Chau, PH

Yip, PSF

Hong Kong Medical Journal

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Title Modelling the severe acute respiratory syndrome epidemic [3]Author(s) Chau, PH; Yip, PSFCitation Hong Kong Medical Journal, 2003, v. 9 n. 4, p. 310-311Issued Date 2003URL http://hdl.handle.net/10722/45364Rights Creative Commons: Attribution 3.0 Hong Kong License310      Hong Kong Med J Vol 9 No 4 August 2003To the Editor—The most direct way to assess the trend inthe severe acute respiratory syndrome (SARS) epidemic isto study the number of reported cases. There are twoquantities related to reported cases: the cumulativenumber and the daily number of cases. Based on theseModelling the severe acute respiratory syndrome epidemicobservations, epidemiologists try to fit models to describethe epidemic.Firstly, fitting a statistical model by extrapolation notonly ignores the possibility of the effect of interventions,Treating emerging viral infectionsTo the Editor—I read with interest the recently publishedarticle on the use of plasma from a convalescent patient totreat severe acute respiratory syndrome.1 The therapeuticuse of serum products in managing infectious diseasereminds us of the pioneering work of Robert Koch’s students,who developed a sheep antiserum against diphtheria toxinin 1891; a girl dying of diphtheria received the antiserum,recovered within hours and survived.2 Since then, the strategyof administering plasma from survivors of various epidemicsof viral illness has been used with success. Examples includetreatment of Bolivian haemorrhagic fever (during anepidemic in the 1960s caused by Machupo virus),3 Argen-tinian haemorrhagic fever (caused by Junin virus, a closerelative of Machupo virus),4 and Lassa fever in Nigeria.5Reduction in mortality by giving this type of therapy hasbeen attributed to the immunoglobulin fraction of theplasma—the source of neutralising antibody. A perhapsmore familiar example is the experimental use of immuno-globin from survivors of West Nile encephalitis,6 which isbeing considered for further clinical trials to manage infectionwith West Nile virus.Clearly, plasma from convalescent patients who had aviral infection has a unique role in therapeutic medicine,especially in the face of emerging (and often devastating)viral infection outbreaks. Above all, these accounts make astrong case for public health authorities to store batches ofhyperimmune plasma in case outbreaks of these diseasesstrike in the future.KM Chow, MB, ChB, MRCP(e-mail: chow_kai_ming@alumni.cuhk.net)Artificial Cells and Organs Research CentreFaculty of MedicineMcGill UniversityMontreal, QuebecCanadaReferences1. Wong VW, Dai D, Wu AK, Sung JJ. Treatment of severe acuterespiratory syndrome with convalescent plasma. Hong Kong Med J2003;9:199-201.2. Rousell RH, Pennington JE. An historical overview of immunoglobulintherapy. In: Yap PL, editor. Clinical applications of intravenous im-munoglobulin therapy. Edinburgh: Churchill Livingstone; 1992:1-15.3. Stinebaugh BJ, Schloeder FX, Johnson KM, Mackenzie RB, EntwisleG, De Alba E. Bolivian hemorrhagic fever. A report of four cases. AmJ Med 1966;40:217-30.4. Ruggiero HA, Perez Isquierdo F, Milani HA, et al. Treatment ofArgentine hemorrhagic fever with convalescent’s plasma. 4433 cases[in French]. Presse Med 1986;15:2239-42.5. Frame JD, Verbrugge GP, Gill RG, Pinneo L. The use of Lassa feverconvalescent plasma in Nigeria. Trans R Soc Trop Med Hyg 1984;78:319-24.6. Solomon T, Ooi MH, Beasley DW, Mallewa M. West Nile encephalitis.BMJ 2003;326:865-9.To the Editor—We thank Drs Chow, Burnouf and Rado-sevich for their valuable comments. Dr Chow providedimportant examples of when convalescent plasma has beenused to treat other severe viral illnesses. Drs Burnouf andRadosevich suggested ways of improving convalescentplasma therapy. Our institution has analysed more than 20patients who received convalescent plasma for severe acuterespiratory syndrome. Among patients who had pulsedmethylprednisolone for more than 1.5 g, those receivingconcomitant plasma had better survival and earlier dischargefrom hospital (unpublished data).Authors’ replyVWS Wong, MB, ChB, MRCP(e-mail: wonws1@yahoo.com.hk)D Dai, MB, BS, FRCPAKL Wu, MB, ChB, MRCPJJY Sung, MD, PhDDepartment of Medicine and TherapeuticsThe Chinese University of Hong KongPrince of Wales HospitalShatinNew TerritoriesHong KongHong Kong Med J Vol 9 No 4 August 2003      311but also ignores unique features of the transmission of theepidemic. That is, useful information concerning theincubation period, the time between infection and onset ofdisease when there is contact between susceptible andinfectious individuals, is not fully utilised.Secondly, some extraordinary events, such as the majoroutbreak in the housing estate (Amoy Gardens) in HongKong, will greatly distort the shape of the original curve.This will result in a poor fit of the statistical model.Furthermore, initially epidemics tend to experience a periodof exponential growth that then levels off when more thanhalf of the population is infected. Modelling the epidemicby extrapolation cannot capture this characteristic. The useof an exponential model or a linear model has also beencriticised for these reasons by Razum et al.1Alternatively, there are epidemic models that are spec-ially designed for modelling infectious disease.2-4 However,the application of such models requires detailed informationincluding, for example, the time of infection and the numberof infectious individuals over the course of epidemic. Thisinformation is usually incomplete and/or unavailable.As suggested by Razum et al,1 studying the daily numberof reported SARS cases is easy for the public to understand,and can indirectly show the change in the reproductivenumber (R0), defined as the average number of secondarycases generated by one primary case in a susceptiblepopulation.2,3 However, due to the incubation period, thereis a time lag between the day of infection and the day ofreporting. As a result, the epidemic curve of the daily numberof SARS cases may not adequately monitor the change inR0. Further, as there is variation in the length of the incuba-tion period, people reported on the same day may have beeninfected on different days.We propose the back-projection approach to be used toreconstruct the infection curve, based on the daily reportednumber of cases and an estimated incubation period.5-7 TheSARS infection curve for Hong Kong up to 6 June 2003 wasreconstructed using the back-projection method. Theestimated curve and the fitted daily reported number of casesare shown in Fig a and b. The estimated infection curve iseasy to interpret and the effect of major events on the spreadof the epidemic can be readily identified.Modelling the SARS epidemic using a simple extra-polation model is definitely inaccurate, while a complicatedstochastic epidemic model may not be feasible. The back-projection method is thus preferred. Further, theassumptions made for each model need to be explicitlystated when the model is used in order to avoid any mis-leading conclusions.PH Chau, BSS (Stat)PSF Yip, PhD(e-mail: sfpyip@hku.hk)Department of Statistics and Actuarial ScienceThe University of Hong KongPokfulamHong KongReferences1. Razum O, Becher H, Kapaun A, Junghanss T. SARS, lay epidemiology,and fear. Lancet 2003;361:1739-40.2. Anderson RM, May RM. Infectious diseases of humans: dynamicsand control. London: Oxford University Press; 1991.3. Yip PS, Chen QZ. Statistical inference for a multi-type epidemic model.J Stat Inference Planning 1998;71:229-44.4. Riley S, Fraser C, Donnelly CA, et al. Transmission dynamics of theetiological agent of SARS in Hong Kong: impact of public healthinterventions. Science 2003 (in press).5. Brookmeyer R, Gail MH. Minimum size of the acquired immuno-deficiency syndrome (AIDS) epidemic in the United States. Lancet1986;2:1320-2.6. Chau PH, Yip PS, Cui JS. Reconstructing the incidence of humanimmunodeficiency virus (HIV) in Hong Kong using data from HIVpositive tests and diagnoses of acquired immune deficiency syndrome.J R Stat Soc Ser C Appl Stat 2003;52:237-48.7. Chau PH, Yip PSF. Reconstructing the severe acute respiratorysyndrome incidence using back-projection in Hong Kong SpecialAdministrative Region. Hong Kong: Department of Statistics andActuarial Science, University of Hong Kong; 2003;353:1-13.Fig. (b) Observed and fitted daily number of severe acuterespiratory syndrome reported cases in Hong KongObservedFittedNumber of reported casesDate of report80604020090705030101- 8- 15- 22- 29- 5- 12- 19- 26- 3- 10- 17- 24- 31-Mar Mar Mar Mar Mar Apr Apr Apr Apr May May May May May100Number of infectionFig. (a) Estimated daily number of infection of severe acuterespiratory syndrome in Hong KongDate of infection80604020090705030101- 8- 15- 22- 29- 5- 12- 19- 26- 3- 10- 17- 24- 31-Mar Mar Mar Mar Mar Apr Apr Apr Apr May May May May May100

Modelling the severe acute respiratory syndrome epidemic [3]

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Modelling the severe acute respiratory syndrome epidemic [3]

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