Optimal Control Brain Tumor System with Drog and Its Stability

Volume 4, Issue 3, pp 473--486 http://dx.doi.org/10.22436/jmcs.04.03.22

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Authors

S. A. Alavi - Dept. of Maths, College of Mathematicsand Computer Science, Hakim Sabzevari University, Sabzevar, Iran J. Norabadi - Dept. of Maths, College of Mathematicsand Computer Science, Hakim Sabzevari University, Sabzevar, Iran M. Arjmand - Dept. of Maths, College of Mathematicsand Computer Science, Hakim Sabzevari University, Sabzevar, Iran

Abstract

It is quite known that there are various methods for treatment of cancer. Although virus therapy has been proved to effective in the improvement of cancer, this method is still at its primary stage. Therefore, treatment methods such as chemotherapy and radiotherapy are still versatile. In these methods, drugs are prescribed. The most important question in the treatment of brain tumors is the rate of drug prescription for the patient so that it can help the patient recover and minimize damages to the healthy cells. A.El-Ghohary demonstrated that a mathematical model of brain tumor system can be seen in an optimal nonlinear control problem. In this paper, attempt is made to transform the nonlinear optimal control problem into an optimal control problem in the measure theory and to approximate a new problem with a linear programming problem and subsequently, to specify the drug dose for the patients with cancer. In addition, we deal with the examination of stability of system balance points. Using drug dose control stabilizes the unstable balance points of the tumor system. In the end, a comparison is made between the results obtained from the above mentioned method and the approximate solution proposed by Al-Gohary.

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Keywords

• Nonlinear optimal control
• Measure theory
• Tumor
• linear programming.

MSC

•  92C50
•  49J20

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