Open AccessModeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior
Author(s) -
Jie Lou,
Tommaso Ruggeri,
Claudio Tebaldi
Publication year - 2006
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.2006.3.313
Subject(s) - hopf bifurcation , chaotic , cancer , human immunodeficiency virus (hiv) , steady state (chemistry) , carcinogenesis , stability (learning theory) , bifurcation , biology , mathematics , immunology , virology , physics , nonlinear system , genetics , computer science , chemistry , quantum mechanics , artificial intelligence , machine learning
For HIV-infected individuals, cancer remains a significant burden. Gaining insight into the epidemiology and mechanisms that underlie AIDS- related cancers can provide us with a better understanding of cancer immunity and viral oncogenesis. In this paper, an HIV-1 dynamical model incorporat- ing the AIDS-related cancer cells was studied. The model consists of three components, cancer cells, healthy CD4+ T lymphocytes and infected CD4+ T lymphocytes, and can have six steady states. We discuss the existence, the stability properties and the biological meanings of these steady states, in par- ticular for the positive one: cancer-HIV-healthy cells steady state. We find conditions for Hopf bifurcation of the positive steady state, leading to periodic solutions, sequences of period doubling bifurcations and appearance of chaos. Further, chaos and periodic behavior alternate. Our results are consistent with some clinical and experimental observations.