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International Conference on Applied Mathematics, Modeling and Computational Science

AMMCS 2017: Recent Advances in Mathematical and Statistical Methods pp 451–463Cite as

Optimal Control of Breast Cancer: Investigating Estrogen as a Risk Factor

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 259))

Abstract

Breast cancer is the most common cancer in women both in the developed and underdeveloped world. In this paper, the dynamics of breast cancer disease is modeled in the presence of two control strategies. The model describes evolution of the cancer in the body system when anti-cancer drugs and ketogenic-diet are implemented as control strategies against the tumor cells. We analysed the necessary and sufficient conditions, optimality and transversality conditions using Pontryagin Maximum Principle. We conclude through numerical simulations that estrogen level need to be monitored and combination of the two control is the best to reduce tumor-size and toxicity side effects.

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Acknowledgements

The corresponding author appreciate National Research Foundation (NRF), South Africa for the grant towards my Ph.D.; Grant Number: 109824. The authors also acknowledges the support of Research Office of University of Zululand for providing the funds for attending AMMCS2017, Canada. The authors are grateful to Adeniyi Michael (LASPOTECH, Nigeria) and Alex Adekiya (Unizulu) for their useful comments in the preparation of the manuscript. The authors are grateful to the anonymous Reviewers and the Handling Editor for their constructive comments, which have enhanced the paper.

Conflicts of Interest: The authors declare no conflicts of interest.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Zululand, Private Bag X1001, KwaDlangezwa, 3886, South Africa

    S. I. Oke, M. B. Matadi & S. S. Xulu

Authors
  1. S. I. Oke
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  2. M. B. Matadi
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  3. S. S. Xulu
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Corresponding author

Correspondence to S. I. Oke .

Editor information

Editors and Affiliations

  1. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    D. Marc Kilgour

  2. Department of Mathematics & Statistics, University of Guelph, Guelph, ON, Canada

    Herb Kunze

  3. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Roman Makarov

  4. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Roderick Melnik

  5. Department of Mathematics & MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada

    Xu Wang

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Oke, S.I., Matadi, M.B., Xulu, S.S. (2018). Optimal Control of Breast Cancer: Investigating Estrogen as a Risk Factor. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_41

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