MODELLING TUMOR GROWTH WITH IMMUNE RESPONSE AND DRUG USING ORDINARY DIFFERENTIAL EQUATIONS
DOI:
https://doi.org/10.11113/jt.v79.9791Keywords:
Tumor growth, immune response, cycle phase specific drug, cell cycle, stability regionAbstract
This is a mathematical study about tumor growth from a different perspective, with the aim of predicting and/or controlling the disease. The focus is on the effect and interaction of tumor cell with immune and drug. This paper presents a mathematical model of immune response and a cycle phase specific drug using a system of ordinary differential equations. Stability analysis is used to produce stability regions for various values of certain parameters during mitosis. The stability region of the graph shows that the curve splits the tumor decay and growth regions in the absence of immune response. However, when immune response is present, the tumor growth region is decreased. When drugs are considered in the system, the stability region remains unchanged as the system with the presence of immune response but the population of tumor cells at interphase and metaphase is reduced with percentage differences of 1.27 and 1.53 respectively. The combination of immunity and drug to fight cancer provides a better method to reduce tumor population compared to immunity alone.
References
C. Garvey, T. McBride, L. Nevin, L. Peiperl, A. Ross, and P. Simpson. 2015. Bringing Access to the Full Spectrum of Cancer Research: A Call for Papers. PloS Med. 12(4): 1-3.
A. Jemal, F. Bray, M. M. Center, J. Ferlay, E. Ward, and D. Forman. 2011. Global Cancer Statistics. Ca: A Cancer Journal for Clinicians. 61: 69-90.
N. Rezaei. 2014. Cancer Immunology: A Transitional Medicine Context. London: Springer.
J. Mckay, and T. Schacher. 2009. The Chemotherapy Survival Guide: Everything You Need to Know to get through Treatment. Edisi Ke-3. New Harbinger.
R. A. Lehne. 2013. Pharmacology for Nursing Care. Edisi Ke-5. Elsevier Health Science.
R. K. Noyd, J. A. Krueger, and K. M. Hill. 2013. Biology: Organisms and Adaptations. Cengage Learning.
R. P. Araujo, and D. L. S. McElwain. 2004. A History of the Study of Solid Tumor Growth: The Contribution of Mathematical Modelling. Bulletin of Mathematical Biology. 66: 10391-1091.
J. Adam, and N. Bellomo. 2012. A Survey Models for Tumor-Immune System Dynamics. Springer Science and Business Media.
V. A. Kuznetsov, A. Makalkin, M. A. Taylor, and S. Perelson. 1994. Nonlinear Dynamics of immunogenic Tumors. Bulletin of Mathematical Biology. 56: 295-321.
J. A. Adam. 1996. Effects of Vascularization on Lymphocyte/Tumor Cell Dynamics: Qualitative Features. Mathematical and Computer Modelling. 23: 1-10.
L. G. de Pillis, A. E. Radunskaya, and C. L. Wiseman. 2005. A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth. Cancer Research. 6: 235-252.
R. T. Skeel, and S. N. Khleif. 2011. Handbook of Cancer Chemotherapy. Edisi Ke-8. Lippincott Williams and Wilkins.
F. S. Borges, K. C. Larosz, H. P Ren, A. M. Batista, M. S. Baptista, R. L. Viana, S. R. Lopes, and C. Grebogi. 2014. Model for Tumor Growth with Treatment by Continous and Pulsed Chemotherapy. BioSystems. 116: 43-48.
W. Liu, T. Hillen, and H. I. Freedman. 2007. A Mathematical Model for M-Phase Specific Chemotherapy including the Go Phase and Immunoresponse. Mathematical Biosciences and Engineering. 4: 239-259.
M. Villasana, and A. E. Radunskaya. 2003. A Delay Differential Equation of Tumor Growth. Journal of Mathematical Biology. 47(3): 270-294.
M. L. Workman, and L. A. LaCharity. 2015. Understanding Pharmacology: Essentials for Medication Safety. Elsevier Health Sciences.
S. P. Ellner, and J. Guckenheimer, 2006. Dynamic Models in Biology. Princeton N.J. Oxford: Princeton University Press.
L. Eldestein-Keshet. 1988. Mathematical Models in Biology. New York: Random House.
S. P. Otto, and T. Day. 2007. A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution. Oxford: Princeton University Press.
D. Gonze, M. Kaufman. 1961. Theory of Nonlinear Dynamical Systems. Biophysical Journal. 3: 1405-1415.
K. G. Tay, S. L. Kek, and R. A. Kahar. 2012. A spreadsheet Solution of a System of Ordinary Differential Equations using the Fourth Order Runge Kutta Method. Spreasheets in Education (eJsiE). 5(2): 1-10
M. Villasana, and G. Ochoa. 2004. Heuristic Design of Cancer Chemotherapy. IEE Transactions on Evolutionary Computation. 8: 513-521.
G. Newbury. 2007. A Numerical Study of a Delay Differential Equation Model for Breast Cancer. M. S Thesis, Department of Mathematics, Virgina Polytechnic Institute and State.
Downloads
Published
Issue
Section
License
Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.
