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

Autor:	Anatolij N. Kanatnikov, Konstantin E. Starkov
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	cancer model global stability localization compact invariant set ultimate bounds cancer eradication Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 20, p 4275 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11204275
Popis:	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.
Databáze:	Directory of Open Access Journals
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