Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages
We study the global dynamics of an HIV infection model describing the interaction of the HIV with CD4+ T cells and macrophages. The incidence rate of virus infection and the growth rate of the uninfected CD4+ T cells and macrophages are given by general functions. We have incorporated two types of d...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/264759 |
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| author | A. M. Elaiw A. S. Alsheri |
| author_facet | A. M. Elaiw A. S. Alsheri |
| author_sort | A. M. Elaiw |
| collection | DOAJ |
| description | We study the global dynamics of an HIV infection model describing the interaction of the HIV with CD4+ T cells and macrophages. The incidence rate of virus infection and the growth rate of the uninfected CD4+ T cells and macrophages are given by general functions. We have incorporated two types of distributed delays into the model to account for the time delay between the time the uninfected cells are contacted by the virus particle and the time for the emission of infectious (matures) virus particles. We have established a set of conditions which are sufficient for the global stability of the steady states of the model. Using Lyapunov functionals and LaSalle's invariant principle, we have proven that if the basic reproduction number R0 is less than or equal to unity, then the uninfected steady state is globally asymptotically stable (GAS), and if the infected steady state exists, then it is GAS. |
| format | Article |
| id | doaj-art-0dbd53fb8c2348189132c89bf69d4c75 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-0dbd53fb8c2348189132c89bf69d4c752025-02-03T06:11:36ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/264759264759Global Dynamics of HIV Infection of CD4+ T Cells and MacrophagesA. M. Elaiw0A. S. Alsheri1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe study the global dynamics of an HIV infection model describing the interaction of the HIV with CD4+ T cells and macrophages. The incidence rate of virus infection and the growth rate of the uninfected CD4+ T cells and macrophages are given by general functions. We have incorporated two types of distributed delays into the model to account for the time delay between the time the uninfected cells are contacted by the virus particle and the time for the emission of infectious (matures) virus particles. We have established a set of conditions which are sufficient for the global stability of the steady states of the model. Using Lyapunov functionals and LaSalle's invariant principle, we have proven that if the basic reproduction number R0 is less than or equal to unity, then the uninfected steady state is globally asymptotically stable (GAS), and if the infected steady state exists, then it is GAS.http://dx.doi.org/10.1155/2013/264759 |
| spellingShingle | A. M. Elaiw A. S. Alsheri Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages Discrete Dynamics in Nature and Society |
| title | Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages |
| title_full | Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages |
| title_fullStr | Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages |
| title_full_unstemmed | Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages |
| title_short | Global Dynamics of HIV Infection of CD4+ T Cells and Macrophages |
| title_sort | global dynamics of hiv infection of cd4 t cells and macrophages |
| url | http://dx.doi.org/10.1155/2013/264759 |
| work_keys_str_mv | AT amelaiw globaldynamicsofhivinfectionofcd4tcellsandmacrophages AT asalsheri globaldynamicsofhivinfectionofcd4tcellsandmacrophages |