From the Department for Medical Biometry, University of Tübingen, Tübingen, Germany.
Supplemental material for this article is available with the online version of the Journal at www.epidem.com.
Correspondence: Martin Eichner, Westbahnhofstr. 55, 72070 Tübingen, Germany. E-mail: email@example.com
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Smallpox has become a mere footnote among the scourges of humanity despite being one of the most feared diseases in history. There are several reasons for this turn of fate. In contrast with many other diseases, smallpox is easily diagnosed,1 is of comparatively low infectivity,2–4 and spreads mainly to persons who have close contact with the sick.4–6 With its long incubation and infectious period,4 smallpox spreads rather slowly, which makes it highly amenable to isolation, quarantine, and vaccination of traced cases.7 Because smallpox lacks an environmental or animal reservoir, such interventions have made it possible to eradicate this devastating but vulnerable killer. Unfortunately, the possible use of smallpox as a weapon of bioterrorism has made it necessary to reconsider issues of its spread and containment.
EFFECT OF POSTEXPOSURE VACCINATION
Postexposure vaccination8,9 is known to reduce the severity of disease1 and could actually prevent illness if performed soon enough after infection.9 Using recently published data,8 we estimate the extent to which postexposure vaccination might prevent disease. The circles in Figure 1 show smallpox cases claimed to be vaccinated after infection. Although the actual interval between infection and vaccination is unknown, the authors assumed a constant latent period of 12 days between exposure and onset of disease.8 From this information, we can estimate the time between infection and vaccination. Recent estimates suggest that the mean latent period is 11.6 days with a standard deviation of 1.9 days.4 In Figure 1, we have estimated the distribution of cases by “postexposure day of vaccination,” assuming that the same number of patients were vaccinated on each day.
We find that vaccination up to 3.2 days after infection (95% confidence interval, 2.9–3.6 days) could protect against disease. These values must be interpreted cautiously because of arbitrary assumptions (for details, see supporting material available with the electronic version of this article). The asterisks in Figure 1 display the predicted numbers of cases based on a realistic distribution of latency duration and complete protection with vaccination up to 3.2 days after infection. A recent Delphi analysis estimated that the postexposure vaccine efficacy was 80% to 93% during the first 3 days after infection and 2% to 25% thereafter.9
COMBINING SMALLPOX INTERVENTIONS
Of course, there are more interventions possible than just vaccination. We need a combination of interventions to prevent an outbreak from becoming an epidemic. Under the assumption of no intervention, a new smallpox case would cause a certain number of secondary infections (R0) in a fully susceptible population, known as the basic reproduction number.10 An outbreak can be contained if the number of secondary infections is held to less than one per case. What combination of possible interventions can hold secondary infections to this level?
Figure 2 shows the steps in estimating this. At the initial exposure (step A), there could be a fraction of the population still protected by earlier vaccinations.11 In step B, overtly sick cases are isolated, reducing the opportunity for transmission of infection to other contacts. In step C, known contacts are traced, vaccinated, and taken under surveillance.7 Postexposure vaccination can prevent or alleviate the course of disease in some persons, but we cannot trust that the vaccination of contacts will prevent them from spreading the infection.
Known contacts must therefore be taken under surveillance so they can be isolated at the first signs of disease (before they can infect others). Although this need for continuing surveillance might seem obvious, it has not always been considered in smallpox models.12–14 If known contacts are kept under surveillance, we have only to worry about infections among untraced contacts (labeled “X” in Fig. 2). The effectiveness of postexposure vaccination becomes irrelevant. Unfortunately, infections among untraced contacts cannot be recognized until after the contacts themselves develop the disease—possibly after infecting others and starting a new wave of infections.
To contain an outbreak, interventions must reduce the fraction of untraced contacts such that each case produces on average less than one secondary case who can transmit the disease. Using the assumptions and interventions in Figure 2, we estimate that this goal could be attainable for values of R0 up to 17.7—a far larger number than the estimates for R0 derived from historical outbreaks.2–4
More important than the expected number of secondary infections is the expected total size of an outbreak. Assuming R0 = 6 and using the control strategy in Figure 2, we estimate that an outbreak initiated by 100 index cases could be controlled over several waves of infection without giving rise to more than a total of approximately 200 further cases.7,15 Readers could explore other sets of assumptions using an Internet-based simulation tool that we have designed for this purpose.15
In this issue, Kaplan16 examines how to prevent secondary cases of smallpox. He considers case isolation, but relies exclusively on postexposure vaccination without surveillance of vaccinated contacts. This leads him to conclude that traced vaccination is inferior to mass vaccination under reasonable assumptions. Mass vaccination might be needed with a very large attack. However, to rely solely on this strategy with a small bioterrorist attack could burden society with huge social and financial costs. Countrywide mass vaccination would produce many vaccine-associated cases,17 possibly more than caused by a bioterrorist attack. We believe a more flexible and focused response that includes contact surveillance could adequately protect the population.
ABOUT THE AUTHORS
MARTIN EICHNER is an associate professor of epidemiology and medical biometry at the University of Tübingen, Germany. His expertise is in modeling infectious diseases. He serves as temporary advisor to the German Government and the EU, and is participating in several international projects on bioterrorism intervention. MARKUS SCHWEHM is a senior computer scientist at the University of Tübingen, Germany, with extensive experience in stochastic modeling and optimization. He is currently developing an outbreak investigation and intervention planning tool for the German government.
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