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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Abstract
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.