Skip directly to site content Skip directly to page options Skip directly to A-Z link Skip directly to A-Z link Skip directly to A-Z link
Volume 7, Number 6—December 2001
Research

Modeling Potential Responses to Smallpox as a Bioterrorist Weapon

Martin I. Meltzer*Comments to Author , Inger K. Damon*, James W. LeDuc*, and J. Donald Millar†
Author affiliations: *Centers for Disease Control and Prevention, Atlanta, Georgia, USA;; †Don Millar & Associates, Inc., Atlanta, Georgia, USA

Main Article

Table 4

Doses of vaccine used to control outbreaks of smallpox: Numbers vaccinated per confirmed case from a variety of outbreaks, 1961-1973

Site Year Population % susceptible No. of cases Total vaccinated Doses used per case Source
Saiwara village, India 1968 8 40 1,358a 34 27
Nathawala village, India 1969 12 12 450b 38 27
Bawku, Ghana 1967 n/a 66 165,449 2,507 28
Rural Afghanistan 1969 n/ac 6 508d 85 29
Nuatja sub-division, Togo 1969 n/a 6 10,818 1,803 30
Anéono subdivision, Togo 1969 40 47 294,274 6,261 30
Yugoslavia 1972 n/a 175 18 million 102,857 31
Utinga City, Brazil 1969 57 246 2,188 9 32
Botswana 1973 17-27e 30 50,000 1,667 33
London, UK 1961 n/a 3 62,000 20,667 34
West Bromwich, UK 1961 n/a 2 "limited"f n/a 34
Bradford, UK 1961 n/a 14 250,000 17,857 34
Birmingham, UK 1962 n/a 1 "limited"f n/a 34
Cardiff, UK 1962 n/a 47 900,000 19,148 34
Mean 14,411
Median 2,155
95th perct.g 7,001
90th perct.g 4,329
10th perct.g 3.5

aThis population includes 1,069 revaccinations, accounting for 79% of total vaccinations.
bThis population includes 323 revaccinations, accounting for 72% of total vaccinations.
cThe source did not provide population-based estimates of preoutbreak vaccination coverage (as determined by a vaccine scar survey). However, in the four households that contained the six cases, of the 18 family members present at the time of the investigation, 6 (33%) had evidence of preoutbreak vaccination or variolation.
dThis number excludes some children who had been vaccinated 15 days before the outbreak investigation.
eIn the sample (n=68,065), susceptibility varied by age. Smallpox vaccination scars were noted among 76% of those <5 years of age, 83% of those 6 to 14 years of age, and 79% of those >15 years of age.
fThe health authorities for West Midlands, which dealt with two of the importations (West Bromwich, Birmingham, UK), limited vaccinations to "...established contacts and medical and ancillary staffs placed at definite risk..." (34). Thus, although the source provides no estimates of the number vaccinated, the description of those targeted for vaccination can lead to the hypothesis that <1,000 persons were vaccinated per case.
gThe percentiles were calculated by fitting the data to a Gamma distribution (values of parameters: = 0.25; = 58,400). The chi-square value of the fit of the data to the distribution was 20.57 (p>0.01), the Kolmogorov-Smirnov test value was 0.1262 (p>0.15), and the Anderson-Darling test statistic was 0.3147 (p>0.15).

Main Article

References
  1. Henderson  DA. The looming threat of bioterrorism. Science. 1999;283:1279–82. DOIPubMedGoogle Scholar
  2. Henderson  DA. Smallpox: clinical and epidemiologic features. Emerg Infect Dis. 1999;5:537–9. DOIPubMedGoogle Scholar
  3. O'Toole  T. Smallpox: An attack scenario. Emerg Infect Dis. 1999;5:540–6. DOIPubMedGoogle Scholar
  4. Bardi  J. Aftermath of a hypothetical smallpox disaster. Emerg Infect Dis. 1999;5:547–51. DOIPubMedGoogle Scholar
  5. Henderson  DA, Inglesby  TV, Bartlett  JG, Ascher  MS, Eitzen  E, Jahrling  PB, Smallpox as a biological weapon: medical and public health management. JAMA. 1999;281:2127–37. DOIPubMedGoogle Scholar
  6. Rao  AR. Smallpox. Bombay: The Kothari Book Depot; 1972.
  7. Fenner  F, Henderson  DA, Arita  I, Jezek  Z, Ladnyi  ID. Smallpox and its eradication. Geneva: World Health Organization; 1988.
  8. Dixon  CW. Smallpox. London: Churchill; 1962.
  9. Anderson  RM, May  RM. Infectious diseases of humans: dynamics and control. New York: Oxford University Press; 1991.
  10. Anderson  RM, May  RM. Population biology of infectious diseases: Part II. Nature. 1979;280:455–61. DOIPubMedGoogle Scholar
  11. Cliff  AD, Haggett  P. Statistical modeling of measles and influenza outbreaks. Stat Methods Med Res. 1993;2:43–73. DOIPubMedGoogle Scholar
  12. Anderson  RM, May  RM. Population biology of infectious diseases: Part I. Nature. 1979;280:361–7. DOIPubMedGoogle Scholar
  13. Anderson  RM. Transmission dynamics and control of infectious disease agents. In: Anderson RM, May RM, editors. Population biology of infectious diseases. Berlin: Springer-Verlag; 1982. p. 149-77.
  14. Aron  JL, May  RM. The population dynamics of malaria. In: Anderson RM, editor. The population dynamics of infectious diseases: theory and application. London: Chapman and Hall; 1982.
  15. Frauenthal  JC. Smallpox: when should routine vaccination be discontinued? The UMAP Expository Monograph Series. Boston: Birkhäuser; 1981.
  16. Giordano  FR, Weir  MD, Fox  WP. A first course in mathematical modeling. 2nd ed. Pacific Grove (CA): Brooks/Cole Publishing Company; 1997.
  17. Christie  AR. Infectious diseases: Epidemiology and clinical practice. 3rd ed. New York: Churchill Livingstone; 1980.
  18. Singh  S. Some aspects of the epidemiology of smallpox in Nepal. Geneva: World Health Organization (WHO/SE/69.10); 1969.
  19. Mack  TM. Smallpox in Europe, 1950-1971. J Infect Dis. 1972;125:161–9.PubMedGoogle Scholar
  20. U.S. Bureau of the Census. Statistical abstract of the United States: 1999. 119th ed. Washington: Bureau of the Census; 1999.
  21. Royal Commission on Vaccination. A report on vaccination and its results, based on evidence taken by the Royal Commission during the years 1889-1897. Vol 1. The text of the commission report. London: New Sydenham Society; 1898.
  22. Smith  ADM. Epidemiological patterns in directly transmitted human infections. In: Croll NA, Cross JH, editors. Human ecology and infectious diseases. New York: Academic Press; 1983. p. 333-51.
  23. Bartlett  MS. Measles periodicity and community size. J R Stat Soc [Ser A]. 1957;120:48–60. DOIGoogle Scholar
  24. Bartlett  MS. Critical community size for measles in the United States. J R Stat Soc [Ser A]. 1960;123:37–44. DOIGoogle Scholar
  25. Arita  I, Wickett  J, Fenner  F. Impact of population density on immunization programmes. J Hyg Camb. 1986;96:459–66. DOIPubMedGoogle Scholar
  26. Lane  JM, Millar  JD. Routine childhood vaccination against smallpox reconsidered. N Engl J Med. 1969;281:1220–4. DOIPubMedGoogle Scholar
  27. Pattanayak  S, Sehgal  PN, Raghavan  NGS. Outbreaks of smallpox during 1968 in some villages of Jaipur district, Rajasthan. Geneva: World Health Organization (WHO/SE/70.20); 1970.
  28. de Sario  V. Field investigation of an outbreak of smallpox at Bawku, Ghana: May-October, 1967. Geneva: World Health Organization (WHO/SE/69.24); 1969.
  29. Rangaraj  AG. An outbreak of smallpox in a village in Afghanistan. Geneva: World Health Organization (WHO/SE/69.9); 1969.
  30. Glokpor  GF, Agle  AN. Epidemiological investigations. Smallpox Eradication Programme in Togo: 1969. Geneva: World Health Organization (WHO/SE/70.21); 1970.
  31. Litvinjenko  S, Arsic  B, Borjanovic  S. Epidemiologic aspects of smallpox in Yugoslavia in 1972. Geneva: World Health Organization (WHO/SE/73.57); 1973.
  32. de Costa  EA, Morris  L. Smallpox epidemic in a Brazilian community. Geneva: World Health Organization (WHO/SE/74.64); 1974.
  33. Presthus  GT, Sibiya  JB. A persistent focus of smallpox in Botswana. Geneva: World Health Organization (WHO/SE/74.89); 1974.
  34. Great Britain Ministry of Health. Smallpox, 1961-62. Reports on public health and medical subjects, No. 109. London: Her Majesty's Stationery Office; 1963.
  35. Evans  M, Hastings  N, Peacock  B. Statistical distributions. 2nd ed. New York: John Wiley & Sons, Inc.; 1993.
  36. Kaufmann  AF, Meltzer  MI, Schmid  GP. The economic impact of a bioterrorist attack: Are prevention and postattack intervention programs justifiable? Emerg Infect Dis. 1997;3:83–94. DOIPubMedGoogle Scholar

Main Article

1Others have suggested that the terms "preeruptive" or "initial" are more descriptively accurate of this stage (6). However, because "prodromal" is used in many standard textbooks (7,8,17), we will use this term.

2Prodromal rashes have been recorded, but they were considered to be uncommon occurrences, ". . . not more than 1 in 10." (17).

3The United States stopped routine vaccination of the civilian population in 1972 (5). In July 1998 in the United States, there were approximately 109.9 million persons <30 years of age, representing 41% of the total resident population (20). Most of these people have not been vaccinated against smallpox. In addition, the immunologic status of those who were vaccinated >30 years ago must be considered. Historical data indicate that vaccination 20 to 30 years ago may not protect against infection but will often protect against death (8,21). No reports, however, define the probability of such persons' transmitting the disease to susceptible persons. Faced with such uncertainty, we chose the simplest approach of assuming an unlimited supply of susceptible persons.

4At a 50% daily removal rate, a cohort of all those beginning the first day of overt symptoms is entirely removed in 7 days (8 to 10 days postincubation), with 90% removed in 4 days after they enter the overtly symptomatic period. At a 25% daily removal rate, a cohort is entirely removed 17 days after entering the overtly symptomatic period (18 to 20 days postincubation), with 90% removed in 9 days after entering the overtly symptomatic period. The calculated numbers of those quarantined relate only to those who are infectious (i.e., overtly symptomatic). The model does not take into account those who might also be quarantined along with the infectious persons, such as unvaccinated household contacts and other exposed persons.

5The number, severity, and cost of vaccine-induced side effects is the subject for a separate paper.

6Allowing 3 days for laboratory confirmation assumes that virus loads in clinical specimens may be insufficient to allow use of rapid assays and confirmation must await the results of a culture-based assay, which takes approximately 72 hours. Rapid laboratory confirmation, within 24 hours, is possible.

7Even by reducing transmission from 3 to 2 persons per infectious person and quarantining infectious persons at a rate of 25% per day, the number of new cases at day 365 is 3, not zero (i.e., transmission is not quite completely stopped) (Figure 6). For transmission to cease completely, vaccination must either achieve a 38% reduction in transmission to 1.85 cases per infectious person (assuming a daily quarantine rate of 25%), or quarantine must achieve a 29% daily reduction in the number of infectious persons (assuming vaccination reduces transmission by 33%).

8Although there are some historical data regarding how infected persons interacted and infected others, all such data were collected when circumstances differed from those of today's societies, particularly with regard to travel and spread of information. Although air and other modes of mass travel were common before smallpox was eradicated, the numbers of travelers and the total miles traveled have vastly increased in the past 30 years. Similarly, although mass media were well known and used in the 1960s and 1970s, more outlets are available to spread information than ever before. It is unknown how these and other changes could affect the spread of smallpox.

Page created: December 09, 2010
Page updated: December 09, 2010
Page reviewed: December 09, 2010
The conclusions, findings, and opinions expressed by authors contributing to this journal do not necessarily reflect the official position of the U.S. Department of Health and Human Services, the Public Health Service, the Centers for Disease Control and Prevention, or the authors' affiliated institutions. Use of trade names is for identification only and does not imply endorsement by any of the groups named above.
file_external