https://doi.org/10.1140/epjp/s13360-024-05573-6
Regular Article
Modeling the dynamics of tumor–immune response: a reaction–diffusion approach integrating chemotherapy effects and global sensitivity analysis
Department of Mathematics, Indian Institute of Engineering Science and Technology, 711103, Shibpur, Howrah, India
Received:
26
June
2024
Accepted:
20
August
2024
Published online:
1
September
2024
This work presents a mathematical reaction–diffusion model designed to investigate the intricate dynamics of the immune response to tumors, conceptualizing this interaction as a predator–prey system. The immune system is delineated into resting T cells, serving as stimulators for the transformation of cytotoxic T lymphocytes into active hunting CTL cells which are tasked with the elimination of tumor cells. This model incorporates the influence of chemotherapeutic drugs and focuses on establishing the conditions for both tumor cell elimination and coexistence of resting cells, hunting cells, as well as tumor cells. Analytical and numerical simulations provide various types of local bifurcations in one parametric as well as two-parametric planes such as transcritical, Hopf, saddle-node, and cusp bifurcations. Uncertainty and sensitivity analyses are essential for understanding the behavior of complex models due to structural complexity and significant uncertainty in input parameter estimates. While uncertainty analysis assesses the variability of outcome variables considering parameter uncertainty, sensitivity analysis identifies influential parameters and quantifies their impact on model outcomes. Sampling-based methods like Latin hypercube sampling and global sensitivity analysis techniques such as partial rank correlation coefficient are employed to handle uncertainty and sensitivity in complex models that provide valuable insights into parameter relationships and model behavior. Additionally, a diffusion analysis provides insights into the spatial distribution of cell density. Through linear stability analysis at the local equilibrium, optimal conditions for system’s instability and the emergence of Turing patterns are derived. Numerical simulations illustrate the spatial distributions of cells for the change of various important parameter like rate of chemotherapeutic drugs dosage, proliferation rate of resting cells, etc. These comprehensive approaches, which utilize mathematical analysis and numerical simulation, contribute in figuring out potential patterns and their evolutionary dynamics. Ultimately, it enhances the understanding of biological importance of the immune system.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
