Tumor–Immune Dynamics: A Spatial-Spectral Perspective

Serpil Yılmaz

doi:10.33187/jmsm.1681375

EN

Tumor–Immune Dynamics: A Spatial-Spectral Perspective

Abstract

Mathematical modeling of tumor–immune interactions provides valuable insights into the nonlinear dynamics that govern tumor progression and response to treatment. In this study, a deterministic model of the tumor–immune system under chemotherapy is investigated with a focus on spectral entropy and basin of attraction analyses. Spectral entropy is applied to quantify the temporal complexity of system dynamics and to detect transitions between qualitatively distinct behavioral regimes, such as steady states, oscillatory patterns, and potentially chaotic trajectories. Basin of attraction analysis investigates how variations in the initial populations of tumor and immune cells determine the long-term behavior of the system, including tumor elimination, persistent oscillations, or uncontrolled tumor growth. By combining spectral entropy with basin mapping, the framework captures both the temporal irregularity and the sensitivity to initial conditions inherent in tumor–immune dynamics, which may help guide the design and timing of more effective therapeutic interventions.

Keywords

Basins of attraction, Dynamical systems, Entropy measures, Spectral analysis, Tumor-immune interactions

References

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Serpil Yılmaz ^*
0000-0002-6276-6058
Türkiye

Early Pub Date

June 25, 2025

Publication Date

June 28, 2025

Submission Date

April 21, 2025

Acceptance Date

June 24, 2025

Published in Issue

Year 2025 Volume: 8 Number: 2

DOI

https://doi.org/10.33187/jmsm.1681375

IZ

https://izlik.org/JA88YS39TS

APA

Yılmaz, S. (2025). Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling, 8(2), 86-92. https://doi.org/10.33187/jmsm.1681375

AMA

1.Yılmaz S. Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling. 2025;8(2):86-92. doi:10.33187/jmsm.1681375

Chicago

Yılmaz, Serpil. 2025. “Tumor–Immune Dynamics: A Spatial-Spectral Perspective”. Journal of Mathematical Sciences and Modelling 8 (2): 86-92. https://doi.org/10.33187/jmsm.1681375.

EndNote

Yılmaz S (June 1, 2025) Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling 8 2 86–92.

IEEE

[1]S. Yılmaz, “Tumor–Immune Dynamics: A Spatial-Spectral Perspective”, Journal of Mathematical Sciences and Modelling, vol. 8, no. 2, pp. 86–92, June 2025, doi: 10.33187/jmsm.1681375.

ISNAD

Yılmaz, Serpil. “Tumor–Immune Dynamics: A Spatial-Spectral Perspective”. Journal of Mathematical Sciences and Modelling 8/2 (June 1, 2025): 86-92. https://doi.org/10.33187/jmsm.1681375.

JAMA

1.Yılmaz S. Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling. 2025;8:86–92.

MLA

Yılmaz, Serpil. “Tumor–Immune Dynamics: A Spatial-Spectral Perspective”. Journal of Mathematical Sciences and Modelling, vol. 8, no. 2, June 2025, pp. 86-92, doi:10.33187/jmsm.1681375.

Vancouver

1.Serpil Yılmaz. Tumor–Immune Dynamics: A Spatial-Spectral Perspective. Journal of Mathematical Sciences and Modelling. 2025 Jun. 1;8(2):86-92. doi:10.33187/jmsm.1681375