Qualitative study of a quarantine/isolation model with multiple disease stages
Identifieur interne : 000E01 ( Pmc/Curation ); précédent : 000E00; suivant : 000E02Qualitative study of a quarantine/isolation model with multiple disease stages
Auteurs : Mohammad A. Safi ; Abba B. GumelSource :
- Applied Mathematics and Computation [ 0096-3003 ] ; 2011.
Abstract
Recent studies suggest that, for disease transmission models with latent and infectious periods, the use of gamma distribution assumption seems to provide a better fit for the associated epidemiological data in comparison to the use of exponential distribution assumption. The objective of this study is to carry out a rigorous mathematical analysis of a communicable disease transmission model with quarantine (of latent cases) and isolation (of symptomatic cases), in which the waiting periods in the infected classes are assumed to have gamma distributions. Rigorous analysis of the model reveals that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique endemic equilibrium when the threshold quantity exceeds unity. The endemic equilibrium is shown to be locally and globally-asymptotically stable for special cases. Numerical simulations, using data related to the 2003 SARS outbreaks, show that the cumulative number of disease-related mortality increases with increasing number of disease stages. Furthermore, the cumulative number of new cases is higher if the asymptomatic period is distributed such that most of the period is spent in the early stages of the asymptomatic compartments in comparison to the cases where the average time period is equally distributed among the associated stages or if most of the time period is spent in the later (final) stages of the asymptomatic compartments. Finally, it is shown that distributing the average sojourn time in the infectious (asymptomatic) classes equally or unequally does not effect the cumulative number of new cases.
Url:
DOI: 10.1016/j.amc.2011.07.007
PubMed: NONE
PubMed Central: 7112307
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Qualitative study of a quarantine/isolation model with multiple disease stages</title><author><name sortKey="Safi, Mohammad A" sort="Safi, Mohammad A" uniqKey="Safi M" first="Mohammad A." last="Safi">Mohammad A. Safi</name></author><author><name sortKey="Gumel, Abba B" sort="Gumel, Abba B" uniqKey="Gumel A" first="Abba B." last="Gumel">Abba B. Gumel</name></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmc">7112307</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7112307</idno><idno type="RBID">PMC:7112307</idno><idno type="doi">10.1016/j.amc.2011.07.007</idno><idno type="pmid">NONE</idno><date when="2011">2011</date><idno type="wicri:Area/Pmc/Corpus">000E01</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000E01</idno><idno type="wicri:Area/Pmc/Curation">000E01</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">000E01</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Qualitative study of a quarantine/isolation model with multiple disease stages</title><author><name sortKey="Safi, Mohammad A" sort="Safi, Mohammad A" uniqKey="Safi M" first="Mohammad A." last="Safi">Mohammad A. Safi</name></author><author><name sortKey="Gumel, Abba B" sort="Gumel, Abba B" uniqKey="Gumel A" first="Abba B." last="Gumel">Abba B. Gumel</name></author></analytic><series><title level="j">Applied Mathematics and Computation</title><idno type="ISSN">0096-3003</idno><idno type="eISSN">0096-3003</idno><imprint><date when="2011">2011</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Recent studies suggest that, for disease transmission models with latent and infectious periods, the use of gamma distribution assumption seems to provide a better fit for the associated epidemiological data in comparison to the use of exponential distribution assumption. The objective of this study is to carry out a rigorous mathematical analysis of a communicable disease transmission model with quarantine (of latent cases) and isolation (of symptomatic cases), in which the waiting periods in the infected classes are assumed to have gamma distributions. Rigorous analysis of the model reveals that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique endemic equilibrium when the threshold quantity exceeds unity. The endemic equilibrium is shown to be locally and globally-asymptotically stable for special cases. Numerical simulations, using data related to the 2003 SARS outbreaks, show that the cumulative number of disease-related mortality increases with increasing number of disease stages. Furthermore, the cumulative number of new cases is higher if the asymptomatic period is distributed such that most of the period is spent in the early stages of the asymptomatic compartments in comparison to the cases where the average time period is equally distributed among the associated stages or if most of the time period is spent in the later (final) stages of the asymptomatic compartments. Finally, it is shown that distributing the average sojourn time in the infectious (asymptomatic) classes equally or unequally does not effect the cumulative number of new cases.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Anderson, R M" uniqKey="Anderson R">R.M. Anderson</name></author><author><name sortKey="May, R M" uniqKey="May R">R.M. May</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Chowell, G" uniqKey="Chowell G">G. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Appl Math Comput</journal-id><journal-id journal-id-type="iso-abbrev">Appl Math Comput</journal-id><journal-title-group><journal-title>Applied Mathematics and Computation</journal-title></journal-title-group><issn pub-type="ppub">0096-3003</issn><issn pub-type="epub">0096-3003</issn><publisher><publisher-name>Elsevier Inc.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmc">7112307</article-id><article-id pub-id-type="publisher-id">S0096-3003(11)00926-X</article-id><article-id pub-id-type="doi">10.1016/j.amc.2011.07.007</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Qualitative study of a quarantine/isolation model with multiple disease stages</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Safi</surname><given-names>Mohammad A.</given-names></name></contrib><contrib contrib-type="author"><name><surname>Gumel</surname><given-names>Abba B.</given-names></name><email>gumelab@cc.umanitoba.ca</email><xref rid="cor1" ref-type="corresp">⁎</xref></contrib></contrib-group><aff>Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2</aff><author-notes><corresp id="cor1"><label>⁎</label>Corresponding author. <email>gumelab@cc.umanitoba.ca</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>3</day><month>8</month><year>2011</year></pub-date><pmc-comment> PMC Release delay is 0 months and 0 days and was based on .</pmc-comment>
<pub-date pub-type="ppub"><day>1</day><month>11</month><year>2011</year></pub-date><pub-date pub-type="epub"><day>3</day><month>8</month><year>2011</year></pub-date><volume>218</volume><issue>5</issue><fpage>1941</fpage><lpage>1961</lpage><permissions><copyright-statement>Copyright © 2011 Elsevier Inc. All rights reserved.</copyright-statement><copyright-year>2011</copyright-year><copyright-holder>Elsevier Inc.</copyright-holder><license><license-p>Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.</license-p></license></permissions><abstract><p>Recent studies suggest that, for disease transmission models with latent and infectious periods, the use of gamma distribution assumption seems to provide a better fit for the associated epidemiological data in comparison to the use of exponential distribution assumption. The objective of this study is to carry out a rigorous mathematical analysis of a communicable disease transmission model with quarantine (of latent cases) and isolation (of symptomatic cases), in which the waiting periods in the infected classes are assumed to have gamma distributions. Rigorous analysis of the model reveals that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. The model has a unique endemic equilibrium when the threshold quantity exceeds unity. The endemic equilibrium is shown to be locally and globally-asymptotically stable for special cases. Numerical simulations, using data related to the 2003 SARS outbreaks, show that the cumulative number of disease-related mortality increases with increasing number of disease stages. Furthermore, the cumulative number of new cases is higher if the asymptomatic period is distributed such that most of the period is spent in the early stages of the asymptomatic compartments in comparison to the cases where the average time period is equally distributed among the associated stages or if most of the time period is spent in the later (final) stages of the asymptomatic compartments. Finally, it is shown that distributing the average sojourn time in the infectious (asymptomatic) classes equally or unequally does not effect the cumulative number of new cases.</p></abstract><kwd-group><title>Keywords</title><kwd>Quarantine/isolation</kwd><kwd>Equilibria</kwd><kwd>Reproduction number</kwd><kwd>Stability</kwd><kwd>Gamma distribution</kwd></kwd-group></article-meta></front></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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