Transmission dynamics and control of severe acute respiratory syndrome

Science

Volumn 300, Issue 5627, 2003, Pages 1966-1970

  Lipsitch, Marc ^a   Cohen, Ted ^a   Cooper, Ben ^a   Robins, James M ^a   Ma, Stefan ^b   James, Lyn ^b   Gopalakrishna, Gowri ^b   Chew, Suok Kai ^b   Tan, Chorh Chuan ^b   Samore, Matthew H ^c   Fisman, David ^d,e   Murray, Megan ^a,f  

^a HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

^b MINISTRY OF HEALTH   (Singapore)

^c UNIVERSITY OF UTAH SCHOOL OF MEDICINE   (United States)

^d MCMASTER UNIVERSITY   (Canada)

^e City of Hamilton   (Canada)

^f MASSACHUSETTS GENERAL HOSPITAL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EPIDEMIOLOGY; HEALTH CARE; PULMONARY DISEASES;

EPIDEMIC CURVES;

HEALTH RISKS;

DISEASE SPREAD; DISEASE TRANSMISSION; EPIDEMIOLOGY; INFECTIOUS DISEASE; PUBLIC HEALTH; SEVERE ACUTE RESPIRATORY SYNDROME;

ARTICLE; EPIDEMIC; EPIDEMIOLOGICAL DATA; HUMAN; INFECTION CONTROL; PRIORITY JOURNAL; PUBLIC HEALTH; QUANTITATIVE ANALYSIS; SEVERE ACUTE RESPIRATORY SYNDROME; SINGAPORE; STOCHASTIC MODEL; VIRUS PNEUMONIA; VIRUS TRANSMISSION;

CONTACT TRACING; DISEASE OUTBREAKS; EPIDEMIOLOGIC METHODS; HONG KONG; HUMANS; MATHEMATICS; MODELS, STATISTICAL; PATIENT ISOLATION; PROBABILITY; PUBLIC HEALTH PRACTICE; QUARANTINE; SEVERE ACUTE RESPIRATORY SYNDROME; SINGAPORE; STOCHASTIC PROCESSES;

RNA VIRUSES;

EID: 12444346408     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.1086616     Document Type: Article

References (23)

1. C. A. Donnelly et al., Lancet 361, (2003).
2. See information from the World Health Organization (WHO), available online at www.who.int/csr/ sarscountry/en/.
3. C. Drosten et al., N. Eng. J. Med. 348, 1967 (2003).
4. J. S. M. Peiris et al., Lancet 361, 1318 (2003).
5. T. G. Ksiazek et al., N. Eng. J. Med 348, 1953 (2003).
6. U.S. Centers for Disease Control and Prevention, Morb. Mortal. Wkly. Rep. 52, 405 (2003).
7. 2, where λ = In[Y(t)]/t is the exponential growth rate of the epidemic, calculated as the logarithm of the cumulative number of cases by time t since the first case divided by the time required to generate these cases from a single case; v is the serial interval; and f is the ratio of the mean latent period, i.e., time from infection to onset of infectiousness, to the serial interval.
8. The serial interval is the sum of the mean latent period and the mean duration of infectiousness; neither of these time periods is well defined for SARS. However, there have been no reported cases of transmission of SARS during the presymptomatic period, whereas there is substantial evidence of transmission immediately after onset of symptoms, suggesting that the period of infectiousness begins with the onset of symptoms. The mean incubation period has been variously measured as 5 days (6) and 6.4 days (1), suggesting that reasonable values for f lie in the range of 0.5 to 0.8. Except for the longest serial intervals, estimates of R are relatively insensitive to varying assumptions about f (fig. 51).
9. Increasing the assumed serial interval results in a higher estimate of the value of R, because it implies that fewer generations of the infection have occurred in a given time. This range of estimates also includes values obtained for all possible values of f.
10. R. M. Anderson, R. M. May, Infectious Diseases of Humans: Dynamics and Control (Oxford Univ. Press, Oxford, 1991).
11. j with a kernel smoother; and, finally, estimating f (Y|R) as the height of the kernel density estimator at Y. J was at least 200 for all estimates. When the CV of 3.5 was reduced, the credible intervals became smaller (21).
12. This can be approximated by the probability of persistence of a branching process (22) in which the number of secondary cases is given by a negative binomial distribution with a mean of R and a given variance. The persistence probability is given as one minus the smallest nonnegative fixed point of the probability-generating function of the branching process (22).
13. See information from WHO, available online at www.who.int/csr/sars/archive/2003_05_12/en/.
14. See information from WHO, available online at www.who.int/csr/don/2003_04_09/en/.
15. 0 is defined analogously to the definition of R in the main text. This is a direct generalization of the usual formula for the final size of an epidemic (10) and is linear because we assume that each case, regardless of its source, has equal probability (1 - a) of being symptomatic. More generally, if these assumptions are met, the ratio of symptomatic to asymptomatic cases will be (1 - a):a (discounting the latent cases).
16. If a proportion of infected individuals leave quarantine before they become infectious and are therefore not isolated immediately upon the onset of symptoms, the result is the same as if they had not been quarantined. Our assumption that the proportion of noninfected (still susceptible) contacts of each case who are quarantined will equal the proportion, q, of infected contacts of cases who are successfully quarantined likely represents an underestimate; if contacts are equally easy to trace whether or not they are infected, the proportion of infected contacts quarantined before they become infectious will likely be less than the proportion of susceptible contacts who are quarantined, since some infected contacts will become infectious before they are detected. Since quarantine of infected contacts is more important than quarantine of susceptible ones, we define q in terms of the former.
17. In this model, we assume that quarantine of contacts and isolation of cases are completely effective and that those quarantined are at no further risk of infection. These assumptions are made to illustrate the potential impact of control measures. Clearly, special measures will be required to prevent transmission in such situations, especially if large numbers of people are quarantined together.
18. E. H. Kaplan, D. L. Craft, L. M. Wein, Proc. Natl. Acad. Sci. U.S.A. 99, 10935 (2002).
19. K. A. Callow, H. F. Parry, M. Sergeant, D. A. Tyrrell, Epidemiol. Infect. 105, 435 (1990).
20. S. F. Dowell, Emerg. Infect. Dis. 7, 369 (2002).
21. M. Lipsitch et al., unpublished data.
22. S. Karlin, H. M. Taylor, A First Course in Stochastic Processes (Academic Press, San Diego, 1975).
23. We thank N. Gay and the WHO SARS modeling working group for their support, S. Lambert of WHO for facilitating our collaboration, B. Bloom for guidance and encouragement in many aspects of this work, K. McIntosh for an introduction to coronaviruses, and R. Malley for helpful comments. Supported by the Ellison Medical Foundation (M.L.) and NIH grants R01 AI 48935 (M.L.), R21 AI 55825 (M.L. and B.C.), T32 AI07433 (T.C.), R01 AI 32475 (J.M.R.), and R01 AI 46669(M.M.). The views expressed in this paper do not necessarily represent those of the City of Hamilton.