On the final size of epidemics with seasonality.
Identifieur interne : 001F26 ( Ncbi/Merge ); précédent : 001F25; suivant : 001F27On the final size of epidemics with seasonality.
Auteurs : Nicolas Bacaër [France] ; M Gabriela M. GomesSource :
- Bulletin of mathematical biology [ 1522-9602 ] ; 2009.
Descripteurs français
- KwdFr :
- MESH :
English descriptors
- KwdEn :
- MESH :
- epidemiology : Alphavirus Infections, Influenza, Human.
- statistics & numerical data : Disease Outbreaks.
- Chikungunya virus, Humans, Mathematical Concepts, Models, Biological, Models, Statistical, Seasons.
Abstract
We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number R(0) or of the initial fraction of infected people. Moreover, large epidemics can happen even if R(0) < 1. But like in a constant environment, the final epidemic size tends to 0 when R(0) < 1 and the initial fraction of infected people tends to 0. When R(0) > 1, the final epidemic size is bigger than the fraction 1 - 1/R(0) of the initially nonimmune population. In summary, the basic reproduction number R(0) keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.
DOI: 10.1007/s11538-009-9433-7
PubMed: 19475453
Links toward previous steps (curation, corpus...)
- to stream PubMed, to step Corpus: 001894
- to stream PubMed, to step Curation: 001894
- to stream PubMed, to step Checkpoint: 001825
Links to Exploration step
pubmed:19475453Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">On the final size of epidemics with seasonality.</title><author><name sortKey="Bacaer, Nicolas" sort="Bacaer, Nicolas" uniqKey="Bacaer N" first="Nicolas" last="Bacaër">Nicolas Bacaër</name><affiliation wicri:level="3"><nlm:affiliation>IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143, Bondy, France. bacaer@bondy.ird.fr</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143, Bondy</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Bondy</settlement></placeName></affiliation></author><author><name sortKey="Gomes, M Gabriela M" sort="Gomes, M Gabriela M" uniqKey="Gomes M" first="M Gabriela M" last="Gomes">M Gabriela M. Gomes</name></author></titleStmt><publicationStmt><idno type="wicri:source">PubMed</idno><date when="2009">2009</date><idno type="RBID">pubmed:19475453</idno><idno type="pmid">19475453</idno><idno type="doi">10.1007/s11538-009-9433-7</idno><idno type="wicri:Area/PubMed/Corpus">001894</idno><idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Corpus" wicri:corpus="PubMed">001894</idno><idno type="wicri:Area/PubMed/Curation">001894</idno><idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Curation">001894</idno><idno type="wicri:Area/PubMed/Checkpoint">001825</idno><idno type="wicri:explorRef" wicri:stream="Checkpoint" wicri:step="PubMed">001825</idno><idno type="wicri:Area/Ncbi/Merge">001F26</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">On the final size of epidemics with seasonality.</title><author><name sortKey="Bacaer, Nicolas" sort="Bacaer, Nicolas" uniqKey="Bacaer N" first="Nicolas" last="Bacaër">Nicolas Bacaër</name><affiliation wicri:level="3"><nlm:affiliation>IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143, Bondy, France. bacaer@bondy.ird.fr</nlm:affiliation><country xml:lang="fr">France</country><wicri:regionArea>IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143, Bondy</wicri:regionArea><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Bondy</settlement></placeName></affiliation></author><author><name sortKey="Gomes, M Gabriela M" sort="Gomes, M Gabriela M" uniqKey="Gomes M" first="M Gabriela M" last="Gomes">M Gabriela M. Gomes</name></author></analytic><series><title level="j">Bulletin of mathematical biology</title><idno type="eISSN">1522-9602</idno><imprint><date when="2009" type="published">2009</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Alphavirus Infections (epidemiology)</term><term>Chikungunya virus</term><term>Disease Outbreaks (statistics & numerical data)</term><term>Humans</term><term>Influenza, Human (epidemiology)</term><term>Mathematical Concepts</term><term>Models, Biological</term><term>Models, Statistical</term><term>Seasons</term></keywords><keywords scheme="KwdFr" xml:lang="fr"><term>Concepts mathématiques</term><term>Flambées de maladies ()</term><term>Grippe humaine (épidémiologie)</term><term>Humains</term><term>Infections à alphavirus (épidémiologie)</term><term>Modèles biologiques</term><term>Modèles statistiques</term><term>Saisons</term><term>Virus du chikungunya</term></keywords><keywords scheme="MESH" qualifier="epidemiology" xml:lang="en"><term>Alphavirus Infections</term><term>Influenza, Human</term></keywords><keywords scheme="MESH" qualifier="statistics & numerical data" xml:lang="en"><term>Disease Outbreaks</term></keywords><keywords scheme="MESH" qualifier="épidémiologie" xml:lang="fr"><term>Grippe humaine</term><term>Infections à alphavirus</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Chikungunya virus</term><term>Humans</term><term>Mathematical Concepts</term><term>Models, Biological</term><term>Models, Statistical</term><term>Seasons</term></keywords><keywords scheme="MESH" xml:lang="fr"><term>Concepts mathématiques</term><term>Flambées de maladies</term><term>Humains</term><term>Modèles biologiques</term><term>Modèles statistiques</term><term>Saisons</term><term>Virus du chikungunya</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number R(0) or of the initial fraction of infected people. Moreover, large epidemics can happen even if R(0) < 1. But like in a constant environment, the final epidemic size tends to 0 when R(0) < 1 and the initial fraction of infected people tends to 0. When R(0) > 1, the final epidemic size is bigger than the fraction 1 - 1/R(0) of the initially nonimmune population. In summary, the basic reproduction number R(0) keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.</div></front></TEI><pubmed><MedlineCitation Status="MEDLINE" Owner="NLM"><PMID Version="1">19475453</PMID><DateCompleted><Year>2010</Year><Month>01</Month><Day>06</Day></DateCompleted><DateRevised><Year>2009</Year><Month>10</Month><Day>15</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Electronic">1522-9602</ISSN><JournalIssue CitedMedium="Internet"><Volume>71</Volume><Issue>8</Issue><PubDate><Year>2009</Year><Month>Nov</Month></PubDate></JournalIssue><Title>Bulletin of mathematical biology</Title><ISOAbbreviation>Bull. Math. Biol.</ISOAbbreviation></Journal><ArticleTitle>On the final size of epidemics with seasonality.</ArticleTitle><Pagination><MedlinePgn>1954-66</MedlinePgn></Pagination><ELocationID EIdType="doi" ValidYN="Y">10.1007/s11538-009-9433-7</ELocationID><Abstract><AbstractText>We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number R(0) or of the initial fraction of infected people. Moreover, large epidemics can happen even if R(0) < 1. But like in a constant environment, the final epidemic size tends to 0 when R(0) < 1 and the initial fraction of infected people tends to 0. When R(0) > 1, the final epidemic size is bigger than the fraction 1 - 1/R(0) of the initially nonimmune population. In summary, the basic reproduction number R(0) keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.</AbstractText></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Bacaër</LastName><ForeName>Nicolas</ForeName><Initials>N</Initials><AffiliationInfo><Affiliation>IRD (Institut de Recherche pour le Développement), 32 avenue Henri Varagnat, 93143, Bondy, France. bacaer@bondy.ird.fr</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Gomes</LastName><ForeName>M Gabriela M</ForeName><Initials>MG</Initials></Author></AuthorList><Language>eng</Language><PublicationTypeList><PublicationType UI="D016428">Journal Article</PublicationType><PublicationType UI="D013485">Research Support, Non-U.S. Gov't</PublicationType></PublicationTypeList><ArticleDate DateType="Electronic"><Year>2009</Year><Month>05</Month><Day>28</Day></ArticleDate></Article><MedlineJournalInfo><Country>United States</Country><MedlineTA>Bull Math Biol</MedlineTA><NlmUniqueID>0401404</NlmUniqueID><ISSNLinking>0092-8240</ISSNLinking></MedlineJournalInfo><CitationSubset>IM</CitationSubset><MeshHeadingList><MeshHeading><DescriptorName UI="D018354" MajorTopicYN="N">Alphavirus Infections</DescriptorName><QualifierName UI="Q000453" MajorTopicYN="N">epidemiology</QualifierName></MeshHeading><MeshHeading><DescriptorName UI="D002646" MajorTopicYN="N">Chikungunya virus</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D004196" MajorTopicYN="N">Disease Outbreaks</DescriptorName><QualifierName UI="Q000706" MajorTopicYN="Y">statistics & numerical data</QualifierName></MeshHeading><MeshHeading><DescriptorName UI="D006801" MajorTopicYN="N">Humans</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D007251" MajorTopicYN="N">Influenza, Human</DescriptorName><QualifierName UI="Q000453" MajorTopicYN="N">epidemiology</QualifierName></MeshHeading><MeshHeading><DescriptorName UI="D055641" MajorTopicYN="N">Mathematical Concepts</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D008954" MajorTopicYN="N">Models, Biological</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D015233" MajorTopicYN="N">Models, Statistical</DescriptorName></MeshHeading><MeshHeading><DescriptorName UI="D012621" MajorTopicYN="Y">Seasons</DescriptorName></MeshHeading></MeshHeadingList></MedlineCitation><PubmedData><History><PubMedPubDate PubStatus="received"><Year>2008</Year><Month>12</Month><Day>17</Day></PubMedPubDate><PubMedPubDate PubStatus="accepted"><Year>2009</Year><Month>04</Month><Day>20</Day></PubMedPubDate><PubMedPubDate PubStatus="entrez"><Year>2009</Year><Month>5</Month><Day>29</Day><Hour>9</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="pubmed"><Year>2009</Year><Month>5</Month><Day>29</Day><Hour>9</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="medline"><Year>2010</Year><Month>1</Month><Day>7</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate></History><PublicationStatus>ppublish</PublicationStatus><ArticleIdList><ArticleId IdType="pubmed">19475453</ArticleId><ArticleId IdType="doi">10.1007/s11538-009-9433-7</ArticleId></ArticleIdList></PubmedData></pubmed><affiliations><list><country><li>France</li></country><region><li>Île-de-France</li></region><settlement><li>Bondy</li></settlement></list><tree><noCountry><name sortKey="Gomes, M Gabriela M" sort="Gomes, M Gabriela M" uniqKey="Gomes M" first="M Gabriela M" last="Gomes">M Gabriela M. Gomes</name></noCountry><country name="France"><region name="Île-de-France"><name sortKey="Bacaer, Nicolas" sort="Bacaer, Nicolas" uniqKey="Bacaer N" first="Nicolas" last="Bacaër">Nicolas Bacaër</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Sante/explor/SrasV1/Data/Ncbi/Merge
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001F26 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Ncbi/Merge/biblio.hfd -nk 001F26 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Sante
|area= SrasV1
|flux= Ncbi
|étape= Merge
|type= RBID
|clé= pubmed:19475453
|texte= On the final size of epidemics with seasonality.
}}
Pour générer des pages wiki
HfdIndexSelect -h $EXPLOR_AREA/Data/Ncbi/Merge/RBID.i -Sk "pubmed:19475453" \
| HfdSelect -Kh $EXPLOR_AREA/Data/Ncbi/Merge/biblio.hfd \
| NlmPubMed2Wicri -a SrasV1
| This area was generated with Dilib version V0.6.33. |  |