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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 3: 457-476. doi: 10.3934/mbe.2008.5.457
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Mathematical analysis of a HIV model with frequency dependence and viral diversity

  • 1.
    Graduate School of Science and Technology, Shizuoka University, 3-5-1 Johoku Naka-ku Hamamatsu 432-8561
  • 2.
    Aihara Complexity Modelling Project, ERATO, JST, The Tokyou University, 4-6-1 Komaba Meguro-ku Tokyo 153-8505
  • 3.
    Department of Systems Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561
  • Received: 01 September 2007 Accepted: 29 June 2018 Published: 01 June 2008

  • MSC : Primary: 34D20, 34D23; Secondary: 92B05.

  • We consider the effect of viral diversity on the human immune sys- tem with the frequency dependent proliferation rate of CTLs and the elimina- tion rate of infected cells by CTLs. The model has very complex mathematical structures such as limit cycle, quasi-periodic attractors, chaotic attractors, and so on. To understand the complexity we investigate the global behavior of the model and demonstrate the existence and stability conditions of the equilibria. Further we give some theoretical considerations obtained by our mathematical model to HIV infection.

    Citation: Shingo Iwami, Shinji Nakaoka, Yasuhiro Takeuchi. Mathematical analysis of a HIV model with frequency dependence and viral diversity[J]. Mathematical Biosciences and Engineering, 2008, 5(3): 457-476. doi: 10.3934/mbe.2008.5.457

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  • We consider the effect of viral diversity on the human immune sys- tem with the frequency dependent proliferation rate of CTLs and the elimina- tion rate of infected cells by CTLs. The model has very complex mathematical structures such as limit cycle, quasi-periodic attractors, chaotic attractors, and so on. To understand the complexity we investigate the global behavior of the model and demonstrate the existence and stability conditions of the equilibria. Further we give some theoretical considerations obtained by our mathematical model to HIV infection.


  • This article has been cited by:

    1. Tongqian Zhang, Junling Wang, Yi Song, Zhichao Jiang, Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells, 2020, 2020, 1076-2787, 1, 10.1155/2020/2313102
    2. Yusuke Kato, Hiroshi Kori, Synchronization and stability analysis of an exponentially diverging solution in a mathematical model of asymmetrically interacting agents, 2023, 33, 1054-1500, 10.1063/5.0151174
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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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