due to evolution of the virus as well as individual, population, and regional differences in how the host and viral pathogen interact in a pandemic (Ferguson et al., 2003; Skeik and Jabr, 2008). It is, therefore, critical to assess the potential range of consequences of a pandemic influenza outbreak given the uncertainty about its disease characteristics while investigating multiple mitigation strategies of vaccines, antivirals, and social distancing measures. With the continual potential threat of a possible highly pathogenic influenza outbreak in humans (Longini et al., 2005; Germann et al., 2006) the objectives of this analysis were, using a deterministic computer simulation model, to
1 assess a range of potential consequences of a pandemic influenza outbreak induced by uncertainty about its disease characteristics
2 investigate multiple mitigation strategies of vaccines, antivirals, and social distancing measures
3 assess the interactions between pandemic and the healthcare infrastructure, these latter two include evaluation in the presence of assumed uncertainty about disease characteristics.
There are many sources of uncertainty in studying the potential effects of influenza pandemics. These can be grouped into four categories: biological, policy, sociological response, and infrastructure response.
Measuring the uncertainties of pandemic influenza 5
• Biological uncertainty: Rapidly changing infectious diseases such as influenza have strong elements of uncertainty due to evolution of the virus as well as individual, population, and regional differences in how the host and viral pathogen interact in a pandemic. During a pandemic, the influenza virus continues to evolve, altering its contagiousness and virulence as it adapts to new hosts. The diversity of human populations with regard to immune function, health status, and gene function for responses to infectious diseases represents another element of uncertainty. Even as targeted vaccines are developed for a specific instance of a viral disease, the rapidity of viral evolution and the length of time to develop and deploy a vaccine imply uncertainty in vaccine efficacy. These aspects combine to define biological variation that leads to uncertainty in an analysis of a pandemic.
• Policy uncertainty: There are numerous intervention strategies for fighting infectious diseases. These include vaccinations, antivirals, social distancing, quarantining infectious and susceptible persons, and respiratory protection. Each of these strategies decreases either the transmission or the virulence of the diseases. The selection of particular combinations of interventions, timing of implementation, and resources available (such as vaccine and antiviral drug stockpiles) to implement the strategies are all elements of policy uncertainty. Because state health departments are independent of federal control, it is likely that their approaches to containing a pandemic will vary (Blumenshine et al., 2008; O’Connor et al., 2011). Differences in state and local responses to a pandemic, such as school closures, are likely to exist.
• Sociological uncertainty: It is rarely certain what fraction of the affected people will actually comply with policy guidance in an emergency situation. Within the context of an influenza pandemic, a myriad of other characteristics, including individual values, religious beliefs, perception of risk, confidence in authorised agencies, influence an individual’s decision of whether to comply with recommended policy. Sociological responses to a pandemic today may be very different than those of almost a century ago, diluting the benefit that historical examples may bring to analysing human behavioural responses to a pandemic. The uncertainties addressed in this analysis include the wide variation of non-policy actions undertaken by individuals intending to lower personal risk; for example, self-isolation, refusing vaccination, reliance on over-the-counter drugs, and so forth.
• Infrastructure response uncertainty: The resilience of infrastructure operations in a pandemic is related to the availability of the workforce, flexibility in labour management and usage (for example, overtime), and shifts in demand for infrastructure services. Labour availability is dependent on the disease severity (illnesses) and the sociological response (Hupert et al., 2009). This analysis focuses on the response of the healthcare infrastructure, in particular as an infrastructure facing labour shortages and significantly increased demand.
The analysis described here identifies key uncertain variables in each of these four categories and assesses the variability in outcomes due to assumed uncertainty in the inputs. Feasibility and costs for identified intervention strategies are also assessed. Outcomes and costs are combined in a decision model to assess the relative utility of selected mitigation strategies as a function of event likelihood.
6 J.M. Fair et al.
Influenza pandemics occur relatively infrequently with a range of consequences from mild to extreme. The challenge in predicting and planning for future pandemic events is rooted in the uncertainty of pandemic consequence. To quantify the potential range of consequences of future pandemics we apply well-established methods in uncertainty analysis (Iman and Helton, 1988; Sanchez and Blower, 1997; Granger and Henrion, 1998). In modelling disease progression, the outcomes of the model are determined by the inputs so the range of simulated outcomes is based on the range of inputs. The goal is to quantify the uncertainty of pandemic consequences conditioned on intervention strategies using probabilistic measures. The distribution of outcomes describes both the magnitude and relative likelihood of possible pandemic consequences. Due to a lack of consensus on the relative effectiveness of interventions and the attendant risks of unintended consequences, decision makers need to know the important driving parameters of the situation as well as the range of potential consequences. A simulation-based uncertainty analysis uses repeated evaluations of a model with different combinations of key model parameters sampled from specified probability distributions to estimate not only the range of potential outcomes but the induced probability distribution of those outcomes. The assumed distributions of inputs were selected through subject matter expert and policy maker review and peer-reviewed publications, and are proposed to provide a reasonable basis for evaluating breadth of outcome uncertainty via sampling from the assumed input distributions. Key model parameters were also identified through sensitivity analysis, which determines how the outcomes vary with changes in the values of model parameters and preferentially focuses on inputs that measurably drive the greatest variation in outcomes. In the uncertainty analysis we limited the model inputs to those parameters identified in sensitivity analysis as leading to the most variation in the outcomes, i.e., the important parameters.
2 Methods
2.1 Infectious disease model
We used the critical infrastructure protection decision support system (CIPDSS) (Bush et al., 2005) which is a suite of simulation models that simultaneously represents all US critical infrastructures (Moteff and Parfomak, 2004) in a single integrated framework. CIPDSS models the functionality of each infrastructure as well as the primary interdependencies that link these critical infrastructures together, calculating the impacts that cascade into these interdependent sectors and the national economy, given a modelled disruption event, in this case, pandemic influenza. The key model elements used to perform this analysis include infectious disease spread and intervention, population, travel, labour, and infrastructure operations. The model operates on a national scale with the country partitioned into ten multi-state regions.
The infectious disease model is a modified susceptible-exposed-infected-recovered (SEIR) model (Murray, 1993), using an extended set of disease stages; demographic groupings; an integrated model for vaccination, antiviral prophylaxis and treatment, quarantine, and isolation; and demographic and stage-dependent behaviour. As a variant on the SEIR model paradigm, this implementation represents the populations as inhomogeneously mixed, with exponentially distributed residence times in each stage. However, the use of additional stages and demographic groupings captures differences
Measuring the uncertainties of pandemic influenza 7
between subpopulations for disease spread and response. There are five demographic groups used in the model that includes responders in health and emergency services, who are taken from the two adult groups (young adults and older adults). The young adult and older adult populations exclude the number of responders in each group. Responders are treated separately to enable modelling of different levels of disease exposure compared to the general population and to model alternate policies regarding access to vaccines, antivirals, and other prophylactic measures.
The public health model represents treatment of patients by physicians’ offices and clinics, emergency medical services (EMS), emergency rooms (ERs), and hospitals. Within each region, aggregate values for the region are used for patient-treatment capacities and number of hospital beds. If the numbers of patients increase substantially over normal conditions, backlogs and long waits result, causing a reduction in the quality of care. Also, if significant numbers of healthcare workers are sick or in isolation, the capacity to treat patients is reduced, further exacerbating the overloading of the healthcare system. We simulated people that may also move to temporary facilities or home care.
An economic module estimates the economic impact of the pandemic based on the value of the lost productivity of affected workers. Specifically, the model calculates the lost GDP by multiplying the total value of the GDP per day, by state and industry, by the fraction of workers in that state and industry not working on any given day. The model derives the fraction of unavailable workers from population estimates of sick, dead, and self-isolated workers. This unavailable-worker fraction directly determines the derived economic losses. The summed GDP for all states is equal to the total GDP for the nation. Economic productivity is a function of both capital and labour. In industrialised nations such as the USA, capital plays a significant role, particularly in the automation of manufacturing and services. Using lost GDP per labour unit assumes a degree of linearity between GDP and labour that is justifiable within a relatively small bounded region of the fraction of unavailable labour, roughly zero to about twice the average absenteeism rate. Outside of this region, the lost productivity is underestimated by the lost GDP metric. This mild underestimation has little effect on the study conclusions, as economic losses are dominated by costs associated with loss of life.
2.2 Identification of intervention strategies
We generated 24 mitigation approaches to evaluate, based upon combinations of six vaccination strategies and four secondary strategies determined by social distancing and antiviral usage (Table 1). These 24 included two baseline scenarios representing minimal mitigation measures. The vaccination strategies incorporated mass and targeted vaccination, contact tracing, and the availability of a stockpiled partially effective vaccine (denoted early vaccine). Contact tracing is identifying and diagnosing persons who may have come into contact with an infected person. In contact tracing, public health workers identify symptomatics, interview them for their contacts, and quarantine them and their contacts for the time they are infectious so they do not infect others. A targeted vaccination campaign limits vaccination to contacts of infected people; a mass vaccination program vaccinates all susceptible people until vaccine stockpiles are depleted. A fraction of the population may not be able to receive vaccines due to allergies, immunodeficiency diseases, or other reasons. A partially effective vaccine
8 J.M. Fair et al.
option assumes the use of a stockpiled pre-pandemic vaccine that is not targeted to the specific pandemic strain but available early after a pandemic is identified. This study makes the assumption that traditional flu vaccine methods would be employed to develop a strain-specific vaccine, requiring time for development, production, and distribution. In this analysis, time to production of the vaccine varied from 1.5 to 6 months. After initial introduction, providers continue producing and distributing the vaccine, attaining a stable production rate of approximately 13 million doses per day for mass vaccination. Table 1 Components determining 24 mitigation scenarios
Vaccination strategies:
1 No vaccination or contact tracing
2 Contact tracing without vaccination
3 Mass vaccination only without early vaccine
4 Mass vaccination and early vaccine
5 Targeted vaccination followed by mass and early vaccination
6 Targeted vaccination and early vaccination
Secondary strategies for each vaccination strategy:
1 No social distancing, no antivirals (noSDnoAV)
2 No social distancing, antivirals (noSDAV)
3 Social distancing, antivirals (SDAV)
4 Social distancing, no antivirals (SDnoAV)
2.3 Experimental design and sensitivity analysis
The sensitivity and uncertainty analysis employed statistical experimental design methods to sample pandemic characteristics for simulation in order to obtain information for addressing the questions of interests, including evaluation of statistical quantities and correlation in an efficient manner. The goal of the experimental design was to improve the understanding of the relationship between important inputs that drive variation in a pandemic and responses of interest, as well as to characterise induced uncertainty in the pandemic response due to assumed variability in the important inputs. Orthogonal-array-based Latin hypercube sampling (LHS) is in common use for computer experiments (Williams et al., 2006; Chen et al., 2006; Santner et al., 2003). LHS, an improvement to random sampling, samples input parameters based on stratification of specified marginal distributions of the parameters (McKay et al., 1979). Improvement to the LHS has been demonstrated by selecting LHS with a structure incorporating both orthogonal arrays and distance or correlation-based criteria (John, 1971; Johnson et al., 1990; Tang, 1993; Owen, 1994; Wu and Hamada, 2000). This approach to designing and conducting a simulation experiment provides data that supports both uncertainty analysis and sensitivity analysis (Moore and McKay, 2002). For the pandemic influenza sensitivity study, the experimental design was an orthogonal array-based LHS plan (strength three, allowing evaluation of main effects with reduced bias from two factor interactions), using 80 runs for each of the 24 mitigation scenarios and varying 40 input variables based on their input distributions for a total of 1920 runs. The same
Measuring the uncertainties of pandemic influenza 9
experimental design was used for each of the 24 mitigation scenarios. For this sensitivity study, the input variables were assumed uniformly distributed over broad associated ranges based on subject matter expert, policy maker, and literature review. From this sensitivity study, we confirmed 19 input variables as influential variables for the simulated consequences. These inputs are listed in Table 2 with ranges indicated for the sensitivity study and distributions for the follow-on uncertainty study. Input variables grouped together were varied together (that is, with 100% correlation).
Acknowledging the high degree of uncertainty with the possible variable ranges and difficulty with handling a large number of inputs and conducting a large number of simulations in terms of achieving representative variation in outcomes, the sensitivity analysis highlights the most important variables for driving outcomes of the disease progression. Results showed the output variance of the model due to uncertainty in the parameters of the infectious disease model can be remarkably large. In statistical analysis of variance (ANOVA) or regression, R2 is a standard metric for evaluating goodness of fit of a model to a statistical response and it is also used in computer simulation experiments as a basis for evaluating input sensitivity, although a deterministic computer model clearly does not produce statistical variation (Moore and McKay, 2002; Williams et al., 2006; McKay, 1995). For sensitivity evaluation, the team used R2 as a heuristic tool to rank inputs with respect to relative importance. In implementation, R2 was calculated and compared for two-way interactions as well as main effects when the (strength 3 or higher) oa-based LHS experiment design supported identification of main effects with reduced potential bias from two-way interactions. In this way, sensitivity based on R2 analysis was an effective tool to focus attention on inputs with effects (main or in two-way interactions) that arise as having relatively larger sensitivity metric and hence inducing larger variation in responses. Other common ANOVA assumptions from the heuristic use of R2 as a sensitivity metric might also be exploited, including hierarchy and sparsity of effects so that interaction effects may not be considered ‘important’ if at least one of the main effects was not and it is also commonly assumed that higher order polynomial terms are less likely. However, in computer experiments, a large R2 for an interaction effect without either main effect being ‘important’ would be of interest and focus further evaluation. In analyses here, this situation did not occur and the use of R2 as a sensitivity metric served to both reduce the dimensionality of the input space for uncertainty analysis and ensure large variation in the induced responses of interest.
In summary, if for a certain response, the R2 for a model based on input parameter x1 is larger than R2 for a model based on input parameter x2, then x1 is judged more important or influential than x2 for that response. Also, the evaluation of a large R2 was based on two considerations: a heuristic significance value for R2 from goodness of fit evaluation in ANOVA or regression modelling for random data and by inclusion of a phony input column that is included in the experiment design but is not a genuine simulation input. If R2 for a particular response (xi) is below a threshold determined by one of these strategies, then xi is judged likely unimportant, or certainly less important. The analyses included computing R2 values typically for a simple polynomial fit (linear or quadratic) for each single varied input or pair of inputs, within each mitigation scenario, and each of several outputs or responses of main interest. The results were aggregated so not all of the identified 19 important inputs are actually important for each response of interest. Primarily this sensitivity analysis served as a filter to eliminate substantially less important variables for the subsequent uncertainty analysis.
10 J.M. Fair et al.
Table 2 Probability distributions for uncertainty analysis
Vari
able
Lo
w
rang
e H
igh
rang
e U
nits
D
istr
ibut
ion
Mea
n St
d Pa
ram
1Pa
ram
2Sc
alin
g fa
ctor
Sh
iftRe
fere
nces
Miti
gatio
ns
Initi
al a
ntiv
iral
avai
labi
lity
21 M
81
M
Cou
rses
U
nifo
rm
51 M
17
.3 M
21
M
81 M
1
0 N
icho
l and
Tre
anor
(200
6) a
nd C
DC
(200
7)
Ant
ivira
l sta
ndar
d pr
oduc
tion
rate
2.
5 M
80
M
Cou
rses
U
nifo
rm
41.3
M
22 M
2.
5 M
80
M
1 0
IOM
(200
8)
Frac
tion
antiv
irals
ap
plie
d to
pro
phyl
axis
0.
50
0.90
Fr
actio
nU
nifo
rm
0.70
0.
116
0.50
0.
90
1 0
Ale
xand
er e
t al.
(200
8)
Dea
th ra
te re
duct
ion
from
ant
ivira
ls
0.20
0.
70
Frac
tion
Bet
a 0.
62
0.16
8 4
1.8
1 0
de Jo
ng e
t al.
(200
5), H
HS
(200
5),
Hay
den
(200
6), L
ee a
nd C
hen
(200
7),
and
Lips
itch
et a
l. (2
007)
In
itial
vac
cine
st
ockp
ile (p
artia
lly
effe
ctiv
e)
0 M
12
0 M
D
oses
U
nifo
rm
60 M
35
M
0 12
0 M
1
0 Fe
dson
(200
3), F
auci
(200
5),
WH
O (2
005)
, Fre
ed e
t al.
(200
7)
Vac
cine
eff
ectiv
enes
s (p
artia
lly e
ffec
tive)
0.
1 0.
7 Fr
actio
nB
eta
0.44
0.
18
2.7
3.5
1 0
Mon
to e
t al.
(200
6), D
usho
ff e
t al.
(200
7)
and
Zelic
off (
2007
) V
acci
ne e
ffec
tiven
ess
(ful
ly e
ffec
tive)
0.
4 0.
8 Fr
actio
nB
eta
0.60
0.
11
12
8 1
0 G
ross
et a
l. (1
995)
Qua
rant
ine
and
isol
atio
n
Self-
quar
antin
e si
ck
rate
mod
ifier
0.
1 10
Bet
a 2.
31
0.49
1.
5 5
10
0 Eh
rens
tein
et a
l. (2
006)
, Gla
ss e
t al.
(200
6),
Ale
dort
et a
l. (2
007)
and
Mar
kel (
2007
)
Con
tact
trac
ing
Frac
tion
cont
act
effe
ctiv
enes
s 0.
01
0.5
Frac
tion
Bet
a 0.
033
0.02
4
116
1 0
Klin
kenb
erg
et a
l. (2
006)
Measuring the uncertainties of pandemic influenza 11
Table 2 Probability distributions for uncertainty analysis (continued)
Vari
able
Lo
w
rang
e H
igh
rang
e U
nits
D
istr
ibut
ion
Mea
n St
d Pa
ram
1 Pa
ram
2 Sc
alin
g fa
ctor
Sh
ift
Refe
renc
es
Tran
smis
sion
Rep
rodu
ctiv
e nu
mbe
r (al
l age
s)
1.3
4.5
Lo
gnor
mal
2.
36
1.01
0.
091
0.66
1 1
1 C
how
ell e
t al.
(200
7)
Frac
tion
of tr
ansm
issi
on p
rior t
o cl
ear s
ympt
oms
0.1
0.5
Frac
tion
Bet
a 0.
28
0.11
4.
7 12
1
0 Fo
y et
al.
(198
7),
Mill
s et a
l. (2
004)
, Fe
rgus
on e
t al.
(200
5, 2
006)
and
C
how
ell a
nd N
ishiu
ra (2
008)
R
elat
ive
cont
agio
n of
asy
mpt
omat
ic
0.1
0.8
Frac
tion
Bet
a 0.
42
0.18
2.
6 3.
6 1
0 Fr
ank
et a
l. (1
987)
, Cho
wel
l and
N
ishi
ura
(200
8), H
su a
nd H
sieh
(2
008)
and
Rot
i et a
l. (2
008)
Fr
actio
n ne
wly
infe
cted
clin
ical
0.
2 0.
95
Frac
tion
Bet
a 0.
625
0.20
3
1.8
1 0
Rot
i et a
l. (2
008)
Cas
e fa
talit
y ra
tes
Nom
inal
fata
lity
rate
(in
fant
, you
ng a
dult,
eld
erly
) 0.
005
0.15
Fr
actio
n B
eta
0.03
0.
02
1.5
48.5
1
0 C
ollin
s (19
31),
Fisl
ova
and
Kos
tola
nsky
(200
5), B
asle
r and
A
guila
r (20
08) a
nd L
i et a
l. (2
008)
N
omin
al fa
talit
y ra
te
(you
th, o
ld a
dult
and
resp
onde
rs)
.005
0.
15
Frac
tion
Bet
a .0
2 .0
2 1.
2 58
.8
1 0
Col
lins (
1931
) and
C
hen
and
Hol
mes
(200
6)
Dis
ease
stag
e tim
e pe
riod
s
Tim
e to
incu
bate
12
96
H
ours
Lo
gnor
mal
36
.25
18.0
2 3.
48
0.47
1
0 H
uai e
t al.
(200
8) a
nd H
ui
(200
8)
Dur
atio
n of
pro
drom
al
(infe
ctio
us/a
sym
ptom
atic
) 12
96
H
ours
Lo
gnor
mal
36
.25
18.0
2 3.
48
0.47
1
0 W
ebby
and
Web
ster
(200
1),
Zam
bon
(200
1) a
nd S
keik
and
Ja
br (2
008)
D
urat
ion
of e
arly
sym
ptom
s 24
12
0 H
ours
Lo
gnor
mal
51
.16
19.0
3 3.
87
0.36
1
0 D
ay e
t al.
(200
6) a
nd
Dug
an e
t al.
(200
8)
Tim
e to
reco
ver
120
552
Hou
rs
Logn
orm
al
284.
63
93.4
7 5.
6 0.
32
1 0
Nel
son
et a
l. (2
008)
, R
amba
ut e
t al.
(200
8) a
nd
Skei
k an
d Ja
br (2
008)
Publ
ic h
ealth
fact
ors
Hea
lth th
reat
reac
tion
time
24
672
hour
s G
amm
a 23
0.40
17
1.73
1.8
128
1 0
Nap
et a
l. (2
008)
and
R
eyno
lds e
t al.
(200
8)
12 J.M. Fair et al.
3 Results
The first step in the uncertainty analysis was to narrow the number of input variables. Our initial sensitivity analysis allowed us to select 19 inputs identified as the most influential from an original set of 40. Sensitive variables are defined relative to specific responses. The following variables were some of those deemed unimportant for subsequent analysis in this study (in no particular order): The fraction of patients seeking care at physician offices and clinics; base fraction of influenza patients taken to hospital by emergency management; detection threshold (number of people infected before pandemic identified); amount of time to create vaccine (fully effective); initial vaccine stockpile (partially effective); time before vaccine gives immunity (partially and fully effective); vaccine effectiveness (partially and fully effective); initial antiviral availability; fraction of physicians office and clinic visits that are urgent; self-quarantine tendency (youth, infant, elderly); the fraction antivirals applied to prophylaxis; and the death rate reduction from antivirals.
The most sensitive inputs related to the response ‘total number of illnesses’ in a pandemic were:
1 the fraction of the transmission that occur prior to symptoms presenting themselves in a person (infectious asymptomatics)
2 the reproductive number (R0)
3 the length of each disease stage.
As another example, the ‘fraction of total workers unavailable’ is most sensitive to the duration of their self-imposed quarantine period. Having down-selected to the most sensitive inputs, the set of mitigation simulations were run again so that output variation was due only to the most influential inputs. Using the R2-percent evaluation as in the preliminary sensitivity analysis, the results were identical to those found in the final sensitivity analysis. The results confirmed that some variables have no substantial impact on the outcome of the pandemic in any of the output metrics of interest, at least under the assumptions of this computer model and distributions used.
Overall, there was significant variation between all 24 scenarios (Figure 1) and within scenarios (Figure 2). The most effective mitigation strategy was to give an early vaccination of a partially effective vaccine followed by a mass vaccination once the matched vaccine was ready [Figure 2(b)]. All vaccination strategies and social distancing with some available antivirals most effectively reduced disease propagation. The results show that all of the interventions considered provide some reduction in the number of illnesses and deaths during the pandemic, though the reduction is small in some cases. However, in some scenarios where deaths are reduced, other metrics such as lost GDP increase. Social distancing (in all social distancing scenarios; labelled SD in the figures) provides a slight benefit in death reduction, although it is relatively costly. Mass vaccination provides little reduction in deaths if it only occurs after a fully effective vaccine is developed (vaccination strategy 3), because the pandemic has largely run its course at that point. Mass vaccination with a stockpile of partially effective vaccine (vaccination strategy 4) does not perform as well as social distancing because of the limited quantity of vaccine available in the initial stockpile. With the parameter ranges used in this study, contact tracing and quarantine, with or without vaccination
Measuring the uncertainties of pandemic influenza 13
(vaccination strategies 2, 5, and 6) provide about the same reduction in deaths, on average, as mass vaccination with an initial vaccine stockpile. The scenarios that include antivirals (labelled AV in the figures) have lower death rates than the corresponding scenarios without antivirals, but the reduction in deaths is relatively modest. However, social distancing provides substantial reduction in deaths even without any contact tracing or vaccination. On average, antivirals provide a reduction in deaths of about 5%, social distancing provides a reduction in deaths of about 14%, and the combination of social distancing plus antivirals provides a reduction in deaths of about 19%. Interestingly, the variability in outcomes appears very similar for any one of the 24 mitigation cases.
Figure 1 Average consequences per 40 simulation runs for the 24 scenarios (see online version for colours)
(a) (b)
(c) (d)
Notes: Vaccination strategies are: 1 – no vaccination or contacting tracing, 2 – contact tracing without vaccination, 3 – mass vaccination with no early vaccination, 4 – mass vaccination with early and late vaccination, 5 – targeted vaccination with early vaccine followed by mass vaccination with late vaccine, 6 – targeted vaccination with early and late vaccine. Social distancing (SD) and antiviral (AV) strategies alternate. a – deaths, b – number of people symptomatic (ill), c – peak fraction of workers unavailable, d – number of people hospitalised in temporary facilities.
14 J.M. Fair et al.
Figure 2 Box plots with median, 25th percentile, 75th percentile, minimum and maximum values for the 960 simulation runs of 24 scenarios
Notes: A – numbers of deaths, B – number of symptomatic people, C – peak fraction of workers unavailable.
The total number of hospitalised cases of infections was dependent on a wider variety of both disease and response characteristics, including public health preparedness, the virulence of the influenza virus, number of total cases, vaccine and antiviral mitigations that are available, management of the medical professional workforce, and sociology of the local population in the area.
Measuring the uncertainties of pandemic influenza 15
The total impacts to the economy were predominately dependent on lost worker days during the pandemic through illnesses, deaths, fear, school closures, and other reasons [Figure 2(b)]. The fraction of number of workers who self-quarantine or use social distancing and the number of days that the workers remain self-quarantined affect the peak fraction of workers unavailable.
The ability to effectively find and contact persons that may have been exposed to an infected person (contact tracing) and then have them be quarantined greatly reduced the continued transmission of the influenza virus and thus, reduced the total numbers of illnesses and deaths. Contact tracing alone reduced the impact of the pandemic on average 12%, depending on the degree of social distancing. The best overall vaccination strategy was to have an early and partially effective vaccine that is available immediately, followed by a mass vaccination specific to the strain four to six months later. Using a similar set of scenarios and mean disease characteristics, the agent-based model, EpiSimS, also found that a pre-pandemic vaccine greatly reduced the impacts of the pandemic (Stroud et al., 2006).
Immediate administration of antivirals consistently reduced the impact of the pandemic across all vaccination and social distancing scenarios by a small amount, about 5% on average, but this is not a significant amount compared to any other interventions. This may be due to our consideration of biological variation and the timing of antiviral administration within the model. Some studies have found that immediate administration of antivirals does not have a large impact upon the number of cases in pandemic with the current stockpile (Flahault et al., 2006; Stroud et al., 2006). Other studies have shown that targeted antiviral prophylaxis could be effective for outbreaks with a low R0 and provided adequate contact tracing and distribution capacities exist (Longini et al., 2005; Germann et al., 2006), however treatment must be for as long as eight weeks for 80% of exposed persons (Longini et al., 2004). This study found that a stockpile of 71 million treatment course (IOM, 2008) may or may not affect the pandemic, depending upon the infectivity and virulence of the virus. The impact of antivirals will depend on the severity of the disease (Yen et al., 2005) and the number of stockpiled courses (IOM, 2008), but variability of the effectiveness was found to be considerable, even when using an antiviral stockpile of 120 million. Our study did not investigate the additional fact that antivirals themselves may affect the evolution of influenza although our disease characteristics include the possibility of antiviral resistance (Ferguson et al., 2005).
The use of social distancing reduced the pandemic outcomes for all of the vaccination strategies. Social distancing with antivirals reduced the number of simulated symptomatic on average by 20%. However, social distancing also greatly increased the percent loss to the GDP for all scenarios due to worker unavailability, by an average 51%. When combining all mitigation strategies available, it was found that the overall pandemic impact could be reduced dramatically. The more infective, asymptomatic, and virulent an influenza virus is, the more it will limit the effectiveness of any or even a combination of mitigation strategies. All scenarios simulated in this study contained a significant amount of variation. However, even for R0 of greater than three, using the combination strategy of a partially effective early vaccine followed by a mass vaccination when the specific strain was available along with social distancing can reduce the pandemic significantly. Containing a pandemic that is highly infective and has a higher case fatality rate is possible with a combination of strategies. Our simulations show that although uncertainty
16 J.M. Fair et al.
and variability is large, coordinated efforts for response and stockpiled pharmaceuticals can reduce the impacts felt by potentially millions of people.
Overall, large variability was observed in the outcomes using all of the possible biological, sociological, interventions, and policy uncertainties. The top parameters that significantly contributed to the variance of the output variables of interest, such as the number of illnesses/deaths or unavailable workers, include:
1 fraction of transmission prior to clear symptoms (infectious asymptomatics)
2 reproductive number (R0)
3 time to recover (all stages)
4 contagious, yet asymptomatic infections
5 fraction of infections that are asymptomatic
6 contact-effectiveness fraction (for scenarios with contact tracing), (6) case fatality rate
7 antiviral production rate.
The ranges of the total outbreak size are quite large for each scenario, ranging from near zero to an extreme numbers of illnesses. The highest values in these figures would represent extremely severe consequences, far more severe than any pandemic in recent history. The wide ranges of the consequence measures result, of course, from the large amount of uncertainty in the sampled input parameters.
Simulation output included illnesses, deaths, and an estimate of economic loss for each model run. It is convenient to use a single metric of merit to compare outcomes. In this study we use equivalent fatalities which are defined to be:
( )equiv s s sf f e bs α ,= + +
where
fequiv is the number of equivalent fatalities
fs is the total number of fatalities in the scenario
es is the economic loss in dollars
ss is the cumulative number of symptomatics
α is the trade-off equivalence value for deaths in dollars per death
β is the trade-off equivalence value for a symptomatic illness in dollars per illness.
It is important to note that the trade-off equivalence for a death is not a monetised value of a life, rather, it is representative of a cost to reduce mortality risk based on a willingness to pay. As such it is closely related to the value of a statistical life (Viscussi and Aldy, 2003). Similarly, the trade-off equivalent for sickness is the price one would pay to avoid contracting the disease. The equivalent fatality metric accounts for the economic costs incurred when combating the pandemic and is informative in determining cost effective mitigation strategies. We found that the relative ranking of the scenarios with respect to equivalent fatalities did not change as α varied from $3M to $10M. For this study, we chose a modest value of five million dollars per death (compare to
Measuring the uncertainties of pandemic influenza 17
$7 million for EPA value of statistical life) (Viscussi and Aldy, 2003; Viscussi, 2004) and ten thousand dollars per illness for α and β, respectively (EPA, 2010). Meltzer et al. (1999) provides a per case cost for non-fatal illness of $24,115 for a 30% attack rate. The cost ranged between $12,000 and $28,000 (15% to 35% attack rate). Meltzer et al. (1999) also found that 83% of the economic cost is due to deaths, irrespective of attack rate, implying that the trade-off equivalent value for a death is the dominant parameter and that the cost of illness would need to be significantly higher before it would affect the relative ranking of equivalent fatalities.
Figure 3 depicts the distributions of equivalent fatalities for the base case and the best case. The average best case scenario reduced equivalent fatalities by slightly more than two million compared to the average base case equivalent fatalities. In our study, actual deaths comprised about 90% of the equivalent fatality metric; less than 5% was attributed to economic loss.
Figure 3 (a) Combined equivalent fatalities for the base case (noSDnoAV1) and (b) for social distancing, antivirals, early partially effective vaccination, and mass vaccination with matched vaccine (SDAV4)
(a)
(b)
18 J.M. Fair et al.
Another way to view the efficacy of the strategies is to examine the average time at which the population achieves its highest fraction of symptomatics. We examined the maximum fraction of symptomatics that had been achieved up to a given time (Figure 4). Over all vaccination strategies, the relative ranking of the scenario sets are constant. Social distancing with antivirals is better than social distancing with no antivirals which is better than no social distancing with antivirals, which is better than no social distancing and no antivirals. There are differences among the vaccination strategies, with strategies 1 and 3 clearly inferior whereas the remaining strategies have only small differences with respect to this measure. These data raise the question of what is the effect of antivirals in delaying the peak of the pandemic? Our results show that antivirals delay the peak of the pandemic by 2.5 days on average and increase the duration of the pandemic by 6.3 days.
Figure 4 Time series for the total fraction of workers that are unavailable for the six different vaccine scenarios
Measuring the uncertainties of pandemic influenza 19
Table 3 Sensitivity analysis results for all varied parameters (R2 values)
Not
e: S
igni
fican
t R2 v
alue
s in
ital
ics
for e
ach
outc
ome
endp
oint
.
Tota
l de
aths
Va
riab
les
Tota
l ill
Vari
able
s At
tack
ra
te
Vari
able
s To
tal
lost
GD
PVa
riab
les
Tota
l eq
uiv.
fata
l Va
riab
les
0.48
9 Fa
talit
y ra
te
0.40
1 Re
prod
uctiv
e nu
mbe
r 0.
671
Repr
oduc
tive
num
ber
0.26
1 St
age
dura
tions
0.
464
Fata
lity
rate
0.10
8 Re
prod
uctiv
e nu
mbe
r 0.
222
% N
ew in
fect
ion
clin
ical
0.
128
Tran
smis
sion
pr
ior
sym
ptom
s 0.
250
% N
ew
infe
ctio
n cl
inic
al
0.11
9 Re
prod
uctiv
e nu
mbe
r
0.09
1 So
cial
dis
tanc
ing
0.13
1 So
cial
dis
tanc
ing
0.08
7 So
cial
dis
tanc
ing
0.21
7 Fa
talit
y ra
te
0.09
2 So
cial
dis
tanc
ing
0.06
2 %
New
infe
ctio
n cl
inic
al
0.08
3 Tr
ansm
issi
on
prio
r sym
ptom
s 0.
068
Patie
nts
seek
ing
phys
icia
n 0.
196
Rep
rodu
ctiv
e nu
mbe
r 0.
069
% N
ew in
fect
ion
clin
ical
0.
058
AV
dea
th ra
te
redu
ctio
n 0.
075
Stag
e du
ratio
ns
0.06
8 In
itial
AV
av
aila
ble
0.18
9 A
V d
eath
rate
re
duct
ion
0.05
7 A
V d
eath
rate
re
duct
ion
0.05
5 Tr
ansm
issi
on p
rior
sym
ptom
s 0.
070
Initi
al A
V
avai
labl
e 0.
066
Fata
lity
rate
(e
lder
ly/in
fant
s)
0.17
7 So
cial
di
stan
cing
0.
056
Tran
smis
sion
pr
ior s
ympt
oms
0.04
5 Pa
tient
s se
ekin
g ph
ysic
ian
0.05
9 A
ffec
ted
patie
nts
seek
ing
care
0.
064
Aff
ecte
d pa
tient
s se
ekin
g ca
re
0.17
4 In
itial
vac
cine
st
ockp
ile
0.04
5 Pa
tient
s se
ekin
g ph
ysic
ian
0.03
3 V
acci
ne
effe
ctiv
enes
s (f
ull)
0.05
7 Fa
talit
y ra
te
(eld
erly
/infa
nts)
0.
064
Con
tact
ef
fect
iven
ess
0.16
9 Pa
tient
s se
ekin
g ph
ysic
ian
0.03
2 V
acci
ne
effe
ctiv
enes
s (f
ull)
0.03
3 Th
reat
re
actio
n tim
e 0.
056
% A
Vs
prop
hyla
xis
0.06
2 St
age
dura
tions
0.
165
Tran
smis
sion
pr
ior
sym
ptom
s
0.03
1 Th
reat
re
actio
n tim
e
0.02
9 In
itial
vac
cine
st
ockp
ile
0.05
5 Ph
ony
X
0.06
1 Ph
ony
X
0.15
9 C
onta
ct
effe
ctiv
enes
s 0.
029
Initi
al v
acci
ne
stoc
kpile
0.
018
Asy
mpt
omat
ic
cont
agio
usne
ss
0.05
1 C
onta
ct
effe
ctiv
enes
s 0.
061
Soci
al d
ista
ncin
g (e
lder
ly/in
fant
s)
0.15
8 %
AV
s pr
ophy
laxi
s 0.
018
Asy
mpt
omat
ic
cont
agio
usne
ss
0.01
7 Pr
oduc
tion
rate
0.
050
Thre
at re
actio
n tim
e 0.
053
Vac
cine
ef
fect
iven
ess
0.15
6 In
itial
AV
av
aila
ble
0.01
7 Ph
ony
X
20 J.M. Fair et al.
Table 3 Sensitivity analysis results for all varied parameters (R2 values) (continued)
Not
e: S
igni
fican
t R2 v
alue
s in
ital
ics
for e
ach
outc
ome
endp
oint
.
Tota
l de
aths
Va
riab
les
Tota
l ill
Vari
able
s At
tack
rat
eVa
riab
les
Tota
l lo
st G
DP
Vari
able
s To
tal
equi
v. fa
tal
Vari
able
s
0.01
7 Ph
ony
X
0.04
8 In
itial
vac
cine
st
ockp
ile
0.05
1 %
New
in
fect
ion
clin
ical
0.14
8 V
acci
ne
effe
ctiv
enes
s 0.
016
Prod
uctio
n ra
te
0.01
4 St
age
dura
tions
0.
048
Fata
lity
rate
0.
050
Initi
al v
acci
ne
stoc
kpile
0.
147
Phon
y X
0.
015
Aff
ecte
d pa
tient
s se
ekin
g ca
re
0.01
4 A
ffec
ted
patie
nts
seek
ing
care
0.
048
Vac
cine
ef
fect
iven
ess
(ful
l)
0.04
8 %
AV
s pr
ophy
laxi
s 0.
145
Soci
al
dist
anci
ng
(eld
erly
/infa
nts)
0.01
4 St
age
dura
tions
0.01
3 C
onta
ct
effe
ctiv
enes
s 0.
047
Patie
nts
seek
ing
phys
icia
n 0.
047
Fata
lity
rate
0.
145
Prod
uctio
n ra
te
0.01
3 C
onta
ct
effe
ctiv
enes
s 0.
013
Soci
al d
ista
ncin
g (e
lder
ly/in
fant
s)
0.04
7 So
cial
di
stan
cing
(e
lder
ly/in
fant
s)
0.04
6 Th
reat
reac
tion
time
0.14
5 A
sym
ptom
atic
co
ntag
ious
ness
0.
013
Soci
al
dist
anci
ng
(eld
erly
/infa
nts)
0.
012
Initi
al A
V
avai
labl
e 0.
046
AV
dea
th ra
te
redu
ctio
n 0.
046
Asy
mpt
omat
ic
cont
agio
usne
ss
0.14
4 Fa
talit
y ra
te
(eld
erly
/infa
nts)
0.
012
Fata
lity
rate
(e
lder
ly/in
fant
s)
0.01
2 Fa
talit
y ra
te
(eld
erly
/infa
nts)
0.
046
Prod
uctio
n ra
te
0.04
4 Pr
oduc
tion
rate
0.
143
Affe
cted
pa
tient
s se
ekin
g ca
re
0.01
2 In
itial
ant
ivira
l av
aila
ble
0.01
1 %
AV
s pr
ophy
laxi
s 0.
045
Asy
mpt
omat
ic
cont
agio
usne
ss
0.04
4 A
V d
eath
rate
re
duct
ion
0.14
3 Th
reat
reac
tion
time
0.01
2 %
AV
s pr
ophy
laxi
s 0.
011
Scen
ario
0.
045
Scen
ario
0.
043
Scen
ario
0.
141
Scen
ario
0.
011
Scen
ario
Measuring the uncertainties of pandemic influenza 21
The model parameters significantly related to the epidemic outcomes of mortality, total illnesses, total lost GDP, and total equivalent fatalities include the fatality rate, reproductive number, the number of transmissions prior to clear symptoms, and the disease stage durations (Table 3). Social distancing was correlated with lowering the total number of illnesses but not necessarily lowering the number of fatalities.
4 Discussion
The impact of the next pandemic will depend on how infectious the virus is as well as how infectious the disease is prior to an infected person showing symptoms. The majority of the important inputs, those that induce the greatest variation in pandemic responses, deal with biological variability, with the exception of the effectiveness of contact tracing and antiviral production rate. Mitigation strategies for pandemic influenza that reduce impact of the top disease variables will be the most effective. The results show that all of the interventions considered provide some reduction in the number of deaths caused by the pandemic, but social distancing and mass vaccination show the best results in this analysis. However, the timing of the administration of a mass vaccination is critical, as it provides little reduction in deaths if it occurs late due to the development of a fully effective vaccine, because the pandemic has largely run its course in the USA.
Uncertainty in disease transmission modelling can be grouped into four categories: biological variation, policy differences, sociological response, and infrastructure response. During a pandemic, the influenza viral strain continues to evolve, altering its contagiousness and virulence as it adapts to new hosts. The diversity of human populations with regard to immune function, health status, and gene function for responses to infectious diseases represents biological variation. Even as targeted vaccines are developed for a specific instance of a viral disease, the rapidity of viral evolution and the length of time required to develop and deploy a vaccine imply uncertainty in vaccine efficacy (Fedson, 2003; Rossiter, 2005; Monto et al., 2006). In addition, antiviral resistance adds to uncertainty in treatment recommendations (Yen et al., 2005; Lipsitch et al., 2007).
Although there are numerous intervention strategies for fighting infectious diseases, there is uncertainty in how well they may work for containing epidemics. These strategies include vaccinations, antivirals, social distancing, quarantining infectious and susceptible persons, and respiratory protection. Each of these strategies decreases either the transmission or the virulence of the diseases. The selection of particular combinations of interventions, timing of implementation, and resources available (such as vaccine and antiviral drug stockpiles) to implement the strategies are all elements of policy uncertainty. Because state health departments are autonomous of federal control, it is likely that their approaches to containing a pandemic will vary (Holmberg et al., 2006). For example, differences in the season of the outbreak or state and local responses to a pandemic, such as school closures, are likely to exist (Cauchemez et al., 2008).
It is rarely certain what fraction of the affected people will actually comply with policy guidance in an emergency situation. Within the context of an influenza pandemic, sociological responses, which include individual values, religious beliefs, perception of risk, confidence in authorised agencies, and a myriad of other characteristics, influence an individual’s decision of whether to comply with recommended policy. Sociological
22 J.M. Fair et al.
responses to a pandemic today may be very different than those of almost a century ago, minimising the benefit that historical examples may bring to analysing the patterns of human behavioural responses to a pandemic. The uncertainties addressed in this simulation-based analysis include the wide variation of non-policy actions undertaken by individuals intending to lower personal risk; for example, self-isolation, refusing vaccination, reliance on over-the-counter drugs, and so forth.
The resilience of infrastructure operations in a pandemic is related to the availability of the workforce, flexibility in labour management and usage (for example, overtime), and shifts in demand for infrastructure services. Highly automated infrastructures such as Telecommunications, energy, and water are less susceptible to degradation from loss of labour. Other more labour-intensive infrastructures such as food/agriculture, public health, emergency services, and transportation, may be more likely to have negative impacts from the pandemic. Labour availability is dependent on the disease severity (number and severity of illnesses) and the sociological response. With respect to infrastructure response our analysis focused on the response of the public health infrastructure, in the face of labour shortages and significantly increased demand.
5 H1N1 uncertainty
Decision-makers faced substantial uncertainties during the recent H1N1 (2009) pandemic. Uncertainties were both biological (e.g., unknowns about likely virulence and transmission) as well as policy such as unknowns about when vaccines would be available. Pandemic H1N1, which first emerged in Mexico in April 2009, spread worldwide and in the first three months resulted in more than 130,000 laboratory-confirmed cases and 800 deaths in over 100 countries (WHO, 2009). The World Health Organisation declared the first influenza pandemic of the 21st century in June 2009 and initially most cases were clustered in households and schools, (Iuliano et al., 2011) with over 50% of the reported cases in schoolchildren (Yang et al., 2009). The first uncertainty of H1N1 behaviour involved the higher case fatality ratio in Mexico of 1.2% (95% confidence interval from 1.03%. to 1.5%) (Garske et al., 2009). However, as H1N1 expanded it range into the USA, Canada, the UK, and the European Union data suggested a case fatality ratios ranging from 0.20% to 0.68 (Garske et al., 2009). Yang et al. (2009) used maximum likelihood methods to give the best estimate of 27.3% of a secondary attack rate of pandemic H1N1 in US households with confirmed index cases of pandemic H1N1. One of the most important lessons of H1N1 was to demonstrate the rapid evolution of the virus within the first three months of the pandemic that impacted important disease variables used in epidemic models.
The uncertainty analysis of this simulation study provides additional insights compared to previous studies on pandemic influenza that includes using a broad scope of possibilities of the behaviour of a pandemic induced by assumed distributions on parameters that effect disease progression and severity and public response impacted by policy or individual behaviour. There continues to be a lack of definitive empirical data on possible case morality rates that may be expected in a pandemic, which are an important assumption for predicting future pandemic impacts. First, the biological variability is such that the pandemic of 1917–1918, although the most severe for which substantial historical data exists, may not be indicative of the worst case future scenario.
Measuring the uncertainties of pandemic influenza 23
Using data to construct a worst-case scenario for all possibilities with confining distributions, it is important to emphasise the lack of predictive knowledge on the outcome of viral evolution for avian influenza H5N1 and resulting case mortality rate if it was easily transmitted between people. In this study the 90-percentile unmitigated case has seven million fatalities out of a population of 300 million (a mortality rate of 0.023), compared to the USA. 1917–1918 pandemic which had approximately 0.5 million deaths in a population of 103 million (a mortality rate of 0.005) (Brundage, 2006). In the simulated results, the 90-percentile event is roughly four times worse, in terms of mortality rate, compared to the 1917–1918 pandemic in the USA. Second, antivirals appear to be less helpful than some previous studies have indicated. Third, the study indicates that even with uncertainty over the degree of social distancing, it is an effective measure to reduce disease transmission, reducing symptomatics by an average of 16%, although it has 50% higher economic costs. Fourth, the use of rapidly available partially effective pre-pandemic vaccines can reduce mortality by 9%. Lastly, the study supports earlier findings that no single, pure strategy is best; a mix of pharmaceutical and non-pharmaceutical interventions is required. Based on this study, it would be prudent to incorporate this information in planning for the next pandemic, i.e., accounting for the probability of a pandemic more severe than the 1918, carefully considering dependency on antivirals, maintaining awareness of the economic costs associated with social distancing, and including multiple mitigations in a robust intervention strategy.
References Aledort, J.E., Lurie, N., Wasserman, J. and Bozzette, S.A. (2007) ‘Non-pharmaceutical public
health interventions for pandemic influenza: an evaluation of the evidence base’, BMC Public Health, Vol. 7, pp.1–9.
Alexander, M.E., Moghadas, S.M., Rost, G. and Wu, J.H. (2008) ‘A delay differential model for pandemic influenza with antiviral treatment’, Bulletin of Mathematical Biology, Vol. 70, No. 2, pp.382–397.
Basler, C.F. and Aguilar, P.V. (2008) ‘Progress in identifying virulence determinants of the 1918 H1N1 and the Southeast Asian H5N1 influenza A viruses’, Antiviral Research, Vol. 79, No. 3, pp.166–178.
Blumenshine, P., Reingold, A., Egerter, S., Mockenhaupt, R., Braveman, P. and Marks, J. (2008) ‘Pandemic influenza planning in the United States from a health disparities perspective’, Emerging Infectious Diseases, Vol. 14, No. 5, pp.709–715.
Brundage, J.F. (2006) ‘Cases and deaths during influenza pandemics in the United States’, American Journal of Preventive Medicine, Vol. 31, No. 3, pp.252–256.
Bush, B., Dauelsberg, L., LeClaire, R., Powell, D., DeLand, S. and Samsa, M. (2005) Critical Infrastructure Protection Decision Support System (CIPDSS) Project Overview, Los Alamos National Laboratory.
Cauchemez, S., Valleron, A.J., Boelle, P.Y., Flahault, A. and Ferguson, N.M. (2008) ‘Estimating the impact of school closure on influenza transmission from Sentinel data’, Nature, Vol. 452, No. 7188, pp.750–U756.
CDC (2007) Interim Pre-Pandemic Planning Guidance: Community Strategy for Pandemic Influenza in the United States-Early, Targeted, and Layered Use of Nonpharmaceutical Interventions, US Centers for Disease Control and Prevention, Atlanta, GA.
Chen, R.B. and Holmes, E.C. (2006) ‘Avian influenza virus exhibits rapid evolutionary dynamics’, Molecular Biology and Evolution, Vol. 23, No. 23, pp.2336–2341.
24 J.M. Fair et al.
Chen, V.C.P., Kwok-Leung, T.., Russell, B.R. and Meckesheimer, M. (2006) ‘A review on design, modeling and applications of computer experiments’, IIE Transactions, Vol. 38, No. 4, pp.273–291.
Chowell, G. and Nishiura, H. (2008) ‘Quantifying the transmission potential of pandemic influenza’, Physics of Life Reviews, Vol. 5, No. 1, pp.50–77.
Chowell, G., Bettencourt, L.M.A., Johnson, N., Alonso, W.J. and Viboud, C. (2008) ‘The 1918-1919 influenza pandemic in England and Wales: spatial patterns in transmissibility and mortality impact’, Proceedings of the Royal Society B-Biological Sciences, Vol. 275, No. 1634, pp.501–509.
Chowell, G., Nishiura, H. and Bettencourt, L.M.A. (2007) ‘Comparative estimation of the reproduction number for pandemic influenza from daily case notification data’, Journal of the Royal Society Interface, Vol. 4, No. 4, pp.155–166.
Collins, S.D. (1931) ‘Age and sex incidence of influenza and pneumonia morbidity and mortality in the pandemic of 1928-29 with comparative data for the epidemic 1918-1919’, Public Health Report, Vol. 33, pp.1909–1937.
Day, T., Andre, J.B. and Park, A. (2006) ‘The evolutionary emergence of pandemic influenza’, Proceedings of the Royal Society B-Biological Sciences, Vol. 273, pp.2945–2953.
de Jong, M.D., Thanh, T.T., Khanh, T.H., Hien, V.M., Smith, G.J.D., Chau, N.V., Cam, B.V., Qui, P.T., Ha, D.Q., Guan, Y., Peiris, J.S.M., Hien, T.T. and Farrar, J. (2005) ‘Oseltamivir resistance during treatment of influenza A (H5N1) infection’, New England Journal of Medicine, Vol. 353, No. 25, pp.2667–2672.
Dugan, V.G., Chen, R., Spiro, D.J., Sengamalay, N., Zaborsky, J., Ghedin, E., Nolting, J., Swayne, D.E., Runstadler, J.A., Happ, G.M., Senne, D.A., Wang, R., Slemons, R.D., Holmes, E.C. and Taubenberger, J.K. (2008) ‘The evolutionary genetics and emergence of avian influenza viruses in wild birds’, PLoS Pathogens, Vol. 4, No. 5.
Dushoff, J., Plotkin, J.B., Viboud, C., Simonsen, L., Miller, M., Loeb, M. and Earn, D.J.D. (2007) ‘Vaccinating to protect a vulnerable subpopulation’, Plos Medicine, Vol. 4, No. 4, pp.921–927.
Ehrenstein, B.P., Hanses, F. and Salzberger, B. (2006) ‘Influenza pandemic and professional duty: family or patients first? A survey of hospital employees’, Bmc Public Health, Vol. 6, pp.1–3.
EPA (2010) Guidelines for Preparing Economic Analysis, National Center for Environmental Economics, Office of Policy, US Environmental Protection Agency.
Fauci, A.S. (2005) ‘Pandemic influenza: the road to preparedness’, Statement to Committee on Foreign Relations, United States Senate, 9 November 2005, available at http://www.hhs.gov/asl/testify/t051109.html (accessed on 6 March 2006).
Fedson, D.S. (2003) ‘Pandemic influenza and the global vaccine supply’, Clinical Infectious Diseases, Vol. 36, No. 12, pp.1552–1561.
Ferguson, N.M., Cummings, D.A.T., Cauchemez, S., Fraser, C., Riley, S., Meeyai, A., Iamsirithaworn, S. and Burke, D.S. (2005) ‘Strategies for containing an emerging influenza pandemic in Southeast Asia’, Nature, Vol. 437, No. 7056, pp.209–214.
Ferguson, N.M., Cummings, D.A.T., Fraser, C., Cajka, J.C., Cooley, P.C. and Burke, D.S. (2006) ‘Strategies for mitigating an influenza pandemic’, Nature, Vol. 442, No. 7101, pp.448–452.
Ferguson, N.M., Galvani, A.P. and Bush, R.M. (2003) ‘Ecological and immunological determinants of influenza evolution’, Nature, Vol. 422, No. 6930, pp.428–433.
Fislova, T. and Kostolansky, F. (2005) ‘The factors of virulence of influenza A virus’, Acta Virologica, Vol. 49, No. 3, pp.147–157.
Flahault, A., Vergu, E., Coudeville, L. and Grais, R.F. (2006) ‘Strategies for containing a global influenza pandemic’, Vaccine, Vol. 24, Nos. 44–46, pp.6751–6755.
Foy, N.M., Cooney, M.K., Allen, I.D. and Albrecht, J.K. (1987) ‘Influenza B in households: virus shedding without symptoms or antibody response’, American Journal of Epidemiology, Vol. 126, No. 3, pp.506–515.
Measuring the uncertainties of pandemic influenza 25
Frank, A.L., Taber, L.H., Wells, C.R., Wells, J.M., Glezen, W.P. and Paredes, A. (1987) ‘Patterns of shedding of myxoviruses and paramyxoviruses in children’, Journal of Infectious Diseases, Vol. 144, No. 5, pp.433–441.
Freed, N.E., Myers, C.A., Russell, K.L., Walter, E.A., Irvine, M., Coon, R.G. and Metzgar, D. (2007) ‘Diagnostic discrimination of live attenuated influenza vaccine strains and community-acquired pathogenic strains in clinical samples’, Molecular and Cellular Probes, Vol. 21, No. 2, pp.103–110.
Garske, T., Legrand, J., Donnelly, C.A., Ward, H., Cauchemez, S., Fraser, C., Ferguson, N.M. and Ghani, A.C. (2009) ‘Assessing the severity of the novel influenza A/H1N1 pandemic’, British Medical Journal, Vol. 339.
Germann, T.C., Kadau, K., Longini, I.M. and Macken, C.A. (2006) ‘Mitigation strategies for pandemic influenza in the United States’, Proceedings of the National Academy of Sciences of the United States of America, Vol. 103, pp.5935–5940.
Glass, R.J., Glass, L.M., Beyeler, W.E. and Min, H.J. (2006) ‘Targeted social distancing design for pandemic influenza’, Emerging Infectious Diseases, Vol. 12, No. 11, pp.1671–1681.
Granger, M.G. and Henrion, M. (1998) Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge University Press, New York, NY.
Gross, P.A., Hermogenes, A.W., Sacks, H.S., Lau, J. and Levandowski, R.A. (1995) ‘The efficacy of influenza vaccine in elderly persons: a meta-analysis and review of the literature’, Ann. Intern. Med., Vol. 123, No. 7, pp.518–527.
Hayden, F.G. (2006) ‘Antiviral resistance in influenza viruses – implications for management and pandemic response’, New England Journal of Medicine, Vol. 354, No. 8, pp.785–788.
HHS (2005) HHS Pandemic Influenza Plan, US Department of Health and Human Services. Holmberg, S.D., Layton, C.M., Ghneim, G.S. and Wagener, D.K. (2006) ‘State plans
for containment of pandemic influenza’, Emerging Infectious Diseases, Vol. 12, No. 9, pp.1414–1417.
Hsu, S.B. and Hsieh, Y.H. (2008) ‘On the role of asymptomatic infection in transmission dynamics of infectious diseases’, Bulletin of Mathematical Biology, Vol. 70, No. 1, pp.134–155.
Huai, Y., Xiang, N.J., Zhou, L., Feng, L.H., Peng, Z.B., Chapman, R.S., Uyeki, T.M. and Yu, H.J. (2008) ‘Incubation period for human cases of avian influenza A (H5N1) infection, China’, Emerging Infectious Diseases, Vol. 14, No. 11, pp.1819–1821.
Hui, D.S.C. (2008) ‘Review of clinical symptoms and spectrum in humans with influenza A/H5N1 infection’, Respirology, Vol. 13, Supplement 1, pp.S10–S13.
Hupert, N., Xiong, W., King, K., Castorena, M., Hawkins, C., Wu, C. and Muckstadt, J.A. (2009) ‘Uncertainty and operational considerations in mass prophylaxis workforce planning’, Disaster Medicine and Public Health Preparedness, Vol. 3, Supplement 2, pp.S121–S131.
Iman, R.L. and Helton, J.C. (1988) ‘An investigation of uncertainty and sensitivity analysis techniques for computer models’, Risk Analysis, Vol. 8, No. 1, pp.71–90.
IOM (2008) Antivirals for Pandemic Influenza: Guidance on Developing a Distribution and Dispensing Program, I.o.M. Committee on Implementation of Antiviral Medication Strategies for an Influenza Pandemic, Washington, DC.
Iuliano, A.D., Dawood, F.S., Silk, B.J., Bhattarai, A., Copeland, D., Doshi, S., France, A.M., Jackson, M.L., Kennedy, E., Loustalot, F., Marchbanks, T., Mitchell, T., Averhoff, F., Olsen, S.J., Swerdlow, D.L. and Finelli, L. (2011) ‘Investigating 2009 pandemic influenza A (H1N1) in US schools: what have we learned?’, Clinical Infectious Diseases, Vol. 52, Supplement 1, pp.S161–S167.
John, P. (1971) Statistical Design and Analysis of Experiments, Macmillan Co. New York, NY. Johnson, M., Moore, L.M. and Ylvisaker, D. (1990) ‘Minimax and maximin distance designs’,
Journal Statistical Planning Inference, Vol. 26, No. 2, pp.131–148. Klinkenberg, D., Fraser, C. and Heesterbeek, J.A.P. (2006) ‘The effectiveness of contact tracing in
emerging epidemics’, European Journal of Epidemiology, Vol. 21, No. 1, pp.64–65.
26 J.M. Fair et al.
Lee, V.J. and Chen, M.I. (2007) ‘Effectiveness of neuraminidase inhibitors for preventing staff absenteeism during pandemic influenza’, Emerging Infectious Diseases, Vol. 13, No. 3, pp.449–457.
Li, F.C.K., Choi, B.C.K., Sly, T. and Pak, A.W.P. (2008) ‘Finding the real case-fatality rate of H5N1 avian influenza’, Journal of Epidemiology and Community Health, Vol. 62, No. 6, pp.555–559.
Lipsitch, M., Cohen, T., Murray, M. and Levin, B.R. (2007) ‘Antiviral resistance and the control of pandemic influenza’, Plos Medicine, Vol. 4, No. 1, pp.111–121.
Longini, I.M., Halloran, M.E., Nizam, A. and Yang, Y. (2004) ‘Containing pandemic influenza with antiviral agents’, American Journal of Epidemiology, Vol. 159, No. 7, pp.623–633.
Longini, I.M., Nizam, A., Xu, S.F., Ungchusak, K., Hanshaoworakul, W., Cummings, D.A.T. and Halloran, M.E. (2005) ‘Containing pandemic influenza at the source’, Science, Washington DC, Vol. 309, No. 5737, pp.1083–1078.
Markel, H. (2007) ‘Non-pharmaceutical interventions implemented by US cities during the 1918–1919 influenza pandemic’, Jama-Journal of the American Medical Association, Vol. 298, No. 6, pp.2264–2264.
McKay, M.D. (1995) ‘Evaluating prediction uncertainty’, Technical Report LA-12915-MS, Los Alamos National Laboratory, Los Alamos New Mexico, USA.
McKay, M.D., Conover, W.J. and Beckman, R.J. (1979) ‘A comparison of three methods for selecting values of input variables in the analysis of output from a computer code’, Technometrics, Vol. 21, No. 2, pp.239–245.
Meltzer, M.I., Cox, N.J. and Fukuda, K. (1999) ‘The economic impact of pandemic influenza in the United States: Priorities for intervention’, Emerging Infectious Diseases, Vol. 5, No. 5, pp.659–671.
Mills, C.E., Robins, J.M. and Lipsitch, M. (2004) ‘Transmissibility of 1918 pandemic influenza’, Nature, Vol. 432, No. 7019, pp.904–906.
Monto, A.S., Comanor, L., Shay, D.K. and Thompson, W.W. (2006) ‘Epidemiology of pandemic influenza: use of surveillance and modeling for pandemic preparedness’, Journal of Infectious Diseases, Vol. 194, Supplement 2, pp.S92–S97.
Moore, L.M. and McKay, M.D. (2002) ‘Orthogonal arrays for computer experiments to assess important inputs’, in Proceedings of PSAM6, 6th International Conference on Probabilistic Safety Assessment and Management.
Moteff, J. and Parfomak, P. (2004) Critical Infrastructure and Key Assets: Definition and Identification, Congressional Research Office, RL32631, Washington, DC.
Murray, J.D. (1993) Mathematical Biology, Springer, New York, NY. Nap, R.E., Andriessen, M., Meessen, N.E.L., Miranda, D.D.R. and van der Werf, T.S. (2008)
‘Pandemic influenza and excess intensive-care workload’, Emerging Infectious Diseases, Vol. 14, No. 10, pp.1518–1525.
Nelson, M.I., Viboud, C., Simonsen, L., Bennett, R.T., Griesemer, S.B., George, K.S., Taylor, J., Spiro, D.J., Sengamalay, N.A., Ghedin, E., Taubenberger, J.K. and Holmes, E.C. (2008) ‘Multiple reassortment events in the evolutionary history of H1N1 influenza A virus since 1918’, Plos Pathogens, Vol. 4, No. 2.
Nichol, K.L. and Treanor, J.J. (2006) ‘Vaccines for seasonal and pandemic influenza’, Journal of Infectious Diseases, Vol. 194, Supplement 2, pp.S111–S118.
O’Connor, J., Jarris, P., Vogt, R. and Horton, H. (2011) ‘Public health preparedness laws and policies: where do we go after pandemic 2009 H1N1 influenza?’, Journal of Law Medicine & Ethics, Vol. 39, No. 1, pp.51–55.
Owen, A. (1994) ‘Controlling correlations in Latin hypercube samples’, Journal American Statistical Association, Vol. 89, No. 428, pp.1517–1522.
Measuring the uncertainties of pandemic influenza 27
Rambaut, A., Pybus, O.G., Nelson, M.I., Viboud, C., Taubenberger, J.K. and Holmes, E.C. (2008) ‘The genomic and epidemiological dynamics of human influenza A virus’, Nature, Vol. 453, No. 7195, pp.615–619.
Reynolds, D.L., Garay, J.R., Deamond, S.L., Moran, M.K., Gold, W. and Styrai, R. (2008) ‘Understanding, compliance and psychological impact of the SARS quarantine experience’, Epidemiology and Infection, Vol. 136, No. 7, pp.997–1007.
Rossiter, L.F. (2005) ‘Vaccine and the next pandemic’, Health Affairs, Vol. 24, No. 5, pp.1380. Roti, M., Yang, J., Berger, D., Huston, L., James, E.A. and Kwok, W.W. (2008) ‘Healthy human
subjects have CD4+ T cells directed against H5N1 influenza virus’, Journal of Immunology, Vol. 180, No. 3, pp.1758–1768.
Sanchez, M.A. and Blower, S.M. (1997) ‘Uncertainty and sensitivity analysis of the basic reproductive rate: tuberculosis as an example’, American Journal Epidemiology, Vol. 145, No. 12, pp.1127–1137.
Santner, T.J., Williams, B.J. and Notz, W. (2003) The Design and Analysis of Computer Experiments, New York, USA, Springer.
Skeik, N. and Jabr, F.L. (2008) ‘Influenza viruses and the evolution of avian influenza virus H5N1’, International Journal Infectious Diseases, Vol. 12, No. 3, pp.233–238.
Stroud, P.D., Sydoriak, S.J., Riese, J.M., Smith, J.P., Mniszewski, S.M. and Romero, P.R. (2006) ‘Semi-empirical power-law scaling of new infection rate to model epidemic dynamics with inhomogeneous mixing’, Mathematical Biosciences, Vol. 203, No. 2, pp.301–308.
Tang, B. (1993) ‘Orthogonal array-based Latin hypercube’, Journal American Statistical Association, Vol. 88, No. 424, pp.1392–1397.
Viscussi, W.K. (2004) ‘The value of life: estimates with risk by occupation and industry’, Economic Inquiry, Vol. 42, No. 1, pp.29–48.
Viscussi, W.K. and Aldy, J.E. (2003) ‘The value of a statistical life: a critical review of market estimates throughout the world’, Journal Risk Uncertainty, Vol. 27, pp.5–76.
Webby, R.J. and Webster, R.G. (2001) ‘Emergence of influenza A viruses’, Philosophical Transactions of the Royal Society of London Series B-Biological Sciences, Vol. 356, No. 1416, pp.1817–1828.
WHO (2005) H5N1 Avian Influenza – First Steps Towards Development of a Human Vaccine, World Health Organization.
WHO (2009) Novel Influenza A (H1N1) Update 59 July 2009, World Health Organization. Williams, B., Higdon, D., Gattticker, J., Moore, L.M. and Keller-McNulty, S. (2006) ‘Combining
experimental data and computer simulations with an open application to flyer plate experiments’, Bayesian Analysis, Vol. 1, No. 4, pp.765–792.
Wu, C. and Hamada, M.S. (2000) Experiments: Planning, Analysis, and Parameter Design Optimization, John Wiley & Sons, New York, NY.
Yang, Y., Sugimoto, J.D., Halloran, M.E., Basta, N.E., Chao, D.L., Matrajt, L., Potter, G., Kenah, E. and Longini, I.M. (2009) ‘The transmissibility and control of pandemic influenza A (H1N1) virus’, Science, Vol. 326, No. 5953, pp.729–733.
Yen, H.L., Monto, A.S., Webster, R.G. and Govorkiva, E.A. (2005) ‘Virulence may determine the necessary duration and dosage of oseltamivir treatment for highly pathogenic A/Vietnam/1203/04 influenza virus in mice’, Journal Infectious Diseases, Vol. 437, No. 4, pp.209–214.
Zambon, M.C. (2001) ‘The pathogenesis of influenza in humans’, Reviews in Medical Virology, Vol. 11, No. 4, pp.227–241.
Zelicoff, A. (2007) ‘Avian flu: risk of a human pandemic from H5N1’, Santa Fe, NM, World Bank Working Paper Avian Flu Task Force.