Optimal control analysis of a mathematical model for breast cancer

9 Jul 2018, 15:00
New Law School/--020 (University of Sydney)

New Law School/--020

University of Sydney

Oral Presentation Disease - non-infectious Cancer & therapies


Mr Segun Oke (University of Zululand, South Africa)


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 are presented to validate our theoretical results.

Primary author

Mr Segun Oke (University of Zululand, South Africa)


Dr Matadi Maba (University of Zululand) Prof. Xulu Sibusiso (University of Zululand)

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