# American Institute of Mathematical Sciences

2008, 5(3): 457-476. doi: 10.3934/mbe.2008.5.457

## 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, Japan 2 Aihara Complexity Modelling Project, ERATO, JST, The Tokyou University, 4-6-1 Komaba Meguro-ku Tokyo 153-8505, Japan 3 Department of Systems Engineering, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561

Received  September 2007 Revised  April 2008 Published  June 2008

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. Mathematical Biosciences & Engineering, 2008, 5 (3) : 457-476. doi: 10.3934/mbe.2008.5.457
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