Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages
In this paper, we study the global properties of an SIR epidemicmodel with distributed delays, where there are several parallelinfective stages, and some of the infected cells are detected andtreated, which others remain undetected and untreated. The modelis analyzed by determining a basic reproduct...
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AIMS Press
2012-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.685 |
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| author | Xia Wang Shengqiang Liu |
| author_facet | Xia Wang Shengqiang Liu |
| author_sort | Xia Wang |
| collection | DOAJ |
| description | In this paper, we study the global properties of an SIR epidemicmodel with distributed delays, where there are several parallelinfective stages, and some of the infected cells are detected andtreated, which others remain undetected and untreated. The modelis analyzed by determining a basic reproduction number $R_0$, andby using Lyapunov functionals, we prove that the infection-freeequilibrium $E^0$ of system (3) is globallyasymptotically attractive when $R_0\leq 1$, and that the uniqueinfected equilibrium $E^*$ of system (3) exists and it isglobally asymptotically attractive when $R_0>1$. |
| format | Article |
| id | doaj-art-5b2f38a1a51c46d382b30eed7b285609 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5b2f38a1a51c46d382b30eed7b2856092025-01-24T02:07:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-06-019368569510.3934/mbe.2012.9.685Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stagesXia Wang0Shengqiang Liu1Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street Harbin, 150080 and College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street Harbin, 150080 and College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000In this paper, we study the global properties of an SIR epidemicmodel with distributed delays, where there are several parallelinfective stages, and some of the infected cells are detected andtreated, which others remain undetected and untreated. The modelis analyzed by determining a basic reproduction number $R_0$, andby using Lyapunov functionals, we prove that the infection-freeequilibrium $E^0$ of system (3) is globallyasymptotically attractive when $R_0\leq 1$, and that the uniqueinfected equilibrium $E^*$ of system (3) exists and it isglobally asymptotically attractive when $R_0>1$.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.685distributed delayglobalattractivitylyapounov functional.sir epidemic model |
| spellingShingle | Xia Wang Shengqiang Liu Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages Mathematical Biosciences and Engineering distributed delay globalattractivity lyapounov functional. sir epidemic model |
| title | Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages |
| title_full | Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages |
| title_fullStr | Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages |
| title_full_unstemmed | Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages |
| title_short | Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages |
| title_sort | global properties of a delayed sir epidemicmodel with multiple parallel infectious stages |
| topic | distributed delay globalattractivity lyapounov functional. sir epidemic model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.685 |
| work_keys_str_mv | AT xiawang globalpropertiesofadelayedsirepidemicmodelwithmultipleparallelinfectiousstages AT shengqiangliu globalpropertiesofadelayedsirepidemicmodelwithmultipleparallelinfectiousstages |