Impact of heterogeneity on the dynamics of an SEIR epidemic model
An SEIR epidemic model with an arbitrarily distributed exposed stage is revisited to study the impact of heterogeneity on the spread of infectious diseases. The heterogeneity may come from age or behavior and disease stages, resulting in multi-group and multi-stage models, respectively. For each mod...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.393 |
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| author | Zhisheng Shuai P. van den Driessche |
| author_facet | Zhisheng Shuai P. van den Driessche |
| author_sort | Zhisheng Shuai |
| collection | DOAJ |
| description | An SEIR epidemic model with an arbitrarily distributed exposed stage is revisited to study the impact of heterogeneity on the spread of infectious diseases. The heterogeneity may come from age or behavior and disease stages, resulting in multi-group and multi-stage models, respectively. For each model, Lyapunov functionals are used to show that the basic reproduction number $\mathcal{R}_0$ gives a sharp threshold. If $\mathcal{R}_0\leq 1$, then the disease-free equilibrium is globally asymptotically stable and the disease dies out from all groups or stages. If $\mathcal{R}_0>1$, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable. |
| format | Article |
| id | doaj-art-d20d75f8ce614a58be48c05d0771e79b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d20d75f8ce614a58be48c05d0771e79b2025-01-24T02:05:29ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-02-019239341110.3934/mbe.2012.9.393Impact of heterogeneity on the dynamics of an SEIR epidemic modelZhisheng Shuai0P. van den Driessche1Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., V8W 3R4Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., V8W 3R4An SEIR epidemic model with an arbitrarily distributed exposed stage is revisited to study the impact of heterogeneity on the spread of infectious diseases. The heterogeneity may come from age or behavior and disease stages, resulting in multi-group and multi-stage models, respectively. For each model, Lyapunov functionals are used to show that the basic reproduction number $\mathcal{R}_0$ gives a sharp threshold. If $\mathcal{R}_0\leq 1$, then the disease-free equilibrium is globally asymptotically stable and the disease dies out from all groups or stages. If $\mathcal{R}_0>1$, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.393lyapunov functional.multi-group modelmulti-stage modelglobal stabilityseir modelheterogeneity |
| spellingShingle | Zhisheng Shuai P. van den Driessche Impact of heterogeneity on the dynamics of an SEIR epidemic model Mathematical Biosciences and Engineering lyapunov functional. multi-group model multi-stage model global stability seir model heterogeneity |
| title | Impact of heterogeneity on the dynamics of an SEIR epidemic model |
| title_full | Impact of heterogeneity on the dynamics of an SEIR epidemic model |
| title_fullStr | Impact of heterogeneity on the dynamics of an SEIR epidemic model |
| title_full_unstemmed | Impact of heterogeneity on the dynamics of an SEIR epidemic model |
| title_short | Impact of heterogeneity on the dynamics of an SEIR epidemic model |
| title_sort | impact of heterogeneity on the dynamics of an seir epidemic model |
| topic | lyapunov functional. multi-group model multi-stage model global stability seir model heterogeneity |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.393 |
| work_keys_str_mv | AT zhishengshuai impactofheterogeneityonthedynamicsofanseirepidemicmodel AT pvandendriessche impactofheterogeneityonthedynamicsofanseirepidemicmodel |