Version 1
: Received: 31 January 2018 / Approved: 1 February 2018 / Online: 1 February 2018 (04:45:40 CET)
How to cite:
Oke, S.; Matadi, M.; Xulu, S. Optimal Control Analysis of a Mathematical Model for Breast Cancer. Preprints2018, 2018020004. https://doi.org/10.20944/preprints201802.0004.v1
Oke, S.; Matadi, M.; Xulu, S. Optimal Control Analysis of a Mathematical Model for Breast Cancer. Preprints 2018, 2018020004. https://doi.org/10.20944/preprints201802.0004.v1
Oke, S.; Matadi, M.; Xulu, S. Optimal Control Analysis of a Mathematical Model for Breast Cancer. Preprints2018, 2018020004. https://doi.org/10.20944/preprints201802.0004.v1
APA Style
Oke, S., Matadi, M., & Xulu, S. (2018). Optimal Control Analysis of a Mathematical Model for Breast Cancer. Preprints. https://doi.org/10.20944/preprints201802.0004.v1
Chicago/Turabian Style
Oke, S., Maba Matadi and Sibusiso Xulu. 2018 "Optimal Control Analysis of a Mathematical Model for Breast Cancer" Preprints. https://doi.org/10.20944/preprints201802.0004.v1
Abstract
In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analysis was carried out using varieties of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs ketogenic diet and cancer emission when anti-cancer drugs, immune-booster, ketogenic diet are included were established. Furthermore, optimal control theory is applied to find out the optimal drug adjustment as an input control of the system therapies to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin’s Maximum Principle. Numerical simulations were presented to validate our theoretical results.
Keywords
breast cancer; optimal control; ketogenic diet; chemotherapy
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
