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Mathematics
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Mathematical Models and Applications in Cancer
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Mathematical Models and Applications in Cancer

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

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 3695

Special Issue Editors

Prof. Dr. Maria Rosa

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Guest Editor
Departamento de Matemáticas, University of Cádiz, Puerto Real, 11003 Cádiz, Spain
Interests: numerical analysis; mathematical modeling; partial differential equations; mathematical oncology
Special Issues, Collections and Topics in MDPI journals
Dr. Salvador Chulián

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Guest Editor
Departamento de Matemáticas, University of Cádiz, Puerto Real, 11003 Cádiz, Spain
Interests: dynamical systems; mathematical modelling; machine learning; mathematical oncology
Dr. Álvaro Martínez-Rubio

E-Mail Website
Guest Editor
Departamento de Matemáticas, University of Cádiz, Puerto Real, 11003 Cádiz, Spain
Interests: dynamical systems; mathematical modelling; discrete models; mathematical oncology

Special Issue Information

Dear Colleagues,

Mathematical models are used routinely in many areas of Science and Engineering as the standard way of providing conceptual frameworks to understand nature and provide solutions to real-world problems. It has been only recently that this methodology, beyond the classical statistical studies, has started to be used in medicine and specifically in cancer research. Many concepts of potential relevance in cancer have been proposed coming from mathematical approaches ranging from evolutionary dynamics concepts to adaptive and metronomic therapies.

The purpose of this Special Issue is to present recent advances in mathematical oncology and applications of mathematical models. Editors invite authors to submit original research articles and high-quality review articles on the development, analysis, and simulation of mathematical models based on ordinary differential equations, dynamical systems, partial differential equations, discrete and stochastic approaches, and others. 

Dr. Maria Rosa
Dr. Salvador Chulián
Dr. Álvaro Martínez-Rubio
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics 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 2600 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

  • mathematical modeling
  • population dynamics
  • mathematical oncology
  • biomedical modeling
  • differential equations

Published Papers (2 papers)

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Research

6 pages, 407 KiB  
Article
Testing Doses and Treatment Timelines of Anti-Angiogenic Drug Bevacizumab Numerically as a Single-Agent for the Treatment of Ovarian Cancer
by Dharma Raj Khatiwada and Miana Wallace
Mathematics 2023, 11(2), 358; https://0-doi-org.brum.beds.ac.uk/10.3390/math11020358 - 10 Jan 2023
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Abstract
An anti-angiogenic drug in cancer treatment prevents the growth of new blood vessels in tumors by binding to VEGF molecules, which otherwise induce endothelial cells inside blood vessels to sprout the blood supply toward the tumor. This would prevent the growth of new [...] Read more.
An anti-angiogenic drug in cancer treatment prevents the growth of new blood vessels in tumors by binding to VEGF molecules, which otherwise induce endothelial cells inside blood vessels to sprout the blood supply toward the tumor. This would prevent the growth of new blood cells which will deprive the tumor of nutrients, thus decreasing its carrying capacity, and ultimately shrinking its volume. With new vascularization absent, the tumor will be isolated, making it easier to treat. Although there is an availability of various anti-angiogenic drugs, their effectiveness is low compared to other cancer treatments. We are specifically pinpointing the various combination of doses and the treatment timelines as reasonable factors to increase the effectiveness of the anti-angiogenic drug Bevacizumab, which can possibly prolong the patient’s survival rate and offer lower toxicity compared to other treatment modalities such as radiotherapy and chemotherapy. We have numerically analyzed different doses of Bevacizumab, including 15 mg/kg, an FDA-approved dose if offered in conjunction with chemotherapy drugs, carboplatin and paclitaxel, as a single-agent treatment option. Based on the results, the tumor volume was observed to be stabilizing for the duration of the treatment, which was chosen to be 400 days. The toxicity levels of these doses with Bevacizumab as a single-agent treatment option have not been tested in a clinical setting. However, these mathematically promising results can provide a gateway for the successful treatment of ovarian cancer in the future. Full article
(This article belongs to the Special Issue Mathematical Models and Applications in Cancer)
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14 pages, 12502 KiB  
Article
A Discrete Dynamics Approach to a Tumor System
by Tareq Saeed, Kamel Djeddi, Juan L. G. Guirao, Hamed H. Alsulami and Mohammed Sh. Alhodaly
Mathematics 2022, 10(10), 1774; https://0-doi-org.brum.beds.ac.uk/10.3390/math10101774 - 23 May 2022
Cited by 2 | Viewed by 1514
Abstract
In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the cancer system. We [...] Read more.
In this paper, we present a cancer system in a continuous state as well as some numerical results. We present discretization methods, e.g., the Euler method, the Taylor series expansion method, and the Runge–Kutta method, and apply them to the cancer system. We studied the stability of the fixed points in the discrete cancer system using the new version of Marotto’s theorem at a fixed point; we prove that the discrete cancer system is chaotic. Finally, we present numerical simulations, e.g., Lyapunov exponents and bifurcations diagrams. Full article
(This article belongs to the Special Issue Mathematical Models and Applications in Cancer)
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