The effect of obesity and cancer stem cells in tumor model with time delay
Keywords:
Obesity, Stem cells, Tumor model, Time delay, Stability AnalysisAbstract
In this paper, the obesity and tumor model with cancer stem cells has been analyzed. We aim to show that all solutions of the model are non-negative and bounded. Next, we find all equilibria of the models. We also investigate the conditions for the existence of positive equilibria for the model. Next, the local of the positive equilibrium is determined by the linearization method. Finally, we illustrate the numerical results using some advantages of mathematical software to support the analytic results and show the effect of some parameters for the model.
References
S. Friberg and S. Mattson, “On the growth rates of human malignant tumors: implications for medical decision making,” Journal of surgical oncology, vol. 65, no. 4, pp. 284 - 297, 1997.
F. J. Santonja, A. Morales, R. J. Villanueva, and J. C. Cortcs, “Analyzing the effect of public health campaigns on reducing excess weight: A modelling approach for the Spanish autonomous region of the community of Valencia,” Evaluation and program planning, vol. 35, no. 1, pp. 34 - 39, 2012.
C. Oh and M. MA, “Optimal intervention strategies for the spread of obesity,” Journal of Applied Mathematics, vol. 2015, 2015.
D. Aldila, N. Rarasati, N. Nuraini and E. Soewono, “Optimal control problem of treatment for obesity in a closed population,” International Journal of Mathematics and Mathematical Sciences, vol. 2014, 2014.
D. Laudisio, G. Muscogiuri, L. Barrea, S. Savastano and A. Colao, “Obesity and breast cancer in premenopausal women: Current evidence and future perspectives,” European Journal of Obstetrics & Gynecology and Reproductive Biology, vol. 230, pp. 217 - 221, 2018.
C. A. A. Rojas, M. T. Alvarez-Bauelos, J. Morales-Romero, H. Suarez-Diaz, J. C. Hernandez-Fonseca and G. Contreras-Alarcon, “Breast cancer: Metastasis, molecular subtypes, and overweight and obesity in Veracruz, Mexico,” Clinical breast cancer, vol. 19, no. 1, pp. e166 - e171, 2019.
H. Rubin, “Promotion and selection by serum growth factors drive field cancerization, which is anticipated in vivo by type 2 diabetes and Obesity,” Proceedings of the National Academy of Sciences, vol. 110, no. 34, pp. 13927 - 13931, 2013.
S. D. Hursting, “Mini review: the year in obesity and cancer,” Molecular endocrinology, vol. 26, no. 12, pp. 1961 - 1966, 2012.
M. Schwab, Encyclopedia of cancer, Springer Science & Business Media, 2008.
R. A. Ku-Carrillo, S. E. Delgadillo, and B. Chen-Charpentier, “A mathematical model for the effect of obesity on cancer growth and on the immune system response,” Applied Mathematical Modelling, vol. 40, no. 7, pp. 4908 - 4920, 2016.
J. Jo, O. Gavrilova, S. Pack, W. Jou, S. Mullen, A. E. Sumner, S. W. Cushman and V. Periwal, “Hypertrophy and/or hyperplasia: dynamics of adipose tissue growth,” PLoS computational biology, vol. 5, no. 3, p. e1000324, 2009.
K. Abernathy and J. Burke, “Modeling the treatment of glioblastoma multiforme and cancer stem cells with ordinary differential equations,” Computational and Mathematical Methods in Medicine, vol. 2016, 2016.
D. Okwan-Duodu, G. E. Umpierrez, O. W. Brawley and R. Diaz, “Obesity-driven inflammation and cancer risk: role of myeloid derived suppressor cells and alternately activated macrophages,” American journal of cancer research, vol. 3, no. 1, p. 21, 2013.
M. Villasana and A. Radunskaya, “A delay differential equation model for tumor growth,” Journal of Mathematical Biology, vol. 47, no. 3, pp. 270 - 294, 2003.
F. A. Rihan, D. Abdelrahman, F. Al-Maskari, F. Ibrahim and M. A. Abdeen, “Delay differential model for tumour-immune response with chemoimmunotherapy and optimal control,” Computational and mathematical methods in medicine, vol. 2014, 2014.
K. Abernathy, Z. Abernathy, A. Baxter and M. Stevens, “Global dynamics of a breast cancer competition model,” Differential Equations and Dynamical Systems, pp. 1 - 15, 2017.
A. Halanay and A. Halanay, Differential equations: Stability, oscillations, time lags, vol. 6, Academic press New York, 1966.
A. A. Abdullah, Surface Tension Instability in a Horizontal Nanofluid Layer, Journal of Computer Science and Computational Mathematics, vol. 7, no. 3, 2017.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2020 COMPUSOFT: An International Journal of Advanced Computer Technology
This work is licensed under a Creative Commons Attribution 4.0 International License.
©2023. COMPUSOFT: AN INTERNATIONAL OF ADVANCED COMPUTER TECHNOLOGY by COMPUSOFT PUBLICATION is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at COMPUSOFT: AN INTERNATIONAL OF ADVANCED COMPUTER TECHNOLOGY. Permissions beyond the scope of this license may be available at Creative Commons Attribution 4.0 International Public License.
