Open AccessA delay-differential equation model of HIV related cancer--immune system dynamics
Author(s) -
Urszula Foryś,
Jan Poleszczuk
Publication year - 2011
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.2011.8.627
Subject(s) - immune system , delay differential equation , cancer , immunosuppression , human immunodeficiency virus (hiv) , dynamics (music) , stability (learning theory) , simple (philosophy) , biology , differential equation , mathematics , statistical physics , computer science , immunology , physics , mathematical analysis , genetics , philosophy , epistemology , machine learning , acoustics
In the human body, the appearance of tumor cells usually turns on the defensive immune mechanisms. It is therefore of great importance to understand links between HIV related immunosuppression and cancer prognosis. In the paper we present a simple model of HIV related cancer - immune system interactions in vivo which takes into account a delay describing the time needed by CD T lymphocyte to regenerate after eliminating a cancer cell. The model assumes also the linear response of immune system to tumor presence. We perform a mathematical analysis of the steady states stability and discuss the biological meanings of these steady states. Numerical simulations are also presented to illustrate the predictions of the model.