Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue
A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by R, is less than 1, the disease does not invade th...
Gespeichert in:
| Veröffentlicht in: | Bulletin of mathematical biology 2006-11, Vol.68 (8), p.2263-2282 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2282 |
|---|---|
| container_issue | 8 |
| container_start_page | 2263 |
| container_title | Bulletin of mathematical biology |
| container_volume | 68 |
| creator | Coutinho, F A B Burattini, M N Lopez, L F Massad, E |
| description | A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by R, is less than 1, the disease does not invade the populations and when R is greater than 1 it does. By not invading the population we mean that the number of infected individuals always decrease in subsequent seasons of transmission. Using the same threshold, all the qualitative features of the resulting epidemic can be understood. Our model suggests that trans-ovarial infection in the mosquitoes facilitates dengue overwintering. We also explain the delay between the peak in the mosquitoes population and the peak in dengue cases. |
| doi_str_mv | 10.1007/s11538-006-9108-6 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_68112698</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>68112698</sourcerecordid><originalsourceid>FETCH-LOGICAL-c400t-520de668fb7dd7f98f1d7dc288cd4e786ee0fd342ffc545aa341225f251b269f3</originalsourceid><addsrcrecordid>eNqFkbFuFDEURS1ERJbAB9AgiyKdybPH47FLFEFAikQTastrP2cnmrEHe6bYv8erXQmJhuo15169q0PIBw6fOcBwVznvO80AFDMcNFOvyI73QjCjQLwmOwAjmBYSrsnbWl-gZUxn3pBrrkwvgJsdiU-HgvWQp0B9TmFcx5wqjblQR1NOzG1rTnnOW6W4jAHn0dN6rCvONGD1ZdyP6ZmuB6RLXrbJnfI0HJNrYKU5Nio9b_iOXEU3VXx_uTfk17evT_ff2ePPhx_3Xx6ZlwAra08FVErH_RDCEI2OPAzBC619kDhohQgxdFLE6HvZO9dJLkQfRc_3QpnY3ZDbc-9S8u8N62rnsXqcJpewbbBKc95A_V9QQNcLpWUDP_0DvuStpDbCapCyM0bwBvEz5EuutWC0SxlnV46Wgz2psmdVtqmyJ1VWtczHS_G2nzH8TVzcdH8ALQ-QPA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>804439921</pqid></control><display><type>article</type><title>Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue</title><source>MEDLINE</source><source>SpringerNature Journals</source><creator>Coutinho, F A B ; Burattini, M N ; Lopez, L F ; Massad, E</creator><creatorcontrib>Coutinho, F A B ; Burattini, M N ; Lopez, L F ; Massad, E</creatorcontrib><description>A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by R, is less than 1, the disease does not invade the populations and when R is greater than 1 it does. By not invading the population we mean that the number of infected individuals always decrease in subsequent seasons of transmission. Using the same threshold, all the qualitative features of the resulting epidemic can be understood. Our model suggests that trans-ovarial infection in the mosquitoes facilitates dengue overwintering. We also explain the delay between the peak in the mosquitoes population and the peak in dengue cases.</description><identifier>ISSN: 0092-8240</identifier><identifier>EISSN: 1522-9602</identifier><identifier>DOI: 10.1007/s11538-006-9108-6</identifier><identifier>PMID: 16952019</identifier><language>eng</language><publisher>United States: Springer Nature B.V</publisher><subject>Aedes - growth & development ; Aedes - virology ; Animals ; Brazil - epidemiology ; Computer Simulation ; Dengue - epidemiology ; Dengue - transmission ; Dengue - virology ; Dengue Virus - growth & development ; Disease Outbreaks ; Female ; Humans ; Insect Vectors - growth & development ; Insect Vectors - virology ; Models, Biological ; Seasons</subject><ispartof>Bulletin of mathematical biology, 2006-11, Vol.68 (8), p.2263-2282</ispartof><rights>Springer Science+Business Media, Inc. 2006</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c400t-520de668fb7dd7f98f1d7dc288cd4e786ee0fd342ffc545aa341225f251b269f3</citedby><cites>FETCH-LOGICAL-c400t-520de668fb7dd7f98f1d7dc288cd4e786ee0fd342ffc545aa341225f251b269f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/16952019$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Coutinho, F A B</creatorcontrib><creatorcontrib>Burattini, M N</creatorcontrib><creatorcontrib>Lopez, L F</creatorcontrib><creatorcontrib>Massad, E</creatorcontrib><title>Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue</title><title>Bulletin of mathematical biology</title><addtitle>Bull Math Biol</addtitle><description>A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by R, is less than 1, the disease does not invade the populations and when R is greater than 1 it does. By not invading the population we mean that the number of infected individuals always decrease in subsequent seasons of transmission. Using the same threshold, all the qualitative features of the resulting epidemic can be understood. Our model suggests that trans-ovarial infection in the mosquitoes facilitates dengue overwintering. We also explain the delay between the peak in the mosquitoes population and the peak in dengue cases.</description><subject>Aedes - growth & development</subject><subject>Aedes - virology</subject><subject>Animals</subject><subject>Brazil - epidemiology</subject><subject>Computer Simulation</subject><subject>Dengue - epidemiology</subject><subject>Dengue - transmission</subject><subject>Dengue - virology</subject><subject>Dengue Virus - growth & development</subject><subject>Disease Outbreaks</subject><subject>Female</subject><subject>Humans</subject><subject>Insect Vectors - growth & development</subject><subject>Insect Vectors - virology</subject><subject>Models, Biological</subject><subject>Seasons</subject><issn>0092-8240</issn><issn>1522-9602</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqFkbFuFDEURS1ERJbAB9AgiyKdybPH47FLFEFAikQTastrP2cnmrEHe6bYv8erXQmJhuo15169q0PIBw6fOcBwVznvO80AFDMcNFOvyI73QjCjQLwmOwAjmBYSrsnbWl-gZUxn3pBrrkwvgJsdiU-HgvWQp0B9TmFcx5wqjblQR1NOzG1rTnnOW6W4jAHn0dN6rCvONGD1ZdyP6ZmuB6RLXrbJnfI0HJNrYKU5Nio9b_iOXEU3VXx_uTfk17evT_ff2ePPhx_3Xx6ZlwAra08FVErH_RDCEI2OPAzBC619kDhohQgxdFLE6HvZO9dJLkQfRc_3QpnY3ZDbc-9S8u8N62rnsXqcJpewbbBKc95A_V9QQNcLpWUDP_0DvuStpDbCapCyM0bwBvEz5EuutWC0SxlnV46Wgz2psmdVtqmyJ1VWtczHS_G2nzH8TVzcdH8ALQ-QPA</recordid><startdate>20061101</startdate><enddate>20061101</enddate><creator>Coutinho, F A B</creator><creator>Burattini, M N</creator><creator>Lopez, L F</creator><creator>Massad, E</creator><general>Springer Nature B.V</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SS</scope><scope>7TK</scope><scope>7X7</scope><scope>7XB</scope><scope>88A</scope><scope>88E</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FI</scope><scope>8FJ</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FYUFA</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>K9.</scope><scope>L6V</scope><scope>LK8</scope><scope>M0S</scope><scope>M1P</scope><scope>M7P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>7SN</scope><scope>7U9</scope><scope>C1K</scope><scope>H94</scope><scope>7X8</scope></search><sort><creationdate>20061101</creationdate><title>Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue</title><author>Coutinho, F A B ; Burattini, M N ; Lopez, L F ; Massad, E</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c400t-520de668fb7dd7f98f1d7dc288cd4e786ee0fd342ffc545aa341225f251b269f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Aedes - growth & development</topic><topic>Aedes - virology</topic><topic>Animals</topic><topic>Brazil - epidemiology</topic><topic>Computer Simulation</topic><topic>Dengue - epidemiology</topic><topic>Dengue - transmission</topic><topic>Dengue - virology</topic><topic>Dengue Virus - growth & development</topic><topic>Disease Outbreaks</topic><topic>Female</topic><topic>Humans</topic><topic>Insect Vectors - growth & development</topic><topic>Insect Vectors - virology</topic><topic>Models, Biological</topic><topic>Seasons</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Coutinho, F A B</creatorcontrib><creatorcontrib>Burattini, M N</creatorcontrib><creatorcontrib>Lopez, L F</creatorcontrib><creatorcontrib>Massad, E</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Entomology Abstracts (Full archive)</collection><collection>Neurosciences Abstracts</collection><collection>Health & Medical Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Medical Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>Proquest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Health Research Premium Collection</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>Health & Medical Collection (Alumni Edition)</collection><collection>Medical Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>Ecology Abstracts</collection><collection>Virology and AIDS Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>MEDLINE - Academic</collection><jtitle>Bulletin of mathematical biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Coutinho, F A B</au><au>Burattini, M N</au><au>Lopez, L F</au><au>Massad, E</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue</atitle><jtitle>Bulletin of mathematical biology</jtitle><addtitle>Bull Math Biol</addtitle><date>2006-11-01</date><risdate>2006</risdate><volume>68</volume><issue>8</issue><spage>2263</spage><epage>2282</epage><pages>2263-2282</pages><issn>0092-8240</issn><eissn>1522-9602</eissn><abstract>A non-autonomous dynamical system, in which the seasonal variation of a mosquito vector population is modeled, is proposed to investigate dengue overwintering. A time-dependent threshold, R(t), is deduced such that when its yearly average, denoted by R, is less than 1, the disease does not invade the populations and when R is greater than 1 it does. By not invading the population we mean that the number of infected individuals always decrease in subsequent seasons of transmission. Using the same threshold, all the qualitative features of the resulting epidemic can be understood. Our model suggests that trans-ovarial infection in the mosquitoes facilitates dengue overwintering. We also explain the delay between the peak in the mosquitoes population and the peak in dengue cases.</abstract><cop>United States</cop><pub>Springer Nature B.V</pub><pmid>16952019</pmid><doi>10.1007/s11538-006-9108-6</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0092-8240 |
| ispartof | Bulletin of mathematical biology, 2006-11, Vol.68 (8), p.2263-2282 |
| issn | 0092-8240 1522-9602 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_68112698 |
| source | MEDLINE; SpringerNature Journals |
| subjects | Aedes - growth & development Aedes - virology Animals Brazil - epidemiology Computer Simulation Dengue - epidemiology Dengue - transmission Dengue - virology Dengue Virus - growth & development Disease Outbreaks Female Humans Insect Vectors - growth & development Insect Vectors - virology Models, Biological Seasons |
| title | Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-22T05%3A20%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Threshold%20conditions%20for%20a%20non-autonomous%20epidemic%20system%20describing%20the%20population%20dynamics%20of%20dengue&rft.jtitle=Bulletin%20of%20mathematical%20biology&rft.au=Coutinho,%20F%20A%20B&rft.date=2006-11-01&rft.volume=68&rft.issue=8&rft.spage=2263&rft.epage=2282&rft.pages=2263-2282&rft.issn=0092-8240&rft.eissn=1522-9602&rft_id=info:doi/10.1007/s11538-006-9108-6&rft_dat=%3Cproquest_cross%3E68112698%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=804439921&rft_id=info:pmid/16952019&rfr_iscdi=true |