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Letter
Detecting Bioterror Attack
To the Editor: In a recent article (1), Kaplan
et al. addressed the problems in detecting a bioterror attack from blood-donor
screening. The main point of this comment is the "early approximation"
used by Kaplan et al. to derive the probability of detecting an attack.
The simplification used by Kaplan et al. leads to a probability that does
not account for the size of the exposed population and can lead to incorrect
results and misinterpretations.
Consider a single bioterror attack that infects a proportion p of an
exposed population of size N at time τ = 0, such that the initial
number of infected is  .
The quantity of interest is the probability  of finding at least one positive blood
donation and detecting the attack within time τ. For attacks conducted
with contagious agents that could lead to an epidemic, Kaplan et al. used
the early approximation solution of the classic epidemic models (2)
to describe the progression of the number of infected persons. Consequently,
the resulting probability of attack detection [noted  ] is dependent only upon the initial size
of the release  , the basic reproductive number  (the mean number of
secondary cases per initial index case), and other variables (the blood
screening window ω, the mean number k of blood donations per person
and per unit of time, and the mean duration of infectiousness 1/r) (Appendix).
Early approximation can lead to unreliable results because it is valid
only at earlier stages of the epidemics and in the limit where the proportion
p of initially infected is much smaller than the intrinsic steady proportion
 of
the epidemics (Appendix). Relaxing this
approximation and using the full solution for the progression of the number
of infected persons leads to the probability
that takes into account the size of the exposed population (Appendix).
The latter is important because, in contrast to that leads to the same conclusion, indicates that the
probabilities of detecting an attack within two exposed populations of
different sizes, but with the same numbers of initially infected, are
not identical. As illustrated in the Figure, when
the other variables are fixed, decreases as the proportion
p of initially infected increases because the epidemic size decreases
as p approaches the threshold. These subtleties of a simple epidemic
model are even less reliable when using the blood screening to detect
a bioterror attack with agents that cause diseases of very short incubation
period.
Nonetheless, detecting a bioterror attack is very similar to detecting
the response of pathogen-specific immunoglobulin M antibodies (as an indicator
of recent contact of hosts with pathogens) within a population of hosts
by using serologic surveys. Therefore, the reasoning developed for a bioterror
attack can be extended and applied to detect and time the invasion or
early circulation of certain pathogens within a population. In that perspective,
it might be useful to develop an analysis that includes more details of
the epidemic progression within this framework.
Dominique Bicout*
Ecole National Veterinaire Lyon, Marcy-l'Etoile, France
Suggested citation
for this article:
Bicout DJ. Detecting bioterror attack [letter]. Emerg Infect Dis [serial
on the Internet]. 2004 Aug [date cited]. Available from: http://www.cdc.gov/ncidod/EID/vol10no8/03-1044_04-0291.htm
References
- Kaplan EH, Patton CA, FitzGerald WP, Wein LM. Detecting
bioterror attacks by screening blood donors: a best-case analysis.
Emerg Infect Dis. 2003;9:909–14.
- Anderson RM, May RM. Infectious diseases of humans: dynamics and control.
New York: Oxford University Press;1991.
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In Reply: As stated and argued throughout
our article (1), we conducted a best-case analysis under
assumptions that favored blood-donor screening to detect bioterror attacks;
if such an analysis fails to justify donor screening, no analysis will.
Bicout (2) is concerned about our assumption of exponential
infection growth after attack; however, this assumption was one of several
we made deliberately as part of our best-case scenario (1).
Bicout's calculations actually reinforce rather than refute our analysis.
By relaxing our assumption of exponential infection growth and using the
well-known logistic solution to the basic epidemic model (equation 1 in
Bicout's letter), Bicout shows that more time is required to detect a
bioterror attack than when exponential infection growth is assumed (Figure
accompanying Bicout's letter). The number of persons infected over time
under the logistic model will be fewer than the number of persons infected
if exponential growth is assumed; therefore, screening blood donors to
detect a bioterror attack is even less attractive than using our best-case
assumptions. The take-home message from our article was and is: It makes
little sense to screen blood donors to detect a bioterror attack.
Edward H. Kaplan*
and Lawrence M. Wein†
*Yale School of Management , New Haven, Connecticut, USA; and †Stanford
University, Stanford, California, USA
Suggested citation
for this article:
Kaplan EH, Wein LM. Detecting bioterror attack [response to letter].
Emerg Infect Dis [serial on the Internet]. 2004 Aug [date cited].
Available from: http://www.cdc.gov/ncidod/EID/vol10no8/03-1044_04-0291.htm
References
- Kaplan EH, Patton CA, FitzGerald WP, Wein LM. Detecting
bioterror attacks by screening blood donors: a best-case analysis.
Emerg Infect Dis. 2003;9:909–14.
- Bicout DJ. Detecting bioterror attack [letter]. Emerg Infect Dis.
2004;10. [this issue]
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