Analysis of immunotherapeutic control of the TH1/TH2 imbalance in a 4D melanoma model applying the invariant compact set localization method

This paper evaluates the nonlinear dynamics of a melanoma cancer model through the iterative technique of finding compact invariant sets (LMCIS). The objective is to discover equilibrium points, ascertain their stability qualities, and determine the presence of compact invariant sets within the mode...

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Published inAlexandria engineering journal Vol. 107; pp. 838 - 850
Main Authors Gómez-Guzmán, Marco Antonio, Inzunza-González, Everardo, Palomino-Vizcaino, Kenia, Esqueda-Elizondo, José Jaime, García-Guerrero, Enrique Efren, López-Bonilla, Oscar Roberto, Tamayo-Perez, Ulises Jesús, Jiménez-Beristáin, Laura
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2024
Elsevier
Subjects
Compact invariant sets
Immune response
Mathematical model
Melanoma
Nonlinear dynamics
Nonlinear dynamics
Immune response
Mathematical model
Melanoma
Compact invariant sets
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Summary:This paper evaluates the nonlinear dynamics of a melanoma cancer model through the iterative technique of finding compact invariant sets (LMCIS). The objective is to discover equilibrium points, ascertain their stability qualities, and determine the presence of compact invariant sets within the model. For instance, this approach is assessed in a model demonstrating the interplay between four cellular populations and administrating interleukin-12 (IL-12) immunotherapy. Nevertheless, the mechanism by which this anti-cancer therapy operates has yet to be completely defined. The approach is evaluated using severe treatment situations to provide evidence for the presence of equilibrium points inside the iteratively confined zone and to assess its effectiveness. The outcomes derived from using this approach were then compared with a conventional iteration of Newton’s method. Newton’s approach extends to the resolution of the system of equations inside the model, facilitating the identification of the equilibrium points with a small tolerance error. While the iterations of the localization algorithm were set close to the results obtained by this method. Finally, the simulation outcomes are shown via the utilization of MATLAB R2020b. The findings demonstrate the temporal progression of the model under the effect of immunotherapy and without it.
ISSN:1110-0168
DOI:10.1016/j.aej.2024.09.023