Kybernetika 50 no. 4, 563-579, 2014

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

Konstantin E. Starkov and Corina Plata-AnteDOI: 10.14736/kyb-2014-4-0563


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.


cancer growth model, AIDS, compact invariant set, omega-limit set, localization, ultimate cancer free dynamics


34C11, 34D23, 92D25, 93D20


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