Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate
The basic viral infection models, proposed by Nowak et al. and Perelson et al., respectively, have been widely used to describe viral infection such as HBV and HIV infection. However, the basic reproduction numbers of the two models are proportional to the number of total cells of the host's or...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/586035 |
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| _version_ | 1849473230503411712 |
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| author | Yu Ji Muxuan Zheng |
| author_facet | Yu Ji Muxuan Zheng |
| author_sort | Yu Ji |
| collection | DOAJ |
| description | The basic viral infection models, proposed by Nowak et al. and Perelson et al., respectively, have been widely used to describe viral infection such as HBV and HIV infection. However, the basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection, which seems not to be reasonable. In this paper, we formulate an amended model with a general standard incidence rate. The basic reproduction number of the amended model is independent of total cells of the host’s organ. When the basic reproduction number R0<1, the infection-free equilibrium is globally asymptotically stable and the virus is cleared. Moreover, if R0>1, then the endemic equilibrium is globally asymptotically stable and the virus persists in the host. |
| format | Article |
| id | doaj-art-d3ea15f4973348378a2bb53a6121cfb6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d3ea15f4973348378a2bb53a6121cfb62025-08-20T03:24:14ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/586035586035Dynamics Analysis of a Viral Infection Model with a General Standard Incidence RateYu Ji0Muxuan Zheng1Department of Mathematics, Beijing Technology and Business University, Beijing 100048, ChinaDepartment of Mathematics, Beijing Technology and Business University, Beijing 100048, ChinaThe basic viral infection models, proposed by Nowak et al. and Perelson et al., respectively, have been widely used to describe viral infection such as HBV and HIV infection. However, the basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection, which seems not to be reasonable. In this paper, we formulate an amended model with a general standard incidence rate. The basic reproduction number of the amended model is independent of total cells of the host’s organ. When the basic reproduction number R0<1, the infection-free equilibrium is globally asymptotically stable and the virus is cleared. Moreover, if R0>1, then the endemic equilibrium is globally asymptotically stable and the virus persists in the host.http://dx.doi.org/10.1155/2014/586035 |
| spellingShingle | Yu Ji Muxuan Zheng Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate Abstract and Applied Analysis |
| title | Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate |
| title_full | Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate |
| title_fullStr | Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate |
| title_full_unstemmed | Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate |
| title_short | Dynamics Analysis of a Viral Infection Model with a General Standard Incidence Rate |
| title_sort | dynamics analysis of a viral infection model with a general standard incidence rate |
| url | http://dx.doi.org/10.1155/2014/586035 |
| work_keys_str_mv | AT yuji dynamicsanalysisofaviralinfectionmodelwithageneralstandardincidencerate AT muxuanzheng dynamicsanalysisofaviralinfectionmodelwithageneralstandardincidencerate |