Local stability of an SIR epidemic model and effect of time delay

We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stability is give...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2009-11, Vol.32 (16), p.2160-2175
Main Authors: Tchuenche, Jean M., Nwagwo, Alexander
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
local stability
Lyapunov function
Mathematical analysis
Mathematics
Sciences and techniques of general use
SIR model
time delay
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c3336-49fc2be25c3552d9ce86b07286c73406cd21308804e49030f57f16c754d548123
cites cdi_FETCH-LOGICAL-c3336-49fc2be25c3552d9ce86b07286c73406cd21308804e49030f57f16c754d548123
container_end_page 2175
container_issue 16
container_start_page 2160
container_title Mathematical methods in the applied sciences
container_volume 32
creator Tchuenche, Jean M.
Nwagwo, Alexander
description We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stability is given. The proofs are based on linearization and the application of Lyapunov functional approach. An upper bound of the critical time delay for which the model remains valid is derived. Numerical simulations are carried out to illustrate the effect of time delay which tends to reduce the epidemic threshold. Copyright © 2009 John Wiley & Sons, Ltd.
doi_str_mv 10.1002/mma.1136
format article
fullrecord <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1002_mma_1136</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>MMA1136</sourcerecordid><originalsourceid>FETCH-LOGICAL-c3336-49fc2be25c3552d9ce86b07286c73406cd21308804e49030f57f16c754d548123</originalsourceid><addsrcrecordid>eNp1j19LwzAUR4MoOKfgR8iL4EvnvUmatI9j6DbY_C_6FrI0gWi7jqag_fa2bPjm04XfPRw4hFwiTBCA3VSVmSByeURGCHmeoFDymIwAFSSCoTglZzF-AkCGyEZkuqqtKWlszSaUoe1o7anZ0pflM3W7ULgqWFrVhSv7taDOe2fbgWlD5Wg_m-6cnHhTRndxuGPydnf7Olskq4f5cjZdJZZzLhORe8s2jqWWpykrcusyuQHFMmkVFyBtwZBDloFwIgcOPlUe-18qilRkyPiYXO-9tqljbJzXuyZUpuk0gh7SdZ-uh_QevdqjOxP7Ot-YrQ3xj2cMmOJq4JI99x1K1_3r0-v19OA98CG27uePN82Xlr0w1e_3cy2fUH7MHhda8l9bV3Mn</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Local stability of an SIR epidemic model and effect of time delay</title><source>Wiley-Blackwell Read &amp; Publish Collection</source><creator>Tchuenche, Jean M. ; Nwagwo, Alexander</creator><creatorcontrib>Tchuenche, Jean M. ; Nwagwo, Alexander</creatorcontrib><description>We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stability is given. The proofs are based on linearization and the application of Lyapunov functional approach. An upper bound of the critical time delay for which the model remains valid is derived. Numerical simulations are carried out to illustrate the effect of time delay which tends to reduce the epidemic threshold. Copyright © 2009 John Wiley &amp; Sons, Ltd.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.1136</identifier><identifier>CODEN: MMSCDB</identifier><language>eng</language><publisher>Chichester, UK: John Wiley &amp; Sons, Ltd</publisher><subject>Exact sciences and technology ; Global analysis, analysis on manifolds ; local stability ; Lyapunov function ; Mathematical analysis ; Mathematics ; Sciences and techniques of general use ; SIR model ; time delay ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Mathematical methods in the applied sciences, 2009-11, Vol.32 (16), p.2160-2175</ispartof><rights>Copyright © 2009 John Wiley &amp; Sons, Ltd.</rights><rights>2009 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3336-49fc2be25c3552d9ce86b07286c73406cd21308804e49030f57f16c754d548123</citedby><cites>FETCH-LOGICAL-c3336-49fc2be25c3552d9ce86b07286c73406cd21308804e49030f57f16c754d548123</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=22027376$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Tchuenche, Jean M.</creatorcontrib><creatorcontrib>Nwagwo, Alexander</creatorcontrib><title>Local stability of an SIR epidemic model and effect of time delay</title><title>Mathematical methods in the applied sciences</title><addtitle>Math. Meth. Appl. Sci</addtitle><description>We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stability is given. The proofs are based on linearization and the application of Lyapunov functional approach. An upper bound of the critical time delay for which the model remains valid is derived. Numerical simulations are carried out to illustrate the effect of time delay which tends to reduce the epidemic threshold. Copyright © 2009 John Wiley &amp; Sons, Ltd.</description><subject>Exact sciences and technology</subject><subject>Global analysis, analysis on manifolds</subject><subject>local stability</subject><subject>Lyapunov function</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Sciences and techniques of general use</subject><subject>SIR model</subject><subject>time delay</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp1j19LwzAUR4MoOKfgR8iL4EvnvUmatI9j6DbY_C_6FrI0gWi7jqag_fa2bPjm04XfPRw4hFwiTBCA3VSVmSByeURGCHmeoFDymIwAFSSCoTglZzF-AkCGyEZkuqqtKWlszSaUoe1o7anZ0pflM3W7ULgqWFrVhSv7taDOe2fbgWlD5Wg_m-6cnHhTRndxuGPydnf7Olskq4f5cjZdJZZzLhORe8s2jqWWpykrcusyuQHFMmkVFyBtwZBDloFwIgcOPlUe-18qilRkyPiYXO-9tqljbJzXuyZUpuk0gh7SdZ-uh_QevdqjOxP7Ot-YrQ3xj2cMmOJq4JI99x1K1_3r0-v19OA98CG27uePN82Xlr0w1e_3cy2fUH7MHhda8l9bV3Mn</recordid><startdate>20091115</startdate><enddate>20091115</enddate><creator>Tchuenche, Jean M.</creator><creator>Nwagwo, Alexander</creator><general>John Wiley &amp; Sons, Ltd</general><general>Wiley</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20091115</creationdate><title>Local stability of an SIR epidemic model and effect of time delay</title><author>Tchuenche, Jean M. ; Nwagwo, Alexander</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3336-49fc2be25c3552d9ce86b07286c73406cd21308804e49030f57f16c754d548123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Exact sciences and technology</topic><topic>Global analysis, analysis on manifolds</topic><topic>local stability</topic><topic>Lyapunov function</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Sciences and techniques of general use</topic><topic>SIR model</topic><topic>time delay</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tchuenche, Jean M.</creatorcontrib><creatorcontrib>Nwagwo, Alexander</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tchuenche, Jean M.</au><au>Nwagwo, Alexander</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Local stability of an SIR epidemic model and effect of time delay</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><addtitle>Math. Meth. Appl. Sci</addtitle><date>2009-11-15</date><risdate>2009</risdate><volume>32</volume><issue>16</issue><spage>2160</spage><epage>2175</epage><pages>2160-2175</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><coden>MMSCDB</coden><abstract>We describe an SIR epidemic model with a discrete time lag, analyse the local stability of its equilibria as well as the effects of delay on the reproduction number and on the dynamical behaviour of the system. The model has two equilibria—a necessary condition for local asymptotic stability is given. The proofs are based on linearization and the application of Lyapunov functional approach. An upper bound of the critical time delay for which the model remains valid is derived. Numerical simulations are carried out to illustrate the effect of time delay which tends to reduce the epidemic threshold. Copyright © 2009 John Wiley &amp; Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley &amp; Sons, Ltd</pub><doi>10.1002/mma.1136</doi><tpages>16</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0170-4214
ispartof Mathematical methods in the applied sciences, 2009-11, Vol.32 (16), p.2160-2175
issn 0170-4214
1099-1476
language eng
recordid cdi_crossref_primary_10_1002_mma_1136
source Wiley-Blackwell Read & Publish Collection
subjects Exact sciences and technology
Global analysis, analysis on manifolds
local stability
Lyapunov function
Mathematical analysis
Mathematics
Sciences and techniques of general use
SIR model
time delay
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
title Local stability of an SIR epidemic model and effect of time delay
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-30T07%3A00%3A06IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Local%20stability%20of%20an%20SIR%20epidemic%20model%20and%20effect%20of%20time%20delay&rft.jtitle=Mathematical%20methods%20in%20the%20applied%20sciences&rft.au=Tchuenche,%20Jean%20M.&rft.date=2009-11-15&rft.volume=32&rft.issue=16&rft.spage=2160&rft.epage=2175&rft.pages=2160-2175&rft.issn=0170-4214&rft.eissn=1099-1476&rft.coden=MMSCDB&rft_id=info:doi/10.1002/mma.1136&rft_dat=%3Cwiley_cross%3EMMA1136%3C/wiley_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c3336-49fc2be25c3552d9ce86b07286c73406cd21308804e49030f57f16c754d548123%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true