Applied Mathematical Modeling in Oncology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 736

Special Issue Editors


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Guest Editor
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA
Interests: mathematical biology; numerical analysis; problems of fluid flow; random problems
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Interests: quantitative systems modeling; inverse problems; optimal control; medical imaging

E-Mail Website
Guest Editor
Department of Mathematics, The University of Texas at Arlington, Arlington, TX 76019, USA
Interests: nonstandard finite difference methods; modeling and analysis of biological systems

Special Issue Information

Dear Colleagues,

Mathematical modeling is increasingly vital in oncology, offering crucial insights into cancer biology and enabling improved prognosis, prediction, treatment planning, and intervention. Various applications range from analytical models to agent-based simulations of complex dynamics. Furthermore, advancements in imaging systems and experimental techniques provide unparalleled data for testing, validating, and enhancing proposed models.

In this Special Issue, we solicit submissions with a focus on state-of-the-art contributions in the field of mathematical oncology that bring together novel modeling approaches including deterministic, stochastic, and agent-based models, guided and validated by experimental data.

Prof. Dr. Benito Chen-Charpentier
Dr. Souvik Roy
Prof. Dr. Hristo V. Kojouharov
Guest Editors

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Keywords

  • mathematical modeling
  • pharmacokinetics
  • pharmacodynamics
  • stochastic
  • differential equations

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Published Papers (1 paper)

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Research

22 pages, 488 KiB  
Article
Dynamics of a Model of Tumor–Immune Cell Interactions Under Chemotherapy
by Rubayyi T. Alqahtani, Abdelhamid Ajbar and Eman Hamed Aljebli
Mathematics 2025, 13(13), 2200; https://doi.org/10.3390/math13132200 - 5 Jul 2025
Viewed by 263
Abstract
This paper analyzes a mathematical model to investigate the complex interactions between tumor cells, immune cells (natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs)) and chemotherapy. The primary objectives are to analyze tumor–immune interactions without and under treatment, identify critical thresholds [...] Read more.
This paper analyzes a mathematical model to investigate the complex interactions between tumor cells, immune cells (natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs)) and chemotherapy. The primary objectives are to analyze tumor–immune interactions without and under treatment, identify critical thresholds for tumor eradication, and evaluate how chemotherapy parameters influence therapeutic outcomes. The model integrates NK cells and CTLs as effector cells, combining their dynamics linearly for simplicity. Tumor growth follows a logistic function, while immune–tumor interactions are modeled using a Hill function for fractional cell death. Stability and bifurcation analysis are employed to identify equilibria (tumor-free, high-tumor, and a novel middle steady state), bistability regimes, and critical parameter thresholds. Numerical simulations use experimentally validated parameter values from the literature. This mathematical analysis provides a framework for assessing the efficacy of chemotherapy by examining the dynamic interplay between tumor biology and treatment parameters. Our findings reveal that treatment outcomes are sensitive to the balance between the immune system’s biological parameters and chemotherapy-specific factors. The model highlights scenarios where chemotherapy may fail due to bistability and identifies critical thresholds for successful tumor eradication. These insights can guide clinical decision making in dosing strategies and suggest combination therapies such as immunotherapy–chemotherapy synergies to shift the system toward favorable equilibria. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling in Oncology)
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