Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay
A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcati...
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| Language: | English |
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AIMS Press
2015-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015006 |
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| _version_ | 1832590124276252672 |
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| author | Jinhu Xu Yicang Zhou |
| author_facet | Jinhu Xu Yicang Zhou |
| author_sort | Jinhu Xu |
| collection | DOAJ |
| description | A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcation and the stability of the periodic solutions are investigated by normal form and center manifold theory.Numerical simulations are done to explore the rich dynamics,including stability switches, Hopf bifurcations, and chaotic oscillations. |
| format | Article |
| id | doaj-art-757b49560cf0432898ac6f949991373b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-757b49560cf0432898ac6f949991373b2025-01-24T02:35:04ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-11-0113234336710.3934/mbe.2015006Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delayJinhu Xu0Yicang Zhou1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049A within-host viral infection model with both virus-to-cell and cell-to-cell transmissions and time delay in immune response is investigated. Mathematical analysis shows that delay may destabilize the infected steady state and lead to Hopf bifurcation. Moreover, the direction of the Hopf bifurcation and the stability of the periodic solutions are investigated by normal form and center manifold theory.Numerical simulations are done to explore the rich dynamics,including stability switches, Hopf bifurcations, and chaotic oscillations.https://www.aimspress.com/article/doi/10.3934/mbe.2015006time delaycell-to-cell transmissionhopf bifurcationchaotic oscillations.stabilityswitches |
| spellingShingle | Jinhu Xu Yicang Zhou Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay Mathematical Biosciences and Engineering time delay cell-to-cell transmission hopf bifurcation chaotic oscillations. stabilityswitches |
| title | Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay |
| title_full | Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay |
| title_fullStr | Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay |
| title_full_unstemmed | Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay |
| title_short | Bifurcation analysis of HIV-1 infection model with cell-to-cell transmission and immune response delay |
| title_sort | bifurcation analysis of hiv 1 infection model with cell to cell transmission and immune response delay |
| topic | time delay cell-to-cell transmission hopf bifurcation chaotic oscillations. stabilityswitches |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015006 |
| work_keys_str_mv | AT jinhuxu bifurcationanalysisofhiv1infectionmodelwithcelltocelltransmissionandimmuneresponsedelay AT yicangzhou bifurcationanalysisofhiv1infectionmodelwithcelltocelltransmissionandimmuneresponsedelay |