A delay-differential equation model of HIV related cancer--immune system dynamics

Urszula Foryś; Jan Poleszczuk; Urszula Foryś; Jan Poleszczuk

doi:10.3934/mbe.2011.8.627

Mathematical Biosciences and Engineering

2011, Volume 8, Issue 2: 627-641. doi: 10.3934/mbe.2011.8.627

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A delay-differential equation model of HIV related cancer--immune system dynamics

1.
University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 Warsaw

Received: 01 March 2010 Accepted: 29 June 2018 Published: 01 April 2011
MSC : 92C60, 37G15, 34K20, 34K60.

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$4^+$ 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.
- cancer,
- time delay,
- AIDS,
- stability switches.,
- HIV infection
Citation: Urszula Foryś, Jan Poleszczuk. A delay-differential equation model of HIV related cancer--immune system dynamics[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 627-641. doi: 10.3934/mbe.2011.8.627

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Abstract

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$4^+$ 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.
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