Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility

Handle URI:
http://hdl.handle.net/10754/598746
Title:
Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility
Authors:
Korobeinikov, Andrei; Melnik, Andrey V.
Abstract:
We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.
Citation:
Korobeinikov A, Melnik AV (2013) Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility. Mathematical Biosciences and Engineering 10: 369–378. Available: http://dx.doi.org/10.3934/mbe.2013.10.369.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Mathematical Biosciences and Engineering
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2013
DOI:
10.3934/mbe.2013.10.369
PubMed ID:
23458305
Type:
Article
ISSN:
1551-0018
Sponsors:
This work is supported by SFI grant 06/MI/005.This work was supported by the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland Mathematics Initiative Grant 06/MI/005; by the Ministry of Science and Innovation of Spain via Ramon y Cajal Fellowship RYC-2011-08061 (A. Korobeinikov), and by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A. Melnik).
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Full metadata record

DC FieldValue Language
dc.contributor.authorKorobeinikov, Andreien
dc.contributor.authorMelnik, Andrey V.en
dc.date.accessioned2016-02-25T13:40:23Zen
dc.date.available2016-02-25T13:40:23Zen
dc.date.issued2013-01en
dc.identifier.citationKorobeinikov A, Melnik AV (2013) Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility. Mathematical Biosciences and Engineering 10: 369–378. Available: http://dx.doi.org/10.3934/mbe.2013.10.369.en
dc.identifier.issn1551-0018en
dc.identifier.pmid23458305en
dc.identifier.doi10.3934/mbe.2013.10.369en
dc.identifier.urihttp://hdl.handle.net/10754/598746en
dc.description.abstractWe consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.en
dc.description.sponsorshipThis work is supported by SFI grant 06/MI/005.This work was supported by the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland Mathematics Initiative Grant 06/MI/005; by the Ministry of Science and Innovation of Spain via Ramon y Cajal Fellowship RYC-2011-08061 (A. Korobeinikov), and by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A. Melnik).en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectAge structureen
dc.subjectAge structured modelen
dc.subjectCompartment modelen
dc.subjectDirect Lyapunov methoden
dc.subjectDistributed population modelen
dc.subjectEndemic equilibrium stateen
dc.subjectGlobal stabilityen
dc.subjectInfectious diseaseen
dc.subjectLyapunov functionen
dc.titleLyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibilityen
dc.typeArticleen
dc.identifier.journalMathematical Biosciences and Engineeringen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionCentre de Recerca Matematica, Cerdanyola del Valles, Spainen
kaust.grant.numberKUK-C1-013-04en
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