On the Dynamics of Immune-Tumor Conjugates in a Four-Dimensional Tumor Model

Konstantin E. Starkov () and Alexander P. Krishchenko
Additional contact information
Konstantin E. Starkov: Instituto Politecnico Nacional, CITEDI, Av. IPN 1310, Nueva Tijuana, Tijuana 22435, Mexico
Alexander P. Krishchenko: Department of Mathematical Modeling, Bauman Moscow State Technical University, 2-ya Baumanskaya, 5, Moscow 105005, Russia

Mathematics, 2024, vol. 12, issue 6, 1-16

Abstract: We examine the ultimate dynamics of the four-dimensional model describing interactions between host cells, immune cells, tumor cells, and immune-tumor conjugate cells proposed by Abernethy and Gooding in 2018. In our paper, the ultimate upper bounds for all variables of this model are obtained. Formulas for positively invariant sets are deduced. Using these results, we establish conditions for the existence of the global attractor, derive formulas for its location, and present conditions under which immune and immune-tumor conjugate cells asymptotically die out. Next, we study equilibrium points, including the stability property for most of the equilibrium points. We discuss the existence of very low cancer-burden equilibrium points. Next, parametric conditions are derived under which the derivative of the density of the immune-tumor conjugate cell population eventually tends to zero; this mathematically rigorously confirms the correctness of the application of model reduction for this model in studies of its ultimate dynamics. In the final section, we summarize the results of this work and outline how to continue this study.

Keywords: cancer model; attractor; localization; compact invariant set; ultimate bounds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/6/843/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/6/843/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:6:p:843-:d:1356375

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().