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We present an analysis of the first 10 weeks of the severeacute respiratory syndrome (SARS) epidemic in HongKong. The epidemic to date has been characterized by twolarge clusters, initiated by two separate “super-spread”events (SSEs), and ongoing community transmission. Byfitting a stochastic model to data on 1512 cases, includingthese clusters, we show that the etiological agent of SARSis moderately transmissible. Excluding SSEs, we estimate2.7 secondary infections were generated per case onaverage at the start of the epidemic, with a substantialcontribution from hospital transmission. Transmissionrates fell during the epidemic, primarily due to reductionsin population contact rates and improved hospitalinfection control, but also as a result of more rapidhospital attendance by symptomatic individuals. As aresult, the epidemic is now in decline, though continuedvigilance is necessary for this to be maintained.Restrictions on longer-range population movement areshown to be a potentially useful additional controlmeasure in some contexts. We estimate that mostcurrently infected persons are now hospitalized,emphasizing the importance of control of nosocomialtransmission.

The evolution and spread of the etiological agent of severeacute respiratory syndrome (SARS), a novel coronavirus (1),has resulted in an unparalleled international effortcoordinated by the World Health Organization (WHO) tocharacterize the virus, develop diagnostic tests and formulateoptimal treatment protocols to reduce morbidity and mortality(2–4). Great progress has been made with, for example, thefull sequence of the RNA virus reported on the 13th April2003 (5, 6). The epidemic appears to have originated in earlyNovember in the Guandong province of the People’sRepublic of China, and then spread rapidly throughout theworld via air travel. As of the 21st May 2003, 7956 caseshave been reported to WHO from 28 countries with 666deaths recorded (Fig. 1A). The epidemics in Hong Kong,mainland China, Singapore, Taiwan and Toronto, Canada,have been of particular concern due to the multiplegenerations of local transmission seen in those areas. The

extent of these epidemics has been worsened by theoccurrence of large clusters of infection linked to singleindividuals and/or spatial locations.

The rate of spread of an epidemic—and whether suchspread is self-sustaining—depends on the magnitude of a keyepidemiological parameter, the basic reproduction number,R0, defined as the average number of secondary casesgenerated by one primary case in a susceptible population (7).Following introduction of an agent into a population, a relatedquantity—the effective reproduction number, Rt—quantifiesthe number of infections caused by each new case occurringat time t. This quantity is typically lower than the basicreproduction number due to the effect of control measures inreducing transmission and the depletion of susceptibleindividuals during the epidemic. For an epidemic to becontrolled, Rt needs to be reduced below 1, the self-sustainingthreshold. Estimation of reproduction numbers requirespopulation heterogeneity to be accounted for—reflecting, forexample, variation in infection risk with spatial location,variation in contact rates between groups, and between-casevariability in infectiousness (7, 8).

Heterogeneity in Rt between cases appears to beparticularly important for SARS due to the occurrence of“super-spread events” (SSEs)—rare events where, in aparticular setting, an individual may generate many more thanthe average number of secondary cases. The Hong Kongepidemic to date has been characterized by two large clustersof cases, together with ongoing transmission to closecontacts. In the first cluster, at least 125 people were infectedon or soon after March 3rd in the Prince of Wales Hospital(PWH) by the index patient for the Hong Kong epidemic (2).In the second cluster, an unknown number of people wereinfected from a probable environmental source in the AmoyGardens (AG) estate (Kwung Tong district). Followingmixing with fellow residents, families and friends, over 300people became infected. Examination of local reports ofSARS investigations (9) support the distinction between thesetwo large super-spread events and the other contact-basedinfections. It may be that the distinction between typicalinfection events and SSEs reflects the 2 different routes oftransmission so far identified as likely for this virus; namely,respiratory exudates and fecal-oral contact (with

Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact ofPublic Health InterventionsSteven Riley,1* Christophe Fraser,1* Christl A. Donnelly,1 Azra C. Ghani,1 Laith J. Abu-Raddad,1 Anthony J. Hedley,2 GabrielM. Leung,2 Lai-Ming Ho,2 Tai-Hing Lam,2 Thuan Q. Thach,2 Patsy Chau,2 King-Pan Chan,2 Su-Vui Lo,3 Pak-Yin Leung,4

Thomas Tsang,4 William Ho,5 Koon-Hung Lee,5 Edith M. C. Lau,6 Neil M. Ferguson,1 Roy M. Anderson1

1Department of Infectious Disease Epidemiology, Faculty of Medicine, Imperial College London, Exhibition Road, LondonSW7 2AZ, UK. 2Department of Community Medicine, University of Hong Kong, 21 Sassoon Road, Pokfulam, Hong Kong.3Research Office, Health, Welfare and Food Bureau, Government of the Hong Kong Special Administrative Region, 19th Floor,Murray Building, Garden Road, Hong Kong. 4Department of Health, Government of the Hong Kong Special AdministrativeRegion, Wu Chung House, 213 Queen’s Road East, Wanchai, Hong Kong. 5Hong Kong Hospital Authority, 147B Argyle Street,Kowloon, Hong Kong. 6Department of Community and Family Medicine, Chinese University of Hong Kong, School of PublicHealth, Prince of Wales Hospital, Shatin, N.T., Hong Kong.

*These authors contributed equally to this work.

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contaminated surfaces also perhaps being of importance inhospital and residency settings).

As it may be some time before it is possible to characterizethe nature of these SSEs in terms of transmission route, weadapt the usual epidemiological notation and define R0

XSS tobe the average number of infections caused by one typicallyinfectious individual, excluding SSEs, in an entirelysusceptible population. Similarly Rt

XSS is the average numberof infections, excluding SSEs, caused by individuals in latergenerations at time t. The long-term fate of the outbreak(containment, growth or endemic persistence) will thereforeultimately depend on both the extent of typical transmission(and how this is modified by controls) and the relativefrequency and magnitude of SSEs. These two factorscontribute additively to the overall reproduction number Rt:

Rt = RtXSS + pSSENSSE (1)

where pSSE is the probability that any infection leads to anSSE and NSSE is the average number infected during a SSE.As little is currently known about how to influence either pSSE

or NSSE, reducing RtXSS should be the key aim in any early

public health intervention strategy. We therefore focus onestimating Rt

XSS for the outbreak of SARS in Hong Kong andon evaluating the effectiveness of different interventions inreducing transmission.

We estimate RtXSS for the SARS epidemic in Hong Kong

by fitting a detailed mathematical transmission model tospatially-stratified incidence time-series derived from theclinical records of the 1512 cases reported by 6th May 2003(10). The possible effect of asymptomatic and thusunreported cases were not analyzed in the current study dueto lack of population serological survey data with which toestimate infection levels. Three epidemiological parametersdetermine the reproduction number:

RtXSS = βTS (2)

Here β is the transmission coefficient (incorporatinginfectiousness and contact rate), T is the infectiousness-weighted duration of infection, and S is a factor representingthe effect of geographic heterogeneity and susceptibledepletion on disease spread (11). All three factors are likelyto change as an epidemic progresses and control measures areintroduced. This expression illustrates how controls can limittransmission: by reducing local contact rates (affecting β), byshortening the delay between onset of symptoms andhospitalization (affecting T), by improving the effectivenessof isolation measures in hospitals (also affecting T), andimposing restrictions on longer range movements/contacts(affecting S).

However, use of a more sophisticated dynamical model isessential to capture the non-linearity and spatial locality oftransmission and to incorporate information on how keyparameters (such as the incubation period, the time fromexposure to when clinical symptoms of infection first appear,and T) vary between individuals into a coherent estimationframework. Capturing the duration and temporal evolution ofinfectiousness within the infected patient is critical. Data arelimited, but circumstantial evidence, based on contact tracing,tentatively suggests that infectiousness coincides with butdoes not precede clinical symptoms (3). Additionally, thelarge number of SARS cases reported to have resulted fromhospital exposure (approximately 200 cases in addition to thePWH cluster) suggests that infectiousness does not wane

substantially for some time after symptoms become apparent,a conclusion reinforced by the temporal evolution of patients’viral loads (12).

Choice of a suitable model framework is notstraightforward and a variety of approaches are possible,ranging from a simple deterministic compartmental approachto a spatially explicit, individual-based simulation. Given thedata available for Hong Kong, we base our analyses on astochastic, meta-population compartmental model. A meta-population approach is appropriate because the incidence ofSARS has varied substantially by geographical district (Fig.1, A and B). A stochastic model is required since chancefluctuations in case numbers can be large in the early stagesof an epidemic. Stochastic models predict both average trendsand variability, so that a more robust assessment can be madeof what changes are likely to be caused by chance and whatchanges genuinely reflect process and the impact ofinterventions.

We classify the population of each district into susceptible,latent, infectious, hospitalized, recovered and deadindividuals (Fig. 1C). Epidemiological coupling betweendistricts is assumed to depend on their adjacency (Fig. 1A)(11). Incubating and infectious categories are further dividedinto multiple stages, chosen in number and duration so as tomatch accurately the estimated delay distributionsdetermining disease progression and diagnosis (Fig. 1D) (10).Multiple realizations of the stochastic model both forparameter estimation and to generate predicted case incidencetime-series.

The mean time from the onset of symptoms until hospitaladmission and subsequent isolation of suspect SARS caseshas reduced significantly over the course of the epidemic todate (Fig. 1D) (10). Changes in the onset-to-hospitalizationdistribution were treated as an input to the model. Otherpotential factors, such as time variation in the rate or nature ofclose contact between individuals, could also affect Rt

XSS. Theimpact of these can be captured by allowing the underlyingcoefficient of transmission, β, to vary through time. Forsimplicity we assume β could have taken different valuesduring each of three equally spaced time periods over theepidemic observed to date.

We assume infectiousness begins just before the onset ofsymptoms and remains constant during the symptomaticphase. We assigned the relative infectiousness of hospitalizedpatients to match the overall rate of within hospitaltransmission for the epidemic to date. Given its importance indetermining the later pattern of the Hong Kong epidemic,simulations are seeded explicitly with the PWH cluster.Detailed contact tracing identified 125 first-generation casesin this cluster. However, it is also important to take accountof the fact that the index patient arrived in Hong Kong over aweek prior to admission to PWH, during which time heinfected multiple individuals. It is not possible to gain aprecise estimate of the number of SARS infections occurringprior to 3rd March (the index patient’s admission date toPWH), but examination of the case data stratified by onsetand admission date indicate this number to be definitely lessthan 110, and most probably in the 60-70 range. We thereforeinclude within the seeding infection event the first 70 casesadmitted to hospital that were not traced to the PWH cluster(11)—giving a total of 195 infections assumed to occur on 3rd

March.Model fit [see (11) for full list of estimated parameters] to

the case-incidence data was qualitatively good, both in termsof capturing the temporal development of overall incidence

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(Fig. 2A), and the pattern on spatial spread (Fig. 2B).Weestimate the initial value of the reproduction number, R0

XSS,in Hong Kong to have been 2.7 [95% CI: 2.2-3.7]. Therefore,even in the absence of SSEs, the virus was capable ofinducing an epidemic from the first introduced case.Strikingly, in order to reproduce the approximately 20% ofcases known from contact-tracing to have hospital-relatedexposure, hospital transmission comprises approximately50% of the value of R0

XSS, the discrepancy being a result ofthe time delay between infections generated prior to and postadmission and the extreme non-linearity of the epidemiccurve. We estimate patients in hospital transmit infection atapproximately 20% of the rate of symptomatic patients in thecommunity—reflecting the effectiveness of isolationprocedures and perhaps lowered infectiousness once recoverystarts. However, this lowered rate of transmission iscounterbalanced by the longer time spent in hospital relativeto the time spent symptomatic in the community prior tohospitalization.

If the seeding is assumed to include only the 125 contacttraced to the PWH index patient rather than the 195 totalearly infections assumed for the baseline scenario, theestimated value of R0

XSS increases to 3.4, but the quality ofmodel fit is decreased very significantly (p < 0.001). If 35(half of the 70 assumed in the baseline scenario) extra noncontact-traced cases are included in the seeding event, R0

XSS

is estimated to be 2.8 with a comparable quality of fit to thebaseline scenario. This variation in R0

XSS estimates associatedwith the seed size assumed reflects the fact that preciseattribution of early infections into SSE and non-SSEcategories is problematic; by assuming a larger initial seedsize we increase the size of the SSE caused by the PWHindex case, and hence decrease estimates of the level of non-SSE transmission required to reproduce the observedepidemic.

Despite this uncertainty, R0XSS values in the range 2.2-3.7

represent low to moderate transmissibility, with the earlyrapid growth in case numbers observed hence reflecting thechance occurrence of the PWH SSE (without which it isarguable that the Hong Kong outbreak would never havereached epidemic proportions). An important conclusionemerges from this estimate of R0

XSS: epidemic control will beeasier to achieve than for other viral infectious agents such asinfluenza (13) or measles (7) with higher R0 values.

We estimate the Amoy Gardens (AG) SSE to haveoccurred on the 19th March [95% CI: 18th March–20th March]and to have infected 331 [95% CI: 295-331] people. Althoughthe model was constrained to allow only a single SSE afterthe initial seeding of the PWH SSE, it is encouraging that thetiming of the event is consistent with independentinvestigations into that cluster of cases. It is thought that thesewage system became infected when the brother of aresident of AG used a toilet there on either the 14th or 19th ofMarch (14).

We determined that current data do not permit the level ofinfectiousness during the period just prior to symptom onsetto be estimated reliably. A better understanding of howinfectious varies during disease pathogenesis—such as thatwhich might be gained from detailed contact tracing studiesor quantitative assessment of viral shedding through time(12)—would clearly benefit disease control planning.However to date, indications are that most transmissionoccurs late in infection, something that clearly facilitatesinfection control.

Our analysis gives insight into the effect of differentcontrol measures on transmission, as quantified by Rt

XSS (Fig.2C). The mean time from symptom onset to hospitaladmission fell to 79% of its original value by 26th March (areduction of 1 day on average), and to 76% of its originalvalue by April 1st—giving rise to 9% and 11% drops intransmission respectively (10, 11). Changes in thetransmission coefficient were even more significant, with βestimated to have dropped to 37% of its original value by 12th

March, and to 6% of its original value by 1st April.Reductions in β are most easily attributed to increasedawareness of the infection leading to voluntary drops incontact rates, and to improved control measures in hospitals;however control measures such as school closures andrecommendations against unnecessary travel could also haveplayed an effect. Overall, the combination of reductions inonset-to-hospitalization times, in population contact rates andin hospital transmission are estimated to have caused thereproduction number, Rt

XSS, to drop to 1.0 [95% CI: 0.7-1.2]by 21st March, 0.9 [95% CI: 0.6-1.1] by 26th March, and thento 0.14 [95% CI: 0.09-0.35] by 10th April (Fig. 2C).

The Hong Kong epidemic has been characterized bysubstantial levels of transmission occurring in hospitals (Fig.3A). Contact tracing indicates that over 22% cases wereassociated with hospital-related exposure. In part this reflectsthe SSE which occurred in the Prince of Wales hospital.Nonetheless, if we exclude the Amoy Gardens outbreak, then19% of all cases subsequent to the PWH cluster are stilllinked to hospital exposure. Figure 3B shows how well themodel reproduces the separate case time-series for the PWHand Amoy clusters and cases arising from hospital and non-hospital-based exposure, while Fig. 3C illustrates the good fitbetween observed and estimated hospital occupancy levels.Figure 3C also demonstrates that due to the long period spentby SARS patients in hospital, the total prevalence ofhospitalized SARS patients inevitably becomes much higherthan the community prevalence after new admission ratesstart to decline, reinforcing the need for effective hospitalinfection control measures even in the latter stages of theepidemic.

These results indicate RtXSS is now below the self-

sustaining threshold of 1 in Hong Kong and thus thatepidemic is currently under control—in the sense thatinfection rates are declining. They also suggest thatreductions in population contact rates (both in the communityand in hospitals) played the predominant role in achievingcontrol. However, more rapid hospitalization also provided animportant additional effect. It should also be noted that theseestimates assume constant infectiousness from the onset ofsymptoms up to the time of hospitalization; if (as is perhapslikely), infectiousness increases following symptom onset, theeffect of the observed 1 day reduction in onset-to-hospitalization times could have been substantially greater,reducing Rt

XSS by up to 34% (11). However, even in this case,we estimate contact rate reductions and hospital infectioncontrol to have been key in achieving control of transmission.

The structure of the model also allows us to investigate theeffect of contact patterns between districts on diseasetransmission [as quantified by S in the expression for Rt givenabove (11)]. The contact rate of an individual with thepopulation from a contiguous district relative to that from thesame district was estimated as 0.57 [95% CI: 0.42-1.0].However, the contact rate between non-contiguous districtswas much lower, at 0.02 [95% CI: 0-0.10] relative to thewithin-district contact rate. Hence, transmission appears to be

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highly geographically localized, offering further options forcontrol. Given that the most populous districts are highlyconnected, these estimates of between district mixing suggestthat restricting movement could have a substantial impact onnet transmission. A complete ban on travel between districtsis estimated to have the potential to reduce Rt

XSS by 76%.Beyond Hong Kong, this suggests that movement restrictionsmight represent a useful control measure in circumstanceswhere it was not possible to reduce the average onset-to-hospitalization time substantially—for example in resource-poor countries or if a number of SSEs occurred in closesuccession and hospital capacity was temporarily exceeded.

A key advantage of transmission modeling is thatalternative control scenarios can be examined, giving insightinto the potential effectiveness of different interventionstrategies. Figure 4 shows five such scenarios, simulated withparameters estimated for the earliest stages of the Hong Kongepidemic. The scenario of no control measures beingemployed is shown to give rise to a catastrophic epidemic,even in the absence of SSEs. Figure 4 also illustrates thatwhile reductions in onset-to-hospitalization times comparableto those achieved in Hong Kong can achieve some reductionin transmission, on their own they are insufficient to controlSARS—other measures are also needed (such as improvedinfection control in hospitals, voluntary reductions inpopulation contact rates, or movement restrictions).

Given the R0XSS estimate of 2.7, our analyses suggest that

the etiological agent of SARS is moderately rather thanhighly transmissible, except in the very specific settings thathave induced the two major clusters to date. The epidemic inHong Kong appears to have moved through three phases;namely early exponential growth, a plateau period with dailycase numbers fluctuating around 50, and more recently (fromMay onwards) a phase of declining incidence with daily casenumbers below 20. The low value of Rt

XSS in the latter phasein part reflects the considerable changes in human behaviorwithin Hong Kong that have taken place during the epidemic.Individuals have been mixing, travelling and socializing lessin public areas, such as restaurants or venues of sport.Isolation measures in affected hospitals have been improved.As the epidemic wanes and the public perception of riskchanges, there is a danger that increased mixing could act totrigger a resurgence in case numbers, with Rt

XSS againexceeding 1. Furthermore, due to the slow rate of clinicalprogression to recovery or death of order one month, mostinfected people in a decaying epidemic will be found inhospitals, so that hospital control measures should beenforced rigorously. Continued vigilance is necessary duringthe decay phase of the epidemic, with reinforcement of publichealth messages, to ensure eradication of this infection fromHong Kong.

Ensuring as rapid a decline of the epidemic as possible isalso important to minimize the probability that another SSEmight occur—given the frequency of SSEs is likely to berelated to infection prevalence. Epidemic decay is onlyguaranteed where Rt is maintained below 1, which ultimatelydepends not just on controlling regular transmission events(i.e. maintaining Rt

XSS < 1), but also in understanding andcontrolling SSEs. Given our current estimates of Rt

XSS = 0.14and an SSE event size of NSSE ≈ 250, epidemic growth drivenby SSEs would only occur if more than 1 in 300 infectionswere to generate new SSEs (i.e. pSSENSSE > 0.86 from Eq. 1).Given current controls in Hong Kong, and current tally of 2documented SSEs from over 1500 infections, this outcomeappears unlikely. However, without a much better

understanding of the causes of the extreme between-caseheterogeneity in secondary infection rates for SARS, it isimpossible to exclude the possibility that a much higherfrequency of SSE-based transmission might be seen in othercountries and/or contexts. In the context of Hong Kong, ouranalysis shows that further reducing the mean time fromonset of symptoms to hospital admission by a day or sowould speed eradication if contact rates remain low, andensure continued control of the epidemic even in the face ofmoderate increases in population contact rates. Thereforeevery effort to promote more rapid admission and subsequentisolation of suspect SARS cases should continue to be made.The availability of specific and sensitive virologicaldiagnostic tests will help in this task.

The reported cases to date in Hong Kong and elsewheremay simply reflect people with the most severe clinicalsymptoms of infection with the new SARS virus. Ourestimates of case reproductive numbers are based on reportedSARS cases only. If additional asymptomatic infections in thecommunity were not diagnosed, reproduction numberestimates based on all infections may differ, depending on thefrequency of asymptomatic cases, whether this frequencyvaried during the epidemic, and the extent to which suchcases can transmit infection. Community-based serologicalsurveys will therefore be valuable to assess past infectionlevels and should be a priority once a specific and sensitiveserological test is available.

Worldwide, the virus appears to have been contained inmost developed countries. Dangers still persist, however, inpopulous regions of the world with a limited public healthinfrastructure and poor disease reporting systems. Thesituation in mainland China remains severe, with high casesnumbers reported daily. The Chinese government recentlyintroduced more draconian measures, designed to restrictmixing and travel (15). The current analysis provides someoptimism that such methods might be successful at limitingfurther spread, though it remains too early to judge whetherthey will be sufficient to bring the epidemic under control.One of the key lessons from recent events in Hong Kong hasbeen the importance of good quality data capture systems topermit detailed epidemiological analyses day by day, toinform both health policy formulation and the evaluation ofintervention impact.

References and Notes1. J. S. Peiris et al., Lancet 361, 1319 (2003).2. N. Lee et al., N. Engl. J. Med. 348, 1986 (2003).3. S. M. Poutanen et al., N. Engl. J. Med. 348, 1995 (2003).4. T. G. Ksiazek et al., N. Engl. J. Med. 348, 1953 (2003).5. Michael Smith Genome Sciences Centre

(www.bcgsc.ca/bioinfo/SARS) (2003).6. M. A. Marra et al., Science, in press; published online 1

May 2003 (10.1126/science.1085953).7. R. M. Anderson, R. M. May, Infectious Diseases of

Humans: Dynamics and Control (Oxford Univ. Press,Oxford, 1991).

8. O. Diekmann, J. A. P. Heesterbeck, MathematicalEpidemiology of Infectious Diseases: Model Building,Analysis and Interpretation (Wiley, New York, 2002).

9. Hong Kong Police Department, Selection of Daily Reportsof SARS Cases (unpublished).

10. C. A. Donnelly et al., Lancet, published online 7 May2003(http://image.thelancet.com/extras/03art4453web.pdf).

11. See supporting data on Science Online.

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12. J. S. M. Peiris et al., Lancet, published online 9 May 2003(http://image.thelancet.com/extras/03art4432web.pdf).

13. N. M. Ferguson, S. Mallett, H. Jackson, N. Roberts, P.Ward, J. Antimicrob. Chemother. 51, 977 (2003).

14. Outbreak of Severe Acute Respiratory Syndrome (SARS)at Amoy Gardens, Kowloon Bay, Hong Kong, MainFindings of the Investigation (Hong Kong Department ofHealth, 2003).

15. World Health Organization, Communicable DiseaseSurveillance & Response(www.who.int/csr/sars/guidelines/en) (2003).

16. We thank the Hong Kong Government Health, Welfareand Food Bureau, Department of Health and HospitalAuthority for primary data collection, collation andfacilitation of such. Steven Riley and Neil Ferguson thankthe Howard Hughes Medical Institute, Azra Ghani andNeil Ferguson thank the Royal Society, Christophe Fraser,Laith Abu-Raddad and Neil Ferguson thank the MedicalResearch Council, and Roy Anderson thanks theWellcome Trust for research grant support. Above all, wepay tribute to all frontline health care workers who havebeen working around the clock at great personal risk tocare for SARS patients and keep health records ofimportance to epidemiological analysis.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/1086478/DC1SOM TextReferences

6 May 2003; accepted 22 May 2003Published online 23 May 2003; 10.1126/science.1086478Include this information when citing this paper.

Fig. 1. Input data and model structure. (A) Map of HongKong showing the location of each district used in the model.Over 70% of cases reported up to April 16th are from the threecolored districts: Kwung Tong (red), Tai Po (green) and ShaTin (blue). (B) Weekly incidences (by time of hospitaladmission) with the color coding used in (A). (C) Schematicflow diagram of transmission model used. Each district in themeta-population model uses the structure shown. Susceptibleindividuals, S, become infected and enter a latent class, L.They then progress to a short asymptomatic and potentiallyinfectious stage (see text), I, before the onset of symptomsand progression to class Y. It is assumed every infectedindividual eventually attends hospital and either recovers, HR,or dies, HD. (D) Distributions [of Gamma form, see (10)] forthe waiting times of the compartments of the stochastic modelshown in (C). Colors match those used in (C): incubationperiod (red), time from symptoms to hospitalizations (blue),time from hospitalization to death (magenta), time fromhospitalization to recovery (green). Distributions shown areestimates for the start of the epidemic. The onset-to-hospitalization distribution changes during the epidemic as aresult of more rapid hospital admission.

Fig. 2. (A) Estimated reproduction number in the absence ofsuper-spreading events, Rt

XSS, for the period of the epidemicfor which data are available. Confidence intervals are alsoshown. The self-sustaining threshold Rt

XSS = 1 is shown as alight grey line. (B) Model estimates of weekly case incidence(average of 1000 model realizations) for the three districtswith most cases, by date of hospital attendance (to becompared with Fig. 1B). (C) Model estimates of case

incidence (average of 1000 model realizations at the best-fitparameter set with 95% prediction intervals are shown).Prediction intervals are generated from extreme realizationsat the boundaries of the multivariate confidence intervals. Theupper and lower bounds of the data are also shown.

Fig. 3. (A) Weekly admissions stratified by SSE cluster ortype of exposure, as determined by contact tracing. 125 cases(green line) were attributed to direct exposure to the HongKong index patient on or shortly after his admission to thePrince of Wales Hospital on 3rd March [first generation casesonly shown (11)]. 331 cases (blue line) were attributed to theAmoy Gardens outbreak. Of the remaining 1056 cases, 201were attributed to exposure occurring in a hospital or clinic(purple line) and 855 were attributed to other exposures orhad no contact tracing available (ochre line). (B) Best fitmodel predictions stratified by exposure, matching definitionsin (A). The predicted Amoy Gardens case time-series hasbeen further stratified into first generation cases only (dashedline) and first generation plus all additional cases (solid line).The correspondence between (B) and (A) is reasonable,though the discrepancy between the data and modelpredictions for Amoy Gardens suggests only first generationcases were successfully linked to the Amoy cluster bycontact-tracing. The narrow width of the observed Amoycluster peak shown in A suggests cases in that cluster had anarrower onset-to-hospitalization distribution than othercases. Comparing model predictions and data for hospital-exposure related cases also indicates that hospitaltransmission has reduced faster in recent weeks than capturedby the model. (C) Best fit model predictions for the totalprevalence of symptomatic SARS patients, stratified bywhether they are not yet admitted to hospital or hospitalized.

Fig. 4. The effect of alternative control scenarios onprogression of a hypothetical epidemic with Hong Kong-likecharacteristics. No SSEs other than an initial seeding event of50 infections on day 0 are modeled. Five scenarios areshown: (A) No control measures or change in populationbehavior—giving rise to a catastrophic epidemic. (B) nochange in behavior, but a reduction in mean onset-to-hospitalization time of 2 days achieved on day 30—the effectof which is to temporarily increase admission numbers but toreduce transmission by 19%. (C) As B but with completecessation of movement between districts imposed on day 45(the effect of which is to reduce transmission by 76%). Thesecontrol measures are seen to be sufficient to control theepidemic even in the absence of population behavior change.(D) As B but with a 50% drop in population contact rates andhospital infections from day 45—just sufficient to preventepidemic growth. (E) As D but with a 70% reduction inhospital transmission from day 55—sufficient to rapidlycontrol the epidemic. For all scenarios, Hong Kongdemographic parameters were used and the average of 1000model realizations is shown.

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InterventionsTransmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health

Koon-Hung Lee, Edith M. C. Lau, Neil M. Ferguson and Roy M. AndersonLai-Ming Ho, Tai-Hing Lam, Thuan Q. Thach, Patsy Chau, King-Pan Chan, Su-Vui Lo, Pak-Yin Leung, Thomas Tsang, William Ho, Steven Riley, Christophe Fraser, Christl A. Donnelly, Azra C. Ghani, Laith J. Abu-Raddad, Anthony J. Hedley, Gabriel M. Leung,

published online May 23, 2003

ARTICLE TOOLS http://science.sciencemag.org/content/early/2003/05/23/science.1086478.citation

MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2003/06/19/1086478.DC1

CONTENTRELATED

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PERMISSIONS http://www.sciencemag.org/help/reprints-and-permissions

Terms of ServiceUse of this article is subject to the

is a registered trademark of AAAS.ScienceScience, 1200 New York Avenue NW, Washington, DC 20005. The title (print ISSN 0036-8075; online ISSN 1095-9203) is published by the American Association for the Advancement ofScience

No claim to original U.S. Government Works.Copyright © 2003 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science.

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