To assess whether screening blood donors could pro-
vide early warning of a bioterror attack, we combined sto-
chastic models of blood donation and the workings of blood
tests with an epidemic model to derive the probability distri-
bution of the time to detect an attack under assumptions
favorable to blood donor screening. Comparing the attack
detection delay to the incubation times of the most feared
bioterror agents shows that even under such optimistic
conditions, victims of a bioterror attack would likely exhibit
symptoms before the attack was detected through blood
donor screening. For example, an attack infecting 100 per-
sons with a noncontagious agent such as *Bacillus anthracis*
would only have a 26% chance of being detected within 25
days; yet, at an assumed additional charge of $10 per test,
donor screening would cost $139 million per year.
Furthermore, even if screening tests were 99.99% specific,
1,390 false-positive results would occur each year.
Therefore, screening blood donors for bioterror agents
should not be used to detect a bioterror attack.
T
he health and economic consequences of an extensive
bioterror attack could be severe (1–5); thus, early
detection of an otherwise silent bioterror attack is of obvi-
ous importance (6). Ongoing developments in rapid testing
for potential bioterror agents (7–10) led us to consider
whether screening blood donors to detect a bioterror attack
with the most feared bioterror agents (11) could prove use-
ful. The rationale for screening blood donors is twofold.
First, blood donors are numerous, and donations are uni-
formly spread over time and throughout the population. In
the United States, approximately 13.9 million blood dona-
tions are made each year (12); thus, the annual number of
donations roughly equals 5% of the 286 million popula-
tion. Second, in the absence of specific information regard-
ing how such an attack might target the population, we can
assume that blood donors are as likely to be infected in a
bioterror attack as nondonors. In a sizeable attack, infect-
ed donors might donate blood before their infections have
been detected medically. Screening donated blood for
bioterror agents could therefore serve to detect an attack
sooner than would otherwise be possible.
However, the cost of screening donations is proportion-
al to the number of donations tested, in addition to the
resources expended investigating false alarms. To investi-
gate these issues, we developed a model for bioterror
attack detection under assumptions favorable to donor
screening, for if such best-case assumptions fail to justify
screening donors, more realistic assumptions will also. In
particular, we initially assume that the screening test used
is perfectly specific, which removes the possibility of false
alarms, and compare the time required to detect an attack
through donor screening to the incubation periods for var-
ious bioterror agents to see whether donor screening leads
to more rapid detection than simply observing sympto-
matic cases. We then consider tests with imperfect speci-
ficity, examine the false-alarm rate that would result from
donor screening, and compare this rate to the true-positive
rate for blood donations.
**Methods**
Though blood tests with the ability to detect agents
such as smallpox virus or *Francisella tularensis *within
days after infection do not exist at present, research to
develop such sensitive tests is under way (7–10). To ana-
lyze whether screening donors might meaningfully shorten
the time required to detect an attack were such tests avail-
able, we developed a probabilistic model that joins the
workings of a screening test, blood donation, and epidem-
ic spread under assumptions that deliberately favor attack
detection through donor screening (see Appendix). In the
model, the sensitivity of a screening test is determined by
a (random) window period *W *with mean
ω days that must
transpire before a person infected at time 0 can be detect-
ed as infected. Test sensitivity thus depends on the time
from infection until testing. Though the model can accom-
modate any probability distribution desired, we take *W *to
follow an exponential distribution in our examples, an
assumption that favors early detection (since the exponen-
tial likelihood is maximized at *W*=0, that is, no detection
delay, and declines as *W *increases). We assume initially
Emerging Infectious Diseases • Vol. 9, No. 8, August 2003
909
PERSPECTIVES
Detecting Bioterror Attacks
by Screening Blood Donors:
A Best-Case Analysis
**Edward H. Kaplan,*Christopher A. Patton,† William P. FitzGerald,† and Lawrence M. Wein‡ **
*Yale School of Management and Yale Medical School, New
Haven, Connecticut, USA, †American Red Cross, Arlington,
Virginia, USA; and ‡Stanford University, Stanford, California, USA
that the screening test is perfectly specific, though we will
relax this assumption later.
A bioterror attack at time 0 infects *I*(*0*)*=Np *persons in
a population of size *N *(where *p *is the fraction of the pop-
ulation initially infected). We assume that everyone in the
population has the same probability *p *of infection due to
the attack, that is, the attack does not target the population
in a manner that would make blood donors more or less
likely to be infected than nondonors. Given that the total
number of blood donations over time results from the inde-
pendent actions of individual blood donors, the aggregate
number of blood donations over time was modeled as a
Poisson process (13) with rate
λ=*kN*, where *k *is the mean
number of blood donations per person per unit of time. If
the agent used in the attack is contagious, secondary infec-
tions spread according to an epidemic model, governed by
a reproductive number *R*
0
(number of secondary infections
per initial index case) and an exponentially distributed
duration of infectiousness with mean *r*
-1
. To favor donor
screening, we deliberately exclude an explicit latent period
(during which an infected person is not infectious). These
assumptions imply that infections in the population will
grow exponentially with rate (*R*
0
– 1)*r *postattack (14), an
assumption that further favors donor screening as the num-
ber of blood donors who are infected (and by ignoring
latent periods, infectious) will grow exponentially at the
same rate, leading to earlier detection via donor screening
than would occur otherwise.
We assume that the attack is detected once a single
infected donation tests positive for infection with a bioter-
ror agent, another assumption favorable to donor screen-
ing, which enables us to derive the probability distribution
of the time required to detect a bioterror attack of a given
magnitude. However, to demonstrate the extent to which
we have “stacked the deck” in favor of blood donor screen-
ing, we relax the assumption of perfect test specificity for
noncontagious agents. We assume fixed attack rates and
disaster response and recovery periods, which together
determine the fraction of time during which infected dona-
tions can occur. This assumption allows us to model the
rate of false alarms per unit of time and compare this to the
rate of true-positive alarms.
**Results**
For initial attacks ranging from 100 to 1,000 infections,
Figure 1 shows the probability distribution of the attack
detection delay for a noncontagious agent that would result
from using a blood-screening test able to detect infections
an average of
ω = 3 days after infection (an optimistic
assumption, given that such tests do not exist at present),
assuming that blood donations arrive at rate *k *= 0.05 per
person per year, the average rate for blood donation in the
United States (12). The results are not encouraging: for an
attack that infects 100 persons, the chance of detecting the
attack through blood donor screening within 25 days is
26%; even for a large attack that infects 1,000 persons, the
median time to detect the attack is 8 days. Figure 2 (solid
curve) shows the mean delay in attack detection as a func-
tion of the initial attack size for a noncontagious agent. For
an initial attack that affects 1,000 persons, the mean time
to detection is 10 days, while for an attack that affects 100
persons, the mean time to detection is 76 days. In most
infected persons, symptoms would develop during this
period, leading to earlier detection of an attack than blood
donor screening would allow, even when potential delay
from misdiagnosis or failure to recognize symptoms is
accounted for (Table 1; compare to incubation times from
infection through symptoms for *Bacillus anthracis *and
*Clostridium botulinum*, two noncontagious agents). That
we have deliberately made assumptions favorable to blood
donor screening strengthens this finding, for the actual
time required to detect an attack by means of donor screen-
ing would be longer than reported above.
If we also assume that
ω=3 days and *k*=0.05 per person
per year, Figure 3 shows the distribution of delays in attack
detection that would result from a contagious agent char-
acterized by *R*
0
=3 and *r*
-1
=14 days (parameters suggestive
910
Emerging Infectious Diseases • Vol. 9, No. 8, August 2003
PERSPECTIVES
Figure 1. Probability distribution of attack detection delay for a
noncontagious agent. Blood donations occur at rate *k*=0.05 per
person per year, the screening test has a mean window period of
ω=3 days, and initial attack sizes range from 100 through 1,000
infections.
Figure 2. Mean attack detection delays for noncontagious (solid)
and contagious (dashed) agents as a function of the initial attack
size. Other parameters set as in Figures 1 and 3.
of smallpox [3,11,15] and perhaps Ebola virus [11]).
Because additional infections are transmitted to suscepti-
ble persons, the probability of detecting an attack within
any given period is greater than for a noncontagious agent.
Consequently, for a given initial attack size, the attack
detection delay distribution is shorter for a contagious
agent, as is clear from Figure 3. However, symptoms
would develop in many infected persons, and such infec-
tions would be recognized before blood donor screening
would uncover an attack. Under our best-case assump-
tions, an attack that initially infects 100 persons would still
require 15 days on average before donor screening would
detect the attack, while an initial attack infecting 1,000
persons would require 6 days until detection on average
(Figure 2).
Treating the range of incubation times from infection
through symptoms (Table 1) as 99% probability intervals
from agent-specific lognormal distributions, in the case of
smallpox one would expect to see five symptomatic cases
after 7 days, while more than half of those initially infect-
ed with Ebola virus would progress to symptoms within 1
week. The incubation times for plague and tularemia are
much shorter (Table 1), but even after increasing *r *to com-
pensate for this in our model many of those infected would
exhibit symptoms before the bioterror event was detected
through tests of the blood supply (results not shown).
Again, considering that we have made assumptions that
favor donor screening—that the test has an exponentially
distributed window period that detects infection after 3
days on average, that donor screening detects the attack
after the first donor tests positive, that there is no latent
period from infection through infectiousness, and that a
postattack epidemic grows exponentially—donor screen-
ing as a method of attack detection does not seem compet-
itive with simple observation of symptomatic case-
patients.
Until now, we have assumed that screening occurs with
perfect specificity, which eliminates false-positive results
as a consequence. However, if false-positive test results
can occur, they will occur frequently. Table 2 reports the
false-alarm rates that would occur for tests of different
specificities for a noncontagious agent, if one assumes that
all 13.9 million annual blood donations are tested, that on
average one bioterror attack takes place per year (a rate all
would agree is unrealistically high), that on average 1
month is required to respond to and recover from an attack
(so infected donations can occur for up to 1 month after an
attack), and that each attack infects 1,000 persons. Even
with 99.99% specificity, an average of 1,390 false-positive
results would occur per year; at 99% specificity, the aver-
age would be 139,000 false-positive results per year.
In addition to the resources wasted in investigating so
many false alarms, a “crying wolf” mindset could diminish
the attention paid to all screening test results, increasing
the chance of missing a true-positive test result. That this
latter possibility could well occur seems clear because with
the attack rate and duration of response and recovery
assumed above, one would expect only 3.7 donations with
true-positive results each year (again, presuming an expo-
nentially distributed window period with mean
ω*= *3
days). Also, though lowering the attack rate below one per
year to more realistic levels would have no effect on the
false-positive rate, the number of donations with true-pos-
itive results would fall. Similarly, reducing the duration of
the postattack response and recovery during which infect-
ed donations can still occur would have essentially no
impact on the false-positive rate, while again lowering the
number of donations with true-positive results.
**Conclusion**
We have argued that even under assumptions deliber-
ately favorable to blood donor screening, an attack was
unlikely to be detected earlier through donor screening
than from observing symptomatic case-patients. We have
also shown that imperfect test specificity could overwhelm
the blood collection system with false-positive results. In
addition, the costs of screening apply to all blood dona-
tions tested: even if the cost of screening were as low as an
incremental $10 per test, screening all blood donations in
the United States to detect a bioterror attack would cost an
additional $139 million per year at current donation rates.
Emerging Infectious Diseases • Vol. 9, No. 8, August 2003
911
PERSPECTIVES
Table 1. Incubation periods from infection through symptoms for
Centers for Disease Control category A agents
Agent
Incubation time (days)
*Bacillus anthracis *
<7
*Clostridium botulinum *
0.5–1.5
*Yersinia pestis *
1–6
Smallpox virus
7–17
*Francisella tularensis *
3–5
Hemorrhagic fever viruses
2–21 (Ebola); 5–10 (Marburg)
Source: (11).
Figure 3. Probability distribution of attack detection delay for a con-
tagious agent. Blood donations occur at rate *k*=0.05 per person
per year, the screening test has a mean window period of
ω=3
days, the reproductive number R
0
=3, the mean duration of infec-
tiousness r
-1
=14 days, and initial attack sizes range from 100
through 1,000 infections.
Total costs would be even higher when the resources that
would be expended investigating false-positive results are
considered. For all of these reasons, blood donors should
not be screened for bioterror agents for the purpose of
detecting a bioterror attack.
E.H.K. was supported in part by Yale University’s Center for
Interdisciplinary Research on AIDS via Grant MH/DA56826
from the U.S. National Institutes of Mental Health and Drug
Abuse.
Dr. Kaplan is the William N. and Marie A. Beach Professor
of Management Sciences at the Yale School of Management and
professor of public health at the Yale School of Medicine, where
he directs the Methodology and Biostatistics Core of Yale’s
Center for Interdisciplinary Research on AIDS. His interests
include the application of operations research, statistics, and
mathematical modeling to public health policy problems such as
HIV prevention, and more recently bioterror preparedness and
response.
**Appendix**
We consider a single bioterror attack that infects a proportion
*p *of the population at time 0. To model test sensitivity, we pre-
sume that a blood test administered to a person *t *days after
becoming infected will test positive for infection with probabili-
ty *F*
*W*
(*t*), where *W *refers to the window period of the test. In our
examples we assume that *W *follows the exponential distribution
with mean
ω days, that is, *F*
*W*
(*t*)= 1 – *e*
-*t/*
ω
, though the model
allows assessment for any window period distribution. We set
ω=3 days in our examples.
The probability that a randomly selected member of the pop-
ulation would test positive *t *days after the attack is then given by
(1)
where
ι( *u*), the per-capita rate of infection due to transmission
after attack (but before detection) grows exponentially as
(2)
as explained following equation 8 below. In equation (2), *R*
0
is
the reproductive number specifying the number of secondary
infections transmitted by an initially infected individual early in
the outbreak, while *r*
–1
is the mean duration of infectiousness
(14). We set *R*
0
=3 and *r*
–1
=14 days in our contagious examples,
parameters suggestive of smallpox (3,15), while results for
attacks with noncontagious agents are obtained by setting *R*
0
=0.
Note that
π
(*t*) is proportional to *p*, the fraction of the population
initially infected in the attack.
Due to the superposition of many individually arriving donors
(13), we assume that in the aggregate, blood donations occur in
accord with a Poisson process with rate
λ per unit of time. We set
λ =*kN *for some constant *k*, that is, the blood donation rate is pro-
portional to the size of the population (*k*=0.05 to represent the
average U.S. donation rate [12] in our examples). We further
assume that donors are no more or less likely to have been infect-
ed than nondonors. The number of blood donations that would
test positive within time
τ
of the attack then follows a Poisson
distribution with mean
(3)
Note that since
π(*t*) is proportional to *p *while λ is proportional to
*N*,
ρ(τ) is proportional to *I*(0)=*Np*, the initial attack size. Thus the
ability to detect a bioterror attack by means of blood donor
screening when blood donation occurs at a rate proportional to
the population is directly related to the initial number of persons
infected in the attack, independently of the size of the population.
The probability that at least one blood donation would test
positive and detect the attack within
τ days is given by
(4)
while the expected time required to detect such an attack equals
(5)
because the expected value of a nonnegative random variable
equals the integral of its survivor function, as is well-known.
Since
ρ(τ) is proportional to the initial attack size, the probabili-
ty of detecting an attack within any fixed time interval increases
with the initial attack size, while the expected time required to
detect an attack decreases with the size of the attack.
In the event of an attack at time 0 with a contagious agent, we
approximate the progress of the resulting epidemic with the stan-
dard model
(6)
where *N *is the population size, and
(7)
is the disease transmission rate (14). Persons infected in this
model immediately become infectious and remain so for *r*
-1
time
units on average; thus; no latent period occurs during which a
person is infected but not infectious. Early in the epidemic we
912
Emerging Infectious Diseases • Vol. 9, No. 8, August 2003
PERSPECTIVES
Table 2. False-alarm rates with test specificities as shown
Specificity (*s*)
Annual false-alarm rate (FAR)
0.9
1,390,000
0.99
139,000
0.999
13,900
0.9999
1,390
a
If one assumes 13.9 million annual blood donations tested, an average of one
bioterror attack per year that infects 1,000 persons with a noncontagious agent,
and a 1-month response and recovery period during which infected donations
continue to arrive.
∫
−
+
=
*t*
*W*
*W*
*du*
*u*
*t*
*F*
*u*
*t*
*pF*
*t*
0
)
(
)
(
)
(
)
(
ι
π
)
)
1
exp((
)
(
0
0
*ru*
*R*
*r*
*pR*
*u*
−
=
ι
∫
=
τ
λπ
τ
ρ
0
.
)
(
)
(
*dt*
*t*
))
(
exp(
1
)
(
τ
ρ
τ
−
−
=
*D*
∫
∞
−
=
0
))
(
exp(
]
Delay
Detection
Attack
[
τ
τ
ρ
*d*
*E*
)
(
)]
(
)[
(
)
(
*t*
*rI*
*t*
*I*
*N*
*t*
*I*
*dt*
*t*
*dI*
−
−
=
β
*N*
*r*
*R*
0
=
β
have *N–1*( *t*)
≈*N, *which as usual leads to exponential growth in the
number of infections as
(8)
Note that the per-capita transmission of infection before the
detection of the attack in this model is given by
as in equation 2.
The sensitivity of the attack detection delay to the parameters
of this model can be determined directly from the mathematics
above. To summarize, the time to detect an attack via blood donor
screening will decrease if, *ceteris paribus*, any of the following
parameters increase: the initial number of infections, *I*(0), the per
capita blood donation rate (*k*), the reproductive number (*R*
0
), and
the disease progression rate ( *r*). Increasing the mean window
period of the screening test (
ω) would lengthen the time required
to detect an attack.
The screening test employed is perfectly specific in the analy-
sis above, which obviates the problem of false alarms by assump-
tion. We now relax the assumption of perfect specificity and
instead assume that an uninfected donation will test negative with
probability *s*, where *s *is the specificity of the test. With this new
assumption, uninfected donations will test positive with probabil-
ity 1–*s*, which leads to false-positive results.
To compare false-positive and true-positive rates for noncon-
tagious agents, we adopt an alternating renewal process model
(13) of bioterror attack and recovery (a similar analysis could be
conducted for contagious agents, but little insight can be gained
from doing so). Under normal circumstances, we assume that
attacks occur at a mean rate of
α per unit time. Once an attack
occurs, we assume that
δ time units are required for response and
recovery (clearly
δ would depend upon the time required to
detect an attack, which in turn could be influenced by donor
screening, but this effect is minor and not essential for the main
results reported). Infected donations can only occur during the
response and recovery period, while to simplify the analysis, we
presume that no further attacks ensue during the recovery period
(indeed, multiple attacks could simply be modeled within this
framework as one larger attack). Again for simplicity, we further
assume that blood donations occur at the constant rate
λ*= kN*
over time, and that any attack infects a fraction *p *of the popula-
tion.
With these assumptions, it follows immediately that the frac-
tion of time occupied by response and recovery, which coincides
with the fraction of time during which infectious donations can
occur, is given by
(9)
It follows that the false-alarm rate, FAR (i.e., the mean number
of noninfected donations that falsely test positive), is equal to
(10)
for all donations that test positive do so falsely under normal cir-
cumstances, while during the response and recovery period, a
fraction (1–*p*) of donations will be noninfected, and of these (1–*s*)
will falsely test positive.
To obtain a simple formula for the true-positive donation rate,
note first that the overall attack rate per unit time is given by
(11)
because, by assumption, attacks do not occur during the response
and recovery period. Since
ρ(δ) infected and detected donations
will occur on average during the response and recovery period
(where
ρ(δ) ) is given by equation [3]), the overall true-positive
donation rate ( *TPDR) *is given by
(12)
In the text, we report results for
δ=1 month and α'=1 attack
per year, but again the sensitivity of the results to the model
parameters is clear from the mathematics: reducing either the
attack rate or the duration of response and recovery serves to
reduce the true-positive donation rate while marginally increas-
ing the false-positive rate; increasing test specificity obviously
reduces the false-alarm rate.
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Emerging Infectious Diseases • Vol. 9, No. 8, August 2003
913
PERSPECTIVES
).
)
1
exp((
)
0
(
)
)
exp((
)
0
(
)
(
0
*rt*
*R*
*I*
*t*
*r*
*N*
*I*
*t*
*I*
−
=
−
=
β
).
1
/(
αδ
αδ
+
=
*f*
)
1
)(
1
(
)]
1
(
1
)[
1
(
*fp*
*s*
*kN*
*p*
*f*
*f*
*s*
*kN*
*FAR*
−
−
=
−
+
−
−
=
)
1
(
*f*
−
=
′ α
α
).
(
δ
ρ
α′
=
*TPDR*
)
)
1
exp((
/
)
(
0
0
*rt*
*R*
*r*
*pR*
*N*
*t*
*NI*
−
=
β
14. Anderson RM, May RM. Infectious diseases of humans: dynamics
and control. New York: Oxford University Press; 1991.
15. Gani R, Leach S. Transmission potential of smallpox in contempo-
rary populations. Nature 2001;414:748–51.
Address for correspondence: Edward H. Kaplan, Yale School of
Management, 135 Prospect Street, New Haven, CT 06511-3729, USA;
fax: 203-432-9995; email: edward.kaplan@yale.edu
914
Emerging Infectious Diseases • Vol. 9, No. 8, August 2003
PERSPECTIVES
The opinions expressed by authors contributing to this journal do
not necessarily reflect the opinions of the Centers for Disease
Control and Prevention or the institutions with which the authors
are affiliated.
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