Modeling the Treatment of Tumor Cells in a Solid TumorResearch Paper, June 17, 2014 / Lorand Gabriel Parajdi
Published in Journal of Nonlinear Science and Applications, 7(3), 188–195, DOI: 10.22436/jnsa.007.03.05, 2014.
The full paper is available on the JNSA website: https://www.isr-publications.com/jnsa/articles-1896-modeling-the-treatment-of-tumor-cells-in-a-solid-tumor
Abstract: It is well known that the theory of differential equations and some software packages are important tools for solving several actual problems from different real world domains. The novelty of this paper is the fact that the mathematical model of evolution of leukemic cells is adapted to the case of tumor cells, from a solid tumor, together with the treatment of the solid homogeneous tumor. Using the paper Dingli and Michor [D. Dingli, F. Michor, STEM-CELLS, 24 (2006), 2603-2610], we consider the model of evolution of a leukemic population for the case of solid tumors.
Subject Classification: 92B05, 34C60, 34A12
Keywords: Cauchy problem; Mathematical model; Solid tumor; Tumor cells; System of differential equations.
Cite As: Parajdi Lorand, Modeling the treatment of tumor cells in a solid tumor. J. Nonlinear Sci. Appl. (2014); 7(3):188–195.
1. S. Arghirescu, A. Cucuianu, R. Precup, M. Şerban, Mathematical Modeling of Cell Dynamics after Allogeneic Bone Marrow Transplantation in Acute Myeloid Leukemia, Int. J. Biomath., 5 (2012), 18 Pages. [Article]
2. A. Cucuianu, R. Precup, A Hypothetical-Mathematical Model of Acute Myeloid Leukaemia Pathogenesis, Comput. Math. Methods Med., 11 (2010), 49-65. [Article]
3. D. Dingli, F. Michor, Successful Therapy Must Eradicate Cancer Stem Cells, STEM-CELLS, 24 (2006), 2603- 2610. [Article]
4. J. Guckenheimer, P. Holmes, Nonlineat Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, Springer-Verlag, 1983. [Book]
5. C. Iancu, I. A. Rus, Mathematical Modeling, Transilvania Press, Cluj-Napoca 1996. [Book]
6. S. Lynch, Dynamical Systems with Applications using Maple, second edition, Birkhäuser , Boston 2009. [Book]
7. L. Preziosi , Cancer modelling and simulation, Ed. Chapman & Hall/CRC, 2003. [Book]
8. R. Precup, M. A. Şerban, D. Trif , Asymptotic stability for cell dynamics after bone marrow transplantation, The 8th Joint Conference on Mathematics and Computer Science, Komarno, Slovakia, (2010), 1-11. [Book of Abstracts]
9. R. W. Shonkwiler, J. Herod, Mathematical Biology, Ed. Springer, 2009. [Book]
10. Z. Zeng , Scientific Computing with Maple Programming, 2001. [Book]