Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells
By introducing the probability function describing latency of infected cells, we unify some models of viral infection with latent stage. For the case that the probability function is a step function, which implies that the latency period of the infected cells is constant, the corresponding model is...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/632381 |
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| _version_ | 1850157254492291072 |
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| author | Shuo Liu Lina Ma Jianquan Li Qingbo Zhao |
| author_facet | Shuo Liu Lina Ma Jianquan Li Qingbo Zhao |
| author_sort | Shuo Liu |
| collection | DOAJ |
| description | By introducing the probability function describing latency of infected cells, we unify some models of viral infection with latent stage. For the case that the probability function is a step function, which implies that the latency period of the infected cells is constant, the corresponding model is a delay differential system. The model with delay of latency and two types of target cells is investigated, and the obtained results show that when the basic reproduction number is less than or equal to unity, the infection-free equilibrium is globally stable, that is, the in-host free virus will be cleared out finally; when the basic reproduction number is greater than unity, the infection equilibrium is globally stable, that is, the viral infection will be chronic and persist in-host. And by comparing the basic reproduction numbers of ordinary differential system and the associated delayed differential system, we think that it is necessary to elect an appropriate type of probability function for predicting the final outcome of viral infection in-host. |
| format | Article |
| id | doaj-art-2d15d520bc454789af7bebb319e2d5bb |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2d15d520bc454789af7bebb319e2d5bb2025-08-20T02:24:14ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/632381632381Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target CellsShuo Liu0Lina Ma1Jianquan Li2Qingbo Zhao3School of Biomedical Engineering, The Fourth Military Medical University, Xi’an 710032, ChinaCollege of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaCollege of Science, Air Force Engineering University, Xi’an 710051, ChinaSchool of Biomedical Engineering, The Fourth Military Medical University, Xi’an 710032, ChinaBy introducing the probability function describing latency of infected cells, we unify some models of viral infection with latent stage. For the case that the probability function is a step function, which implies that the latency period of the infected cells is constant, the corresponding model is a delay differential system. The model with delay of latency and two types of target cells is investigated, and the obtained results show that when the basic reproduction number is less than or equal to unity, the infection-free equilibrium is globally stable, that is, the in-host free virus will be cleared out finally; when the basic reproduction number is greater than unity, the infection equilibrium is globally stable, that is, the viral infection will be chronic and persist in-host. And by comparing the basic reproduction numbers of ordinary differential system and the associated delayed differential system, we think that it is necessary to elect an appropriate type of probability function for predicting the final outcome of viral infection in-host.http://dx.doi.org/10.1155/2013/632381 |
| spellingShingle | Shuo Liu Lina Ma Jianquan Li Qingbo Zhao Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells Journal of Applied Mathematics |
| title | Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells |
| title_full | Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells |
| title_fullStr | Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells |
| title_full_unstemmed | Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells |
| title_short | Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells |
| title_sort | global analysis of a model of viral infection with latent stage and two types of target cells |
| url | http://dx.doi.org/10.1155/2013/632381 |
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