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Math. Comput. Appl. 2018, 23(2), 21; https://doi.org/10.3390/mca23020021

Optimal Control Analysis of a Mathematical Model for Breast Cancer

Department of Mathematical Sciences, University of Zululand, Private Bag X1001, KwaDlangezwa 3886, South Africa
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Received: 26 March 2018 / Revised: 19 April 2018 / Accepted: 20 April 2018 / Published: 24 April 2018
(This article belongs to the Special Issue Optimization in Control Applications)
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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 analyses were carried out using a variety 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, and ketogenic diet are included were established. Furthermore, optimal control theory is applied to discover the optimal drug adjustment as an input control of the system therapies in order 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 are presented to validate our theoretical results. View Full-Text
Keywords: breast cancer; optimal control; ketogenic diet; chemotherapy breast cancer; optimal control; ketogenic diet; chemotherapy
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Oke, S.I.; Matadi, M.B.; Xulu, S.S. Optimal Control Analysis of a Mathematical Model for Breast Cancer. Math. Comput. Appl. 2018, 23, 21.

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