Global dynamics of a delay virus model with recruitment and saturation effects of immune responses
In this paper, we formulate a virus dynamics model with the recruitment of immune responses, saturation effects and an intracellular time delay. With the help of uniform persistence theory and Lyapunov method, we show that the global stability of the model is totally determined by the basic reproduc...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017063 |
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| _version_ | 1832590072821579776 |
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| author | Cuicui Jiang Kaifa Wang Lijuan Song |
| author_facet | Cuicui Jiang Kaifa Wang Lijuan Song |
| author_sort | Cuicui Jiang |
| collection | DOAJ |
| description | In this paper, we formulate a virus dynamics model with the recruitment of immune responses, saturation effects and an intracellular time delay. With the help of uniform persistence theory and Lyapunov method, we show that the global stability of the model is totally determined by the basic reproductive number $R_0$. Furthermore, we analyze the effects of the recruitment of immune responses on virus infection by numerical simulation. The results show ignoring the recruitment of immune responses will result in overestimation of the basic reproductive number and the severity of viral infection. |
| format | Article |
| id | doaj-art-ac7f7443df5b4376bf3f522d1b0e4fd4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-ac7f7443df5b4376bf3f522d1b0e4fd42025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61233124610.3934/mbe.2017063Global dynamics of a delay virus model with recruitment and saturation effects of immune responsesCuicui Jiang0Kaifa Wang1Lijuan Song2Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, ChinaDepartment of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, ChinaDepartment of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, ChinaIn this paper, we formulate a virus dynamics model with the recruitment of immune responses, saturation effects and an intracellular time delay. With the help of uniform persistence theory and Lyapunov method, we show that the global stability of the model is totally determined by the basic reproductive number $R_0$. Furthermore, we analyze the effects of the recruitment of immune responses on virus infection by numerical simulation. The results show ignoring the recruitment of immune responses will result in overestimation of the basic reproductive number and the severity of viral infection.https://www.aimspress.com/article/doi/10.3934/mbe.2017063global stabilitylyapunov functionalviral dynamicsimmune responsetime delay |
| spellingShingle | Cuicui Jiang Kaifa Wang Lijuan Song Global dynamics of a delay virus model with recruitment and saturation effects of immune responses Mathematical Biosciences and Engineering global stability lyapunov functional viral dynamics immune response time delay |
| title | Global dynamics of a delay virus model with recruitment and saturation effects of immune responses |
| title_full | Global dynamics of a delay virus model with recruitment and saturation effects of immune responses |
| title_fullStr | Global dynamics of a delay virus model with recruitment and saturation effects of immune responses |
| title_full_unstemmed | Global dynamics of a delay virus model with recruitment and saturation effects of immune responses |
| title_short | Global dynamics of a delay virus model with recruitment and saturation effects of immune responses |
| title_sort | global dynamics of a delay virus model with recruitment and saturation effects of immune responses |
| topic | global stability lyapunov functional viral dynamics immune response time delay |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017063 |
| work_keys_str_mv | AT cuicuijiang globaldynamicsofadelayvirusmodelwithrecruitmentandsaturationeffectsofimmuneresponses AT kaifawang globaldynamicsofadelayvirusmodelwithrecruitmentandsaturationeffectsofimmuneresponses AT lijuansong globaldynamicsofadelayvirusmodelwithrecruitmentandsaturationeffectsofimmuneresponses |