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Article: Comparative estimation of the reproduction number for pandemic influenza from daily case notification data

TitleComparative estimation of the reproduction number for pandemic influenza from daily case notification data
Authors
KeywordsInfluenza
Pandemic
Reproduction number
San Francisco
Spanish flu
Issue Date2007
PublisherThe Royal Society. The Journal's web site is located at http://publishing.royalsociety.org/index.cfm?page=1572
Citation
Journal Of The Royal Society Interface, 2007, v. 4 n. 12, p. 154-166 How to Cite?
AbstractThe reproduction number, R, defined as the average number of secondary cases generated by a primary case, is a crucial quantity for identifying the intensity of interventions required to control an epidemic. Current estimates of the reproduction number for seasonal influenza show wide variation and, in particular, uncertainty bounds for R for the pandemic strain from 1918 to 1919 have been obtained only in a few recent studies and are yet to be fully clarified. Here, we estimate R using daily case notifications during the autumn wave of the influenza pandemic (Spanish flu) in the city of San Francisco, California, from 1918 to 1919. In order to elucidate the effects from adopting different estimation approaches, four different methods are used: estimation of R using the early exponential-growth rate (Method 1), a simple susceptible-exposed-infectious-recovered (SEIR) model (Method 2), a more complex SEIR-type model that accounts for asymptomatic and hospitalized cases (Method 3), and a stochastic susceptible-infectious-removed (SIR) with Bayesian estimation (Method 4) that determines the effective reproduction number R t at a given time t. The first three methods fit the initial exponential-growth phase of the epidemic, which was explicitly determined by the goodness-of-fit test. Moreover, Method 3 was also fitted to the whole epidemic curve. Whereas the values of R obtained using the first three methods based on the initial growth phase were estimated to be 2.98 (95% confidence interval (CI): 2.73, 3.25), 2.38 (2.16, 2.60) and 2.20 (1.55, 2.84), the third method with the entire epidemic curve yielded a value of 3.53 (3.45, 3.62). This larger value could be an overestimate since the goodness-of-fit to the initial exponential phase worsened when we fitted the model to the entire epidemic curve, and because the model is established as an autonomous system without time-varying assumptions. These estimates were shown to be robust to parameter uncertainties, but the theoretical exponential-growth approximation (Method 1) shows wide uncertainty. Method 4 provided a maximum-likelihood effective reproduction number 2.10 (1.21, 2.95) using the first 17 epidemic days, which is consistent with estimates obtained from the other methods and an estimate of 2.36 (2.07, 2.65) for the entire autumn wave. We conclude that the reproduction number for pandemic influenza (Spanish flu) at the city level can be robustly assessed to lie in the range of 2.0-3.0, in broad agreement with previous estimates using distinct data. © 2006 The Royal Society.
Persistent Identifierhttp://hdl.handle.net/10722/134228
ISSN
2015 Impact Factor: 3.818
2015 SCImago Journal Rankings: 1.622
PubMed Central ID
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChowell, Gen_HK
dc.contributor.authorNishiura, Hen_HK
dc.contributor.authorBettencourt, LMAen_HK
dc.date.accessioned2011-06-13T07:20:56Z-
dc.date.available2011-06-13T07:20:56Z-
dc.date.issued2007en_HK
dc.identifier.citationJournal Of The Royal Society Interface, 2007, v. 4 n. 12, p. 154-166en_HK
dc.identifier.issn1742-5689en_HK
dc.identifier.urihttp://hdl.handle.net/10722/134228-
dc.description.abstractThe reproduction number, R, defined as the average number of secondary cases generated by a primary case, is a crucial quantity for identifying the intensity of interventions required to control an epidemic. Current estimates of the reproduction number for seasonal influenza show wide variation and, in particular, uncertainty bounds for R for the pandemic strain from 1918 to 1919 have been obtained only in a few recent studies and are yet to be fully clarified. Here, we estimate R using daily case notifications during the autumn wave of the influenza pandemic (Spanish flu) in the city of San Francisco, California, from 1918 to 1919. In order to elucidate the effects from adopting different estimation approaches, four different methods are used: estimation of R using the early exponential-growth rate (Method 1), a simple susceptible-exposed-infectious-recovered (SEIR) model (Method 2), a more complex SEIR-type model that accounts for asymptomatic and hospitalized cases (Method 3), and a stochastic susceptible-infectious-removed (SIR) with Bayesian estimation (Method 4) that determines the effective reproduction number R t at a given time t. The first three methods fit the initial exponential-growth phase of the epidemic, which was explicitly determined by the goodness-of-fit test. Moreover, Method 3 was also fitted to the whole epidemic curve. Whereas the values of R obtained using the first three methods based on the initial growth phase were estimated to be 2.98 (95% confidence interval (CI): 2.73, 3.25), 2.38 (2.16, 2.60) and 2.20 (1.55, 2.84), the third method with the entire epidemic curve yielded a value of 3.53 (3.45, 3.62). This larger value could be an overestimate since the goodness-of-fit to the initial exponential phase worsened when we fitted the model to the entire epidemic curve, and because the model is established as an autonomous system without time-varying assumptions. These estimates were shown to be robust to parameter uncertainties, but the theoretical exponential-growth approximation (Method 1) shows wide uncertainty. Method 4 provided a maximum-likelihood effective reproduction number 2.10 (1.21, 2.95) using the first 17 epidemic days, which is consistent with estimates obtained from the other methods and an estimate of 2.36 (2.07, 2.65) for the entire autumn wave. We conclude that the reproduction number for pandemic influenza (Spanish flu) at the city level can be robustly assessed to lie in the range of 2.0-3.0, in broad agreement with previous estimates using distinct data. © 2006 The Royal Society.en_HK
dc.languageengen_US
dc.publisherThe Royal Society. The Journal's web site is located at http://publishing.royalsociety.org/index.cfm?page=1572en_HK
dc.relation.ispartofJournal of the Royal Society Interfaceen_HK
dc.subjectInfluenzaen_HK
dc.subjectPandemicen_HK
dc.subjectReproduction numberen_HK
dc.subjectSan Franciscoen_HK
dc.subjectSpanish fluen_HK
dc.titleComparative estimation of the reproduction number for pandemic influenza from daily case notification dataen_HK
dc.typeArticleen_HK
dc.identifier.emailNishiura, H:nishiura@hku.hken_HK
dc.identifier.authorityNishiura, H=rp01488en_HK
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1098/rsif.2006.0161en_HK
dc.identifier.pmid17254982-
dc.identifier.pmcidPMC2358966-
dc.identifier.scopuseid_2-s2.0-33846862467en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33846862467&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume4en_HK
dc.identifier.issue12en_HK
dc.identifier.spage154en_HK
dc.identifier.epage166en_HK
dc.identifier.eissn1742-5662-
dc.identifier.isiWOS:000243382600018-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridChowell, G=9845935500en_HK
dc.identifier.scopusauthoridNishiura, H=7005501836en_HK
dc.identifier.scopusauthoridBettencourt, LMA=7003549424en_HK
dc.identifier.citeulike4007540-

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