Ultimate Dynamics of the Two-Phenotype Cancer Model: Attracting Sets and Global Cancer Eradication Conditions

Anatolij N. Kanatnikov and Konstantin E. Starkov ()
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Anatolij N. Kanatnikov: Department of Mathematical Modeling, Bauman Moscow State Technical University, Moscow 105005, Russia
Konstantin E. Starkov: Instituto Politecnico Nacional, CITEDI, Av. IPN 1310, Nueva Tijuana 22435, Mexico

Mathematics, 2023, vol. 11, issue 20, 1-19

Abstract: In this paper we consider the ultimate dynamics of one 4D cancer model which was created for studying the immune response to the two-phenotype tumors. Our approach is based on the localization method of compact invariant sets. The existence of a positively invariant polytope is shown and its size is calculated depending on the parameters of this cancer model. Various convergence conditions to the tumor free equilibrium point were proposed. This property has the biological meaning of global asymptotic tumor eradication (GATE). Further, the case in which local asymptotic tumor eradication (LATE) conditions entail GATE conditions was found. Our theoretical studies of ultimate dynamics are complemented by numerical simulation results.

Keywords: cancer model; global stability; localization; compact invariant set; ultimate bounds; cancer eradication (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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