On the global dynamics of a chronic myelogenous leukemia model

Alexander P. Krishchenko, Konstantin E. Starkov

Research output: Contribution to journalArticle

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Abstract

© 2015 Elsevier B.V. In this paper we analyze some features of global dynamics of a three-dimensional chronic myelogenous leukemia (CML) model with the help of the stability analysis and the localization method of compact invariant sets. The behavior of CML model is defined by concentrations of three cellpopulations circulating in the blood: naive T cells, effector T cells specific to CML and CML cancer cells. We prove that the dynamics of the CML system around the tumor-free equilibrium point is unstable. Further, we compute ultimate upper bounds for all three cell populations and provide the existence conditions of the positively invariant polytope. One ultimate lower bound is obtained as well. Moreover, we describe the iterative localization procedure for refining localization bounds; this procedure is based on cyclic using of localizing functions. Applying this procedure we obtain conditions under which the internal tumor equilibrium point is globally asymptotically stable. Our theoretical analyses are supplied by results of the numerical simulation.
Original languageAmerican English
Pages (from-to)174-183
Number of pages155
JournalCommunications in Nonlinear Science and Numerical Simulation
DOIs
StatePublished - 1 Jan 2016

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