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

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

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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

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.
  Article Metrics

Keywords frequency dependence; viral diversity; stability analysis.; HIV model

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


Reader Comments

your name: *   your email: *  

Copyright Info: 2008, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved