Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells

Abdulsamad Engida Sado; Purnachandra Rao Koya

doi:doi:10.11648/j.ajam.20150303.20

| Peer-Reviewed

Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells

Abdulsamad Engida Sado, Purnachandra Rao Koya

Published in American Journal of Applied Mathematics (Volume 3, Issue 3)

Received: 17 April 2015 Accepted: 29 April 2015 Published: 28 May 2015

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper we have constructed a mathematical model using Brody function and applied to describe the dynamics of breast cancer. To construct the mathematical model we considered that the linear cancer network technique describes the growth of estrogen receptor positive breast cancers. Model validity is verified using simulation study and mathematical analysis. It is verified that the hormone therapy is a technique to treat endocrine receptor positive breast cancers. Hormone therapy is considered as a treatment and used to block the estrogens receptors from the cancer and health cells. Important observations are made from the simulation study and physical interpretations are drawn and presented lucidly in the paper.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 3)
DOI	10.11648/j.ajam.20150303.20
Page(s)	138-145
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Koya – Goshu, Brody Model, Breast Cancer, Cancer Stem Cell, Cancer Tumor Cell, Hormone Therapy and Tamoxifen

References

[1]	J.D. Murray, Mathematical Biology, Interdisciplinary Applied Mathematics, 2002.
[2]	Chipo Mufudza, Walter Sorofa, and Edward T. Chiyaka, Assessing the effects of Estrogen on the Dynamics of Breast Cancer, Hindawi publishing Corporation,Vol.2012 Article ID473572,14pages,doi:10.1155/2012/473572.
[3]	Tesfay Hailu, Hailemariam Berhe, Knowledge of Breast Cancer and its Early detection measures among Female Students in Mekelle University, Tigray region, Ethiopia,2014,p.57-64.
[4]	Purnachandra Rao Koya, Ayele Taye Goshu. Generalized Mathematical Model for Biological Growths, Open Journal of Modelling and Simulation. Vol. 1, 2013, pp. 42-53. http://dx.doi.org/10.4236/ojmsi.2013.14008
[5]	Tsygvintsev, Alexei and Marino, Simeone and Kirschner, Denise E, A Mathematical Model of Gene Therapy for the Treatment of Cancer, Mathematical Methods and Models in Biomedicine, pp.367-385, 2013.
[6]	Gebremedhin A and Shamebo M., Clinical Profile of Ethiopian Patients with Breast Cancer, East African Medical Journal,Vol.75, No.11, pp.640-643, 1998.
[7]	Rachel Roe-Dale, David. I, Michael. K. Â, A Mathematical Model of Breast Cancer Treatment with CMF and Doxorubicin,2010.
[8]	Eric Werner, Cancer Networks: A general Theoretical and Computational Framework for Understanding Cancer, arXiv:1110.5865v1 [q-bio.MN] 26 Oct 2011,University of Oxford.
[9]	Semarya B., Worknish, Mignote H., MesfinA., Alemseged A., Assessment of Knowledge of Breast Cancer and Screening Methods among Nurses in University Hospitals in Addis Ababa, Ethiopia, 2011.
[10]	Michelle McDuffie, A Hormone Therapy Model for Breast Cancer Using Linear Cancer Networks, Volume 15, No. 1, Spring 2014.
[11]	HaftomGebrehiwot1, Tesfay Hailu, Gebreamlak Gidey, Knowledge and Attitude towards Breast Cancer among Mekelle University, Female Regular Undergraduate Students, Tigray Region, Ethiopia, 2013 ,ISSN 2320-6691 (Online)
[12]	Tang, Betty and Wolkowicz, Gail SK, Mathematical Models of Microbial Growth and Competition in the Chemostat Regulated by cell-bound Extracellular Enzymes, Journal of Mathematical Biology, Vol. 31, No. 1, pp. 1–23, 1992, Springer.
[13]	Ferlay, Jacques and Hery, Clarisse and Autier, Philippe and Sankaranarayanan, Rengaswamy, Breast Cancer Epidemiology, pp.1-19,Spring 2010,
[14]	Source: Ferlay J, Soerjomataram I., Ervik M., Dikshit R., Eser S., Mathers C., Rebelo M., Parkin D. M., Forman D., Bray, F.GLOBOCAN 2012 v1.1, Cancer Incidence and Mortality Worldwide: IARC Cancer Base No. 11 [Internet]. Lyon, France: International Agency for Research on Cancer; 2014. Available from: http://globocan.iarc.fr, accessed on 16/01/2015.

Cite This Article

Plain Text BibTeX RIS

APA Style

Abdulsamad Engida Sado, Purnachandra Rao Koya. (2015). Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. American Journal of Applied Mathematics, 3(3), 138-145. https://doi.org/10.11648/j.ajam.20150303.20

Copy | Download

ACS Style

Abdulsamad Engida Sado; Purnachandra Rao Koya. Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. Am. J. Appl. Math. 2015, 3(3), 138-145. doi: 10.11648/j.ajam.20150303.20

Copy | Download

AMA Style

Abdulsamad Engida Sado, Purnachandra Rao Koya. Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. Am J Appl Math. 2015;3(3):138-145. doi: 10.11648/j.ajam.20150303.20

Copy | Download

@article{10.11648/j.ajam.20150303.20,
  author = {Abdulsamad Engida Sado and Purnachandra Rao Koya},
  title = {Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {138-145},
  doi = {10.11648/j.ajam.20150303.20},
  url = {https://doi.org/10.11648/j.ajam.20150303.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.20},
  abstract = {In this paper we have constructed a mathematical model using Brody function and applied to describe the dynamics of breast cancer. To construct the mathematical model we considered that the linear cancer network technique describes the growth of estrogen receptor positive breast cancers. Model validity is verified using simulation study and mathematical analysis. It is verified that the hormone therapy is a technique to treat endocrine receptor positive breast cancers. Hormone therapy is considered as a treatment and used to block the estrogens receptors from the cancer and health cells. Important observations are made from the simulation study and physical interpretations are drawn and presented lucidly in the paper.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells
AU  - Abdulsamad Engida Sado
AU  - Purnachandra Rao Koya
Y1  - 2015/05/28
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150303.20
DO  - 10.11648/j.ajam.20150303.20
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 138
EP  - 145
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150303.20
AB  - In this paper we have constructed a mathematical model using Brody function and applied to describe the dynamics of breast cancer. To construct the mathematical model we considered that the linear cancer network technique describes the growth of estrogen receptor positive breast cancers. Model validity is verified using simulation study and mathematical analysis. It is verified that the hormone therapy is a technique to treat endocrine receptor positive breast cancers. Hormone therapy is considered as a treatment and used to block the estrogens receptors from the cancer and health cells. Important observations are made from the simulation study and physical interpretations are drawn and presented lucidly in the paper.
VL  - 3
IS  - 3
ER  -

Copy | Download

Author Information

Abdulsamad Engida Sado

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Abdulsamad Engida Sado, Purnachandra Rao Koya. (2015). Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. American Journal of Applied Mathematics, 3(3), 138-145. https://doi.org/10.11648/j.ajam.20150303.20

Copy | Download

ACS Style

Abdulsamad Engida Sado; Purnachandra Rao Koya. Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. Am. J. Appl. Math. 2015, 3(3), 138-145. doi: 10.11648/j.ajam.20150303.20

Copy | Download

AMA Style

Abdulsamad Engida Sado, Purnachandra Rao Koya. Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells. Am J Appl Math. 2015;3(3):138-145. doi: 10.11648/j.ajam.20150303.20

Copy | Download

@article{10.11648/j.ajam.20150303.20,
  author = {Abdulsamad Engida Sado and Purnachandra Rao Koya},
  title = {Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {138-145},
  doi = {10.11648/j.ajam.20150303.20},
  url = {https://doi.org/10.11648/j.ajam.20150303.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.20},
  abstract = {In this paper we have constructed a mathematical model using Brody function and applied to describe the dynamics of breast cancer. To construct the mathematical model we considered that the linear cancer network technique describes the growth of estrogen receptor positive breast cancers. Model validity is verified using simulation study and mathematical analysis. It is verified that the hormone therapy is a technique to treat endocrine receptor positive breast cancers. Hormone therapy is considered as a treatment and used to block the estrogens receptors from the cancer and health cells. Important observations are made from the simulation study and physical interpretations are drawn and presented lucidly in the paper.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Application of Brody Growth Function to Describe Dynamics of Breast Cancer Cells
AU  - Abdulsamad Engida Sado
AU  - Purnachandra Rao Koya
Y1  - 2015/05/28
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150303.20
DO  - 10.11648/j.ajam.20150303.20
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 138
EP  - 145
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150303.20
AB  - In this paper we have constructed a mathematical model using Brody function and applied to describe the dynamics of breast cancer. To construct the mathematical model we considered that the linear cancer network technique describes the growth of estrogen receptor positive breast cancers. Model validity is verified using simulation study and mathematical analysis. It is verified that the hormone therapy is a technique to treat endocrine receptor positive breast cancers. Hormone therapy is considered as a treatment and used to block the estrogens receptors from the cancer and health cells. Important observations are made from the simulation study and physical interpretations are drawn and presented lucidly in the paper.
VL  - 3
IS  - 3
ER  -

Copy | Download