On the global dynamics of the cancer AIDS-related mathematical model

Konstantin E. Starkov; Corina Plata-Ante

Kybernetika (2014)

  • Volume: 50, Issue: 4, page 563-579
  • ISSN: 0023-5954

Abstract

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In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive orthant. Finally, we derive the main result of this work: sufficient conditions of ultimate cancer free behavior.

How to cite

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Starkov, Konstantin E., and Plata-Ante, Corina. "On the global dynamics of the cancer AIDS-related mathematical model." Kybernetika 50.4 (2014): 563-579. <http://eudml.org/doc/262011>.

@article{Starkov2014,
abstract = {In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive orthant. Finally, we derive the main result of this work: sufficient conditions of ultimate cancer free behavior.},
author = {Starkov, Konstantin E., Plata-Ante, Corina},
journal = {Kybernetika},
keywords = {cancer growth model; AIDS; compact invariant set; omega-limit set; localization; ultimate cancer free dynamics; cancer growth model; AIDS; compact invariant set; omega-limit set; localization; ultimate cancer free dynamics},
language = {eng},
number = {4},
pages = {563-579},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the global dynamics of the cancer AIDS-related mathematical model},
url = {http://eudml.org/doc/262011},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Starkov, Konstantin E.
AU - Plata-Ante, Corina
TI - On the global dynamics of the cancer AIDS-related mathematical model
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 4
SP - 563
EP - 579
AB - In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive orthant. Finally, we derive the main result of this work: sufficient conditions of ultimate cancer free behavior.
LA - eng
KW - cancer growth model; AIDS; compact invariant set; omega-limit set; localization; ultimate cancer free dynamics; cancer growth model; AIDS; compact invariant set; omega-limit set; localization; ultimate cancer free dynamics
UR - http://eudml.org/doc/262011
ER -

References

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