Geodesic
On the global dynamics of the cancer AIDS-related mathematical model
Kybernetika, Tome 50 (2014) no. 4, pp. 563-579

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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.
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.
DOI : 10.14736/kyb-2014-4-0563
Classification : 34C11, 34D23, 92D25, 92D30, 93D20
Keywords: cancer growth model; AIDS; compact invariant set; omega-limit set; localization; ultimate cancer free dynamics 
Starkov, Konstantin E.; Plata-Ante, Corina. On the global dynamics of the cancer AIDS-related mathematical model. Kybernetika, Tome 50 (2014) no. 4, pp. 563-579. doi: 10.14736/kyb-2014-4-0563
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