Global analysis on a class of multi-group SEIR model with latency and relapse
In this paper, we investigate the global dynamics of a multi-group SEIR epidemic model,allowing heterogeneity of the host population, delay in latency and delay due torelapsedistribution for the human population.Our results indicate that when certain restrictions on nonlinear growth rate and inciden...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.209 |
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| author | Jinliang Wang Hongying Shu |
| author_facet | Jinliang Wang Hongying Shu |
| author_sort | Jinliang Wang |
| collection | DOAJ |
| description | In this paper, we investigate the global dynamics of a multi-group SEIR epidemic model,allowing heterogeneity of the host population, delay in latency and delay due torelapsedistribution for the human population.Our results indicate that when certain restrictions on nonlinear growth rate and incidence are fulfilled, the basic reproduction number $\mathfrak{R}_0$ plays the key role of a global threshold parameter in the sense that the long-time behaviors of the model depend only on $\mathfrak{R}_0$. The proofs of the main results utilize the persistence theory indynamical systems, Lyapunov functionals guided by graph-theoretical approach. |
| format | Article |
| id | doaj-art-ff649e0315124f5a8b50acc4ffcc1d5c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-ff649e0315124f5a8b50acc4ffcc1d5c2025-01-24T02:34:05ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-09-0113120922510.3934/mbe.2016.13.209Global analysis on a class of multi-group SEIR model with latency and relapseJinliang Wang0Hongying Shu1School of Mathematical Science, Heilongjiang University, Harbin 150080Department of Mathematics, Tongji University, Shanghai 200092In this paper, we investigate the global dynamics of a multi-group SEIR epidemic model,allowing heterogeneity of the host population, delay in latency and delay due torelapsedistribution for the human population.Our results indicate that when certain restrictions on nonlinear growth rate and incidence are fulfilled, the basic reproduction number $\mathfrak{R}_0$ plays the key role of a global threshold parameter in the sense that the long-time behaviors of the model depend only on $\mathfrak{R}_0$. The proofs of the main results utilize the persistence theory indynamical systems, Lyapunov functionals guided by graph-theoretical approach.https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.209relapselyapunov functional.global stabilitylatencymulti-group model |
| spellingShingle | Jinliang Wang Hongying Shu Global analysis on a class of multi-group SEIR model with latency and relapse Mathematical Biosciences and Engineering relapse lyapunov functional. global stability latency multi-group model |
| title | Global analysis on a class of multi-group SEIR model with latency and relapse |
| title_full | Global analysis on a class of multi-group SEIR model with latency and relapse |
| title_fullStr | Global analysis on a class of multi-group SEIR model with latency and relapse |
| title_full_unstemmed | Global analysis on a class of multi-group SEIR model with latency and relapse |
| title_short | Global analysis on a class of multi-group SEIR model with latency and relapse |
| title_sort | global analysis on a class of multi group seir model with latency and relapse |
| topic | relapse lyapunov functional. global stability latency multi-group model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016.13.209 |
| work_keys_str_mv | AT jinliangwang globalanalysisonaclassofmultigroupseirmodelwithlatencyandrelapse AT hongyingshu globalanalysisonaclassofmultigroupseirmodelwithlatencyandrelapse |