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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Analysis on stability of an autonomous dynamics system for sars epidemic</title><author><name sortKey="Shuang De, Zhang" sort="Shuang De, Zhang" uniqKey="Shuang De Z" first="Zhang" last="Shuang-De">Zhang Shuang-De</name><affiliation><nlm:aff id="Aff1">Basic Department, Medical College of Chinese People's Armed Police, 300162 Tianjin, P. R. China</nlm:aff></affiliation></author><author><name sortKey="Hai, Hao" sort="Hai, Hao" uniqKey="Hai H" first="Hao" last="Hai">Hao Hai</name><affiliation><nlm:aff id="Aff1">Basic Department, Medical College of Chinese People's Armed Police, 300162 Tianjin, P. R. China</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmc">7111763</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7111763</idno><idno type="RBID">PMC:7111763</idno><idno type="doi">10.1007/BF02464241</idno><idno type="pmid">NONE</idno><date when="2005">2005</date><idno type="wicri:Area/Pmc/Corpus">000263</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000263</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Analysis on stability of an autonomous dynamics system for sars epidemic</title><author><name sortKey="Shuang De, Zhang" sort="Shuang De, Zhang" uniqKey="Shuang De Z" first="Zhang" last="Shuang-De">Zhang Shuang-De</name><affiliation><nlm:aff id="Aff1">Basic Department, Medical College of Chinese People's Armed Police, 300162 Tianjin, P. R. China</nlm:aff></affiliation></author><author><name sortKey="Hai, Hao" sort="Hai, Hao" uniqKey="Hai H" first="Hao" last="Hai">Hao Hai</name><affiliation><nlm:aff id="Aff1">Basic Department, Medical College of Chinese People's Armed Police, 300162 Tianjin, P. R. China</nlm:aff></affiliation></author></analytic><series><title level="j">Applied Mathematics and Mechanics</title><idno type="ISSN">0253-4827</idno><idno type="eISSN">1573-2754</idno><imprint><date when="2005">2005</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>An extended dynamic model for SARS epidemic was deduced on the basis of the K-M infection model with taking the density constraint of susceptible population and the cure and death rates of patients into consideration. It is shown that the infection-free equilibrium is the global asymptotic stability under given conditions, and endemic equilibrium is not the asymptotic stability. It comes to the conclusion that the epidemic system is the permanent persistence existence under appropriate conditions.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Duo, Wang" uniqKey="Duo W">Wang Duo</name></author><author><name sortKey="Xiaofei, Zhao" uniqKey="Xiaofei Z">Zhao Xiaofei</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lansun, Chen" uniqKey="Lansun C">Chen Lansun</name></author><author><name sortKey="Jian, Chen" uniqKey="Jian C">Chen Jian</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Thieme, H R" uniqKey="Thieme H">H R Thieme</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Appl Math Mech</journal-id><journal-id journal-id-type="iso-abbrev">Appl Math Mech</journal-id><journal-title-group><journal-title>Applied Mathematics and Mechanics</journal-title></journal-title-group><issn pub-type="ppub">0253-4827</issn><issn pub-type="epub">1573-2754</issn><publisher><publisher-name>Springer-Verlag</publisher-name><publisher-loc>Berlin/Heidelberg</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmc">7111763</article-id><article-id pub-id-type="publisher-id">BF02464241</article-id><article-id pub-id-type="doi">10.1007/BF02464241</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Analysis on stability of an autonomous dynamics system for sars epidemic</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name><surname>Shuang-de</surname><given-names>Zhang</given-names></name><address><email>zhangsd@sina.com</email></address><xref ref-type="aff" rid="Aff1"></xref></contrib><contrib contrib-type="author"><name><surname>Hai</surname><given-names>Hao</given-names></name><xref ref-type="aff" rid="Aff1"></xref></contrib><aff id="Aff1">Basic Department, Medical College of Chinese People's Armed Police, 300162 Tianjin, P. R. China</aff></contrib-group><author-notes><fn fn-type="com"><p>Communicated by LI Ji-bin</p></fn></author-notes><pub-date pub-type="ppub"><year>2005</year></pub-date><volume>26</volume><issue>7</issue><fpage>914</fpage><lpage>920</lpage><history><date date-type="received"><day>26</day><month>1</month><year>2004</year></date><date date-type="rev-recd"><day>11</day><month>3</month><year>2005</year></date></history><permissions><copyright-statement>© Editorial Committee of Applied Mathematics and Mechanics 2005</copyright-statement><license><license-p>This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.</license-p></license></permissions><abstract id="Abs1"><p>An extended dynamic model for SARS epidemic was deduced on the basis of the K-M infection model with taking the density constraint of susceptible population and the cure and death rates of patients into consideration. It is shown that the infection-free equilibrium is the global asymptotic stability under given conditions, and endemic equilibrium is not the asymptotic stability. It comes to the conclusion that the epidemic system is the permanent persistence existence under appropriate conditions.</p></abstract><kwd-group xml:lang="en"><title>Key words</title><kwd>infection model</kwd><kwd>SARS epidemic</kwd><kwd>equilibrium point</kwd><kwd>asymptotic stability</kwd></kwd-group><kwd-group xml:lang="en"><title>Chinese Library Classification</title><kwd>O175.13</kwd></kwd-group><kwd-group xml:lang="en"><title>2000 Mathematics Subject Classification</title><kwd>39A11</kwd></kwd-group><custom-meta-group><custom-meta><meta-name>issue-copyright-statement</meta-name><meta-value>© Editorial Committee of Applied Mathematics and Mechanics 2005</meta-value></custom-meta></custom-meta-group></article-meta></front><back><fn-group><fn><p>Project supported by the Science Foundation of Chinese People's Armed Police (No. WKH2004-7)</p></fn></fn-group><ref-list id="Bib1"><title>References</title><ref id="CR1"><label>[1]</label><mixed-citation publication-type="other">Riley S, Fraser C, Donnelly C A,<italic>et al.</italic> Transmission Dynamics of the Etiological Agent of SARS in Hong Kong: Impact of Public Health Interventions[J/OL]. Sciencexpress/www. sciencexpress. org/23 May 2003/ Page 1/10. 1126/ science. 1086478.</mixed-citation></ref><ref id="CR2"><label>[2]</label><mixed-citation publication-type="other">Lipsitch M, Cohen T, Cooper B,<italic>et al.</italic> Transmission Dynamics and Control of Severe Acute Respiratory Syndrome[J/OL]. Sciencexpress/www. sciencexpress. org/23 May 2003/ Page 1/10. 1126/ science. 1086616.</mixed-citation></ref><ref id="CR3"><label>[3]</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Duo</surname><given-names>Wang</given-names></name><name><surname>Xiaofei</surname><given-names>Zhao</given-names></name></person-group><article-title>Empirical analysis and forecasting for SARS epidemic situation [J]</article-title><source>Journal of Peking University (Health Science)</source><year>2003</year><volume>35</volume><issue>Supplement</issue><fpage>72</fpage><lpage>74</lpage></element-citation></ref><ref id="CR4"><label>[4]</label><element-citation publication-type="book"><person-group person-group-type="author"><name><surname>Lansun</surname><given-names>Chen</given-names></name><name><surname>Jian</surname><given-names>Chen</given-names></name></person-group><source><italic>Non-Linear Dynamic System of Biology</italic>[M]</source><year>1993</year><publisher-loc>Beijing</publisher-loc><publisher-name>Science Publishing Company</publisher-name><fpage>111</fpage><lpage>162</lpage></element-citation></ref><ref id="CR5"><label>[5]</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Thieme</surname><given-names>H R</given-names></name></person-group><article-title>Persistence under relaxed point-dissipativity (with application to an endemic model)[J]</article-title><source>SIAM J Math Anal</source><year>1993</year><volume>24</volume><issue>2</issue><fpage>407</fpage><lpage>435</lpage><pub-id pub-id-type="doi">10.1137/0524026</pub-id></element-citation></ref></ref-list></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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