Global properties of a class of HIV infection models with Beddington–DeAngelis functional response |
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Authors: | A M Elaiw S A Azoz |
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Institution: | 1. Department of Mathematics, Faculty of Science, King Abdulaziz University, , Jeddah 21589, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Al‐Azhar University, , Assiut, Egypt;3. Department of Mathematics, Faculty of Science, Assiut University, , Assiut, Egypt |
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Abstract: | In this paper, the global properties of a class of human immunodeficiency virus (HIV) models with Beddington–DeAngelis functional response are investigated. Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states of three HIV infection models. The first model considers the interaction process of the HIV and the CD4 + T cells and takes into account the latently and actively infected cells. The second model describes two co‐circulation populations of target cells, representing CD4 + T cells and macrophages. The third model is a two‐target‐cell model taking into account the latently and actively infected cells. We have proven that if the basic reproduction number R0 is less than unity, then the uninfected steady state is globally asymptotically stable, and if R0 > 1, then the infected steady state is globally asymptotically stable. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | global stability HIV/AIDS Beddington– DeAngelis functional response direct Lyapunov method |
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