Latest Research in Mathematical Modeling in Cancer Research

Editor


E-Mail Website
Guest Editor
1. Department of Mathematics, Faculty of Science, Jerusalem College of Technology, Jerusalem 91160, Israel
2. Faculty of Computer Science, College of Management Academic Studies, Rishon LeTsiyon 75190, Israel
Interests: machine learning; tumor-immune system; mathematical modeling; asymptotic analysis; partial differential equations

Special Issue Information

Dear Colleagues,

This Special Issue focuses on the application of mathematical and computational techniques across various scientific disciplines, including biology, chemistry, and physics. We are particularly interested in mathematical modeling related to cancer treatment, emphasizing the interaction between cancerous tumors, the immune system, and therapeutic approaches such as chemotherapy and immunotherapy.

The scope of this Special Issue includes mathematical models for various cancer types, including bladder cancer, breast cancer, prostate cancer, liver cancer, brain cancer, and cervical cancer. Research contributions should employ innovative numerical methods, semi-analytical approaches, analytical techniques, or asymptotic methods to analyze these models.

A crucial aspect of mathematical modeling in cancer research is understanding the stability of equilibrium points within these models, providing insights into the dynamics of tumor progression and treatment responses. We also emphasize the importance of practical applications, and all submitted papers must include real-world examples demonstrating the effectiveness of the proposed methods.

Additionally, this Special Issue welcomes contributions that explore the role of machine learning in cancer research, particularly in handling and analyzing large datasets related to tumor growth, treatment outcomes, and patient responses.

We invite researchers to submit high-quality original work that advances the mathematical and computational understanding of cancer treatment.

Dr. Ophir Nave
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • machine learning
  • tumor–immune system interaction
  • mathematical modeling of cancer treatment
  • immunotherapy and chemotherapy treatment
  • asymptotic analysis
  • numerical methods
  • numerical computation
  • fractional differential equations
  • bifurcation
  • ordinary differential equations
  • partial differential equations
  • big data

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

16 pages, 2922 KB  
Article
Mathematical Modeling for Tumor–Immune Dynamics with Clinical Validation
by Mohsin Kamran, Johari Yap Abdullah and Abdul Majeed
Math. Comput. Appl. 2026, 31(4), 123; https://doi.org/10.3390/mca31040123 - 6 Jul 2026
Viewed by 264
Abstract
Pituitary adenoma is a clinically important brain tumor whose progression and therapeutic outcomes are influenced by intricate interactions between tumor development and the host immune response. Globally, pituitary adenomas account for approximately 15% of all intracranial tumors. This study aims to investigate clinical [...] Read more.
Pituitary adenoma is a clinically important brain tumor whose progression and therapeutic outcomes are influenced by intricate interactions between tumor development and the host immune response. Globally, pituitary adenomas account for approximately 15% of all intracranial tumors. This study aims to investigate clinical MRI data obtained from a patient who recovered from a pituitary adenoma. The collected data provide measurements of tumor volume (mm) at several time points throughout the treatment period. The patient received vaccine-based therapy accompanied by regular clinical assessments, and achieved recovery after nearly twenty-two months. Motivated by the clinical observations and the underlying treatment mechanism, a mathematical model describing tumor–immune–vaccine interactions is developed. The proposed ordinary differential equation (ODE) framework incorporates tumor cells, immune cells, and vaccine components to characterize the temporal evolution of tumor volume during treatment. Fundamental dynamical properties of the model, including positivity, boundedness, existence of solutions, and equilibrium stability, are established through analytical techniques. In addition, numerical simulations are performed using the fourth-order Runge–Kutta (RK4) method and validated against the available clinical measurements. The numerical results exhibit close agreement between the observed and simulated data, yielding a minimal root mean square error (RMSE). Furthermore, sensitivity analysis highlights the significant role of immune- and vaccine-related parameters in regulating tumor suppression. The findings suggest that a relatively simple mechanistic framework can effectively capture the reduction in pituitary adenoma under vaccine-based therapy. Full article
(This article belongs to the Special Issue Latest Research in Mathematical Modeling in Cancer Research)
Show Figures

Figure 1

23 pages, 3625 KB  
Article
Application of Biphasic Numerical Model for the Prediction of Colorectal Carcinoma Cell Response to Co-Treatments
by Dragana Šeklić, Milena Jovanović, Dalibor Nikolić and Tijana Đukić
Math. Comput. Appl. 2026, 31(3), 109; https://doi.org/10.3390/mca31030109 - 17 Jun 2026
Viewed by 305
Abstract
Modern computational biology is increasingly applied in preclinical studies, and mathematical models can provide valuable insights into biological system behavior. Numerical modeling tools can significantly and rapidly help in predicting the cellular response to different treatments, numerous newly synthesized compounds tested on different [...] Read more.
Modern computational biology is increasingly applied in preclinical studies, and mathematical models can provide valuable insights into biological system behavior. Numerical modeling tools can significantly and rapidly help in predicting the cellular response to different treatments, numerous newly synthesized compounds tested on different model systems. This study is devoted to the application of a biphasic numerical model to explain and predict the behavior of colorectal carcinoma cell lines in investigated co-treatments. The model was used to estimate parameters related to cell proliferation and death and to predict cellular behavior through the determination of treatment efficiency and effectiveness. This study showed that the experimental results can be mathematically confirmed, and the data for the most effective treatment can be obtained. The most efficient co-treatment concentration was identified by the model as the condition associated with the lowest proliferation-related parameter and the greatest reduction in cell viability. The model indicated that the most efficient concentration does not appear to induce a rapid adaptive cellular response and may therefore represent a suitable candidate for subsequent treatment cycles. The model suggests that the investigated treatments may have limited therapeutic potential in both cell lines due to the sustained viability of rapidly proliferating cells and evidence of continued de-differentiation. Full article
(This article belongs to the Special Issue Latest Research in Mathematical Modeling in Cancer Research)
Show Figures

Graphical abstract

Back to TopTop