Mathematical analysis of a lymphatic filariasis model with quarantine and treatment
Identifieur interne : 000C78 ( Pmc/Curation ); précédent : 000C77; suivant : 000C79Mathematical analysis of a lymphatic filariasis model with quarantine and treatment
Auteurs : Peter M. Mwamtobe [Afrique du Sud, Malawi] ; Simphiwe M. Simelane [Afrique du Sud] ; Shirley Abelman [Afrique du Sud] ; Jean M. Tchuenche [Afrique du Sud]Source :
- BMC Public Health [ 1471-2458 ] ; 2017.
Abstract
Lymphatic filariasis is a globally neglected tropical parasitic disease which affects individuals of all ages and leads to an altered lymphatic system and abnormal enlargement of body parts.
A mathematical model of lymphatic filariaris with intervention strategies is developed and analyzed. Control of infections is analyzed within the model through medical treatment of infected-acute individuals and quarantine of infected-chronic individuals.
We derive the effective reproduction number,
Numerical simulations are carried out to monitor the dynamics of the filariasis model sub-populations for various parameter values of the associated reproduction threshold. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance on the disease transmission.
Url:
DOI: 10.1186/s12889-017-4160-8
PubMed: 28302096
PubMed Central: 5356380
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Tchuenche</name><affiliation wicri:level="1"><nlm:aff id="Aff1"><institution-wrap><institution-id institution-id-type="ISNI">0000 0004 1937 1135</institution-id><institution-id institution-id-type="GRID">grid.11951.3d</institution-id><institution>School of Computer Science and Applied Mathematics,</institution><institution>University of the Witwatersrand, Johannesburg,</institution></institution-wrap>Private Bag 3, Wits, Johannesburg, 2050 South Africa</nlm:aff><country xml:lang="fr">Afrique du Sud</country><wicri:regionArea>Private Bag 3, Wits, Johannesburg</wicri:regionArea></affiliation></author></analytic><series><title level="j">BMC Public Health</title><idno type="eISSN">1471-2458</idno><imprint><date when="2017">2017</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><sec><title>Background</title><p>Lymphatic filariasis is a globally neglected tropical parasitic disease which affects individuals of all ages and leads to an altered lymphatic system and abnormal enlargement of body parts.</p></sec><sec><title>Methods</title><p>A mathematical model of lymphatic filariaris with intervention strategies is developed and analyzed. Control of infections is analyzed within the model through medical treatment of infected-acute individuals and quarantine of infected-chronic individuals.</p></sec><sec><title>Results</title><p>We derive the effective reproduction number, <inline-formula id="IEq1"><alternatives><tex-math id="M1">\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {R}_{0},$\end{document}</tex-math><mml:math id="M2"><mml:msub><mml:mrow><mml:mi mathvariant="script">R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math><inline-graphic xlink:href="12889_2017_4160_Article_IEq1.gif"></inline-graphic></alternatives></inline-formula> and its interpretation/investigation suggests that treatment contributes to a reduction in lymphatic filariasis cases faster than quarantine. However, this reduction is greater when the two intervention approaches are applied concurrently.</p></sec><sec><title>Conclusions</title><p>Numerical simulations are carried out to monitor the dynamics of the filariasis model sub-populations for various parameter values of the associated reproduction threshold. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance on the disease transmission.</p></sec></div></front><back><div1 type="bibliography"><listBibl><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Critchley, J" uniqKey="Critchley J">J Critchley</name></author><author><name sortKey="Addiss, D" uniqKey="Addiss D">D Addiss</name></author><author><name sortKey="Gamble, C" uniqKey="Gamble C">C Gamble</name></author><author><name sortKey="Garner, P" uniqKey="Garner P">P Garner</name></author><author><name sortKey="Gelband, H" uniqKey="Gelband H">H Gelband</name></author><author><name sortKey="Ejere, H" uniqKey="Ejere H">H Ejere</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Van Den Berg, H" uniqKey="Van Den Berg H">H van den Berg</name></author><author><name sortKey="Kelly Hope, La" uniqKey="Kelly Hope 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<front><journal-meta><journal-id journal-id-type="nlm-ta">BMC Public Health</journal-id><journal-id journal-id-type="iso-abbrev">BMC Public Health</journal-id><journal-title-group><journal-title>BMC Public Health</journal-title></journal-title-group><issn pub-type="epub">1471-2458</issn><publisher><publisher-name>BioMed Central</publisher-name><publisher-loc>London</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">28302096</article-id><article-id pub-id-type="pmc">5356380</article-id><article-id pub-id-type="publisher-id">4160</article-id><article-id pub-id-type="doi">10.1186/s12889-017-4160-8</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title>Mathematical analysis of a lymphatic filariasis model with quarantine and treatment</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name><surname>Mwamtobe</surname><given-names>Peter M.</given-names></name><address><email>pmwamtobe@gmail.com</email></address><xref ref-type="aff" rid="Aff1">1</xref><xref ref-type="aff" rid="Aff2">2</xref><xref ref-type="aff" rid="Aff3">3</xref></contrib><contrib contrib-type="author"><name><surname>Simelane</surname><given-names>Simphiwe M.</given-names></name><address><email>simphinho@gmail.com</email></address><xref ref-type="aff" rid="Aff1">1</xref><xref ref-type="aff" rid="Aff2">2</xref></contrib><contrib contrib-type="author"><name><surname>Abelman</surname><given-names>Shirley</given-names></name><address><email>Shirley.Abelman@wits.ac.za</email></address><xref ref-type="aff" rid="Aff1">1</xref><xref ref-type="aff" rid="Aff2">2</xref></contrib><contrib contrib-type="author"><name><surname>Tchuenche</surname><given-names>Jean M.</given-names></name><address><email>jmtchuenche@gmail.com</email></address><xref ref-type="aff" rid="Aff1">1</xref></contrib><aff id="Aff1"><label>1</label><institution-wrap><institution-id institution-id-type="ISNI">0000 0004 1937 1135</institution-id><institution-id institution-id-type="GRID">grid.11951.3d</institution-id><institution>School of Computer Science and Applied Mathematics,</institution><institution>University of the Witwatersrand, Johannesburg,</institution></institution-wrap>Private Bag 3, Wits, Johannesburg, 2050 South Africa</aff><aff id="Aff2"><label>2</label><institution-wrap><institution-id institution-id-type="ISNI">0000 0004 1937 1135</institution-id><institution-id institution-id-type="GRID">grid.11951.3d</institution-id><institution>DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),</institution><institution>University of the Witwatersrand, Johannesburg,</institution></institution-wrap>Private Bag 3, WitsJohannesburg, 2050 South Africa</aff><aff id="Aff3"><label>3</label><institution-wrap><institution-id institution-id-type="ISNI">0000 0001 2113 2211</institution-id><institution-id institution-id-type="GRID">grid.10595.38</institution-id><institution>Department of Mathematics and Statistics,</institution><institution>University of Malawi,</institution></institution-wrap>Chichiri, Blantyre, Malawi</aff></contrib-group><pub-date pub-type="epub"><day>16</day><month>3</month><year>2017</year></pub-date><pub-date pub-type="pmc-release"><day>16</day><month>3</month><year>2017</year></pub-date><pub-date pub-type="collection"><year>2017</year></pub-date><volume>17</volume><elocation-id>265</elocation-id><history><date date-type="received"><day>3</day><month>11</month><year>2015</year></date><date date-type="accepted"><day>2</day><month>3</month><year>2017</year></date></history><permissions><copyright-statement>© The Author(s) 2017</copyright-statement><license license-type="OpenAccess"><license-p><bold>Open Access</bold> This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">http://creativecommons.org/licenses/by/4.0/</ext-link>), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver(<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/publicdomain/zero/1.0/">http://creativecommons.org/publicdomain/zero/1.0/</ext-link>) applies to the data made available in this article, unless otherwise stated.</license-p></license></permissions><abstract id="Abs1"><sec><title>Background</title><p>Lymphatic filariasis is a globally neglected tropical parasitic disease which affects individuals of all ages and leads to an altered lymphatic system and abnormal enlargement of body parts.</p></sec><sec><title>Methods</title><p>A mathematical model of lymphatic filariaris with intervention strategies is developed and analyzed. Control of infections is analyzed within the model through medical treatment of infected-acute individuals and quarantine of infected-chronic individuals.</p></sec><sec><title>Results</title><p>We derive the effective reproduction number, <inline-formula id="IEq1"><alternatives><tex-math id="M1">\documentclass[12pt]{minimal}
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\begin{document}$\mathcal {R}_{0},$\end{document}</tex-math><mml:math id="M2"><mml:msub><mml:mrow><mml:mi mathvariant="script">R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:math><inline-graphic xlink:href="12889_2017_4160_Article_IEq1.gif"></inline-graphic></alternatives></inline-formula> and its interpretation/investigation suggests that treatment contributes to a reduction in lymphatic filariasis cases faster than quarantine. However, this reduction is greater when the two intervention approaches are applied concurrently.</p></sec><sec><title>Conclusions</title><p>Numerical simulations are carried out to monitor the dynamics of the filariasis model sub-populations for various parameter values of the associated reproduction threshold. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance on the disease transmission.</p></sec></abstract><kwd-group xml:lang="en"><title>Keywords</title><kwd>Lymphatic filariasis</kwd><kwd>Intervention strategies</kwd><kwd>Latent stage</kwd><kwd>Reproduction number</kwd></kwd-group><custom-meta-group><custom-meta><meta-name>issue-copyright-statement</meta-name><meta-value>© The Author(s) 2017</meta-value></custom-meta></custom-meta-group></article-meta></front></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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