Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility
We consider global asymptotic properties for the SIR and SEIRage structured models for infectious diseases where the susceptibilitydepends on the age. Using the direct Lyapunov method with Volterratype Lyapunov functions, we establish conditions for the global stabilityof a unique endemic steady sta...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.369 |
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| author | Andrey V. Melnik Andrei Korobeinikov |
| author_facet | Andrey V. Melnik Andrei Korobeinikov |
| author_sort | Andrey V. Melnik |
| collection | DOAJ |
| description | We consider global asymptotic properties for the SIR and SEIRage structured models for infectious diseases where the susceptibilitydepends on the age. Using the direct Lyapunov method with Volterratype Lyapunov functions, we establish conditions for the global stabilityof a unique endemic steady state and the infection-free steady state. |
| format | Article |
| id | doaj-art-6f7744b573c048c0ba00e21f8a572c5a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-6f7744b573c048c0ba00e21f8a572c5a2025-01-24T02:25:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-12-0110236937810.3934/mbe.2013.10.369Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibilityAndrey V. Melnik0Andrei Korobeinikov1OCCAM, Mathematical Institute, 24 - 29 St Giles', Oxford, OX1 3LBOCCAM, Mathematical Institute, 24 - 29 St Giles', Oxford, OX1 3LBWe consider global asymptotic properties for the SIR and SEIRage structured models for infectious diseases where the susceptibilitydepends on the age. Using the direct Lyapunov method with Volterratype Lyapunov functions, we establish conditions for the global stabilityof a unique endemic steady state and the infection-free steady state.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.369age structured modellyapunov functionage structureglobal stabilityinfectious diseaseendemic equilibrium statecompartmentmodeldirect lyapunov methoddistributed population model. |
| spellingShingle | Andrey V. Melnik Andrei Korobeinikov Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility Mathematical Biosciences and Engineering age structured model lyapunov function age structure global stability infectious disease endemic equilibrium state compartmentmodel direct lyapunov method distributed population model. |
| title | Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility |
| title_full | Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility |
| title_fullStr | Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility |
| title_full_unstemmed | Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility |
| title_short | Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility |
| title_sort | lyapunov functions and global stability for sir and seir models withage dependent susceptibility |
| topic | age structured model lyapunov function age structure global stability infectious disease endemic equilibrium state compartmentmodel direct lyapunov method distributed population model. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.369 |
| work_keys_str_mv | AT andreyvmelnik lyapunovfunctionsandglobalstabilityforsirandseirmodelswithagedependentsusceptibility AT andreikorobeinikov lyapunovfunctionsandglobalstabilityforsirandseirmodelswithagedependentsusceptibility |