Mathematical analysis of a HIV model with frequency dependence and viral diversity

  • 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.


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