Open AccessMathematical analysis of a HIV model with frequency dependence and viral diversity
Author(s) -
Shingo Iwami,
Shinji Nakaoka,
Yasuhiro Takeuchi
Publication year - 2008
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2008.5.457
Subject(s) - attractor , human immunodeficiency virus (hiv) , chaotic , diversity (politics) , statistical physics , stability (learning theory) , mathematical model , limit cycle , mathematics , limit (mathematics) , physics , biology , virology , mathematical analysis , computer science , statistics , sociology , artificial intelligence , machine learning , anthropology
We consider the effect of viral diversity on the human immune system with the frequency dependent proliferation rate of CTLs and the elimination 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.