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

Andrei Korobeinikov; Andrey V. Melnik

doi:10.3934/mbe.2013.10.369

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

Andrei Korobeinikov, Andrey V. Melnik

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

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.

Original language	English (US)
Pages (from-to)	369-378
Number of pages	10
Journal	Mathematical Biosciences and Engineering
Volume	10
Issue number	2
DOIs	https://doi.org/10.3934/mbe.2013.10.369
State	Published - Jan 17 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.3934/mbe.2013.10.369

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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.",

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AB - 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.

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

Abstract

Bibliographical note

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