A Differential Equation Model of HIV Infection of CD4+ T-Cells with Delay
An epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined by the basic reproduction number R0<1....
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/903678 |
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| _version_ | 1849683411561611264 |
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| author | Junyuan Yang Xiaoyan Wang Fengqin Zhang |
| author_facet | Junyuan Yang Xiaoyan Wang Fengqin Zhang |
| author_sort | Junyuan Yang |
| collection | DOAJ |
| description | An epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined by the basic reproduction number R0<1. If R0<1, the disease-free equilibrium is asymptotically stable and the disease dies out. If R0>1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region. In the DDE model, the delay stands for the incubation time. We prove the effect of that delay on the stability of the equilibria. We show that the introduction of a time delay in the virus-to-healthy cells transmission term can destabilize the system, and periodic solutions can arise through Hopf bifurcation. |
| format | Article |
| id | doaj-art-d73d36d3d74746e9828bb16f5c5d6a20 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d73d36d3d74746e9828bb16f5c5d6a202025-08-20T03:23:52ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/903678903678A Differential Equation Model of HIV Infection of CD4+ T-Cells with DelayJunyuan Yang0Xiaoyan Wang1Fengqin Zhang2Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, ChinaDepartment of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, ChinaDepartment of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, ChinaAn epidemic model of HIV infection of CD4+ T-cells with cure rate and delay is studied. We include a baseline ODE version of the model, and a differential-delay model with a discrete time delay. The ODE model shows that the dynamics is completely determined by the basic reproduction number R0<1. If R0<1, the disease-free equilibrium is asymptotically stable and the disease dies out. If R0>1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region. In the DDE model, the delay stands for the incubation time. We prove the effect of that delay on the stability of the equilibria. We show that the introduction of a time delay in the virus-to-healthy cells transmission term can destabilize the system, and periodic solutions can arise through Hopf bifurcation.http://dx.doi.org/10.1155/2008/903678 |
| spellingShingle | Junyuan Yang Xiaoyan Wang Fengqin Zhang A Differential Equation Model of HIV Infection of CD4+ T-Cells with Delay Discrete Dynamics in Nature and Society |
| title | A Differential Equation Model of HIV Infection of CD4+ T-Cells with Delay |
| title_full | A Differential Equation Model of HIV Infection of CD4+ T-Cells with Delay |
| title_fullStr | A Differential Equation Model of HIV Infection of CD4+ T-Cells with Delay |
| title_full_unstemmed | A Differential Equation Model of HIV Infection of CD4+ T-Cells with Delay |
| title_short | A Differential Equation Model of HIV Infection of CD4+ T-Cells with Delay |
| title_sort | differential equation model of hiv infection of cd4 t cells with delay |
| url | http://dx.doi.org/10.1155/2008/903678 |
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