Genealogy with seasonality, the basic reproduction number, and the influenza pandemic.
Identifieur interne : 001291 ( PubMed/Corpus ); précédent : 001290; suivant : 001292Genealogy with seasonality, the basic reproduction number, and the influenza pandemic.
Auteurs : Nicolas Bacaër ; El Hadi Ait DadsSource :
- Journal of mathematical biology [ 1432-1416 ] ; 2011.
English descriptors
- KwdEn :
- MESH :
- epidemiology : Influenza, Human.
- transmission : Influenza, Human.
- Algorithms, Basic Reproduction Number, Humans, Incidence, Influenza A Virus, H1N1 Subtype, Models, Biological, Pandemics, Seasons.
Abstract
The basic reproduction number R (0) has been used in population biology, especially in epidemiology, for several decades. But a suitable definition in the case of models with periodic coefficients was given only in recent years. The definition involves the spectral radius of an integral operator. As in the study of structured epidemic models in a constant environment, there is a need to emphasize the biological meaning of this spectral radius. In this paper we show that R (0) for periodic models is still an asymptotic per generation growth rate. We also emphasize the difference between this theoretical R (0) for periodic models and the "reproduction number" obtained by fitting an exponential to the beginning of an epidemic curve. This difference has been overlooked in recent studies of the H1N1 influenza pandemic.
DOI: 10.1007/s00285-010-0354-8
PubMed: 20607242
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pubmed:20607242Le document en format XML
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But a suitable definition in the case of models with periodic coefficients was given only in recent years. The definition involves the spectral radius of an integral operator. As in the study of structured epidemic models in a constant environment, there is a need to emphasize the biological meaning of this spectral radius. In this paper we show that R (0) for periodic models is still an asymptotic per generation growth rate. We also emphasize the difference between this theoretical R (0) for periodic models and the "reproduction number" obtained by fitting an exponential to the beginning of an epidemic curve. This difference has been overlooked in recent studies of the H1N1 influenza pandemic.</div></front></TEI><pubmed><MedlineCitation Status="MEDLINE" Owner="NLM"><PMID Version="1">20607242</PMID><DateCompleted><Year>2011</Year><Month>11</Month><Day>15</Day></DateCompleted><DateRevised><Year>2018</Year><Month>11</Month><Day>13</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Electronic">1432-1416</ISSN><JournalIssue CitedMedium="Internet"><Volume>62</Volume><Issue>5</Issue><PubDate><Year>2011</Year><Month>May</Month></PubDate></JournalIssue><Title>Journal of mathematical biology</Title><ISOAbbreviation>J Math Biol</ISOAbbreviation></Journal><ArticleTitle>Genealogy with seasonality, the basic reproduction number, and the influenza pandemic.</ArticleTitle><Pagination><MedlinePgn>741-62</MedlinePgn></Pagination><ELocationID EIdType="doi" ValidYN="Y">10.1007/s00285-010-0354-8</ELocationID><Abstract><AbstractText>The basic reproduction number R (0) has been used in population biology, especially in epidemiology, for several decades. But a suitable definition in the case of models with periodic coefficients was given only in recent years. The definition involves the spectral radius of an integral operator. As in the study of structured epidemic models in a constant environment, there is a need to emphasize the biological meaning of this spectral radius. In this paper we show that R (0) for periodic models is still an asymptotic per generation growth rate. We also emphasize the difference between this theoretical R (0) for periodic models and the "reproduction number" obtained by fitting an exponential to the beginning of an epidemic curve. This difference has been overlooked in recent studies of the H1N1 influenza pandemic.</AbstractText></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Bacaër</LastName><ForeName>Nicolas</ForeName><Initials>N</Initials><AffiliationInfo><Affiliation>Research group UMMISCO, IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143 Bondy, France. nicolas.bacaer@ird.fr</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Ait Dads</LastName><ForeName>El Hadi</ForeName><Initials>el H</Initials></Author></AuthorList><Language>eng</Language><PublicationTypeList><PublicationType UI="D016428">Journal Article</PublicationType></PublicationTypeList><ArticleDate DateType="Electronic"><Year>2010</Year><Month>07</Month><Day>06</Day></ArticleDate></Article><MedlineJournalInfo><Country>Germany</Country><MedlineTA>J Math 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