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General Information
Prof. Adrian Olaru
University Politehnica of Bucharest, Romania
I'm happy to take on the position of editor in chief of IJMO. It's a journal that shows promise of becoming a recognized journal in the area of modelling and optimization. I'll work together with the editors to help it progress.
IJMO 2014 Vol.4(4): 257-262 ISSN: 2010-3697
DOI: 10.7763/IJMO.2014.V4.383

Mathematical Modeling and Stability Analysis of the Brain Tumor Glioblastoma Multiforme (GBM)

F. Bozkurt
Abstract—In this paper, a brain tumor growth that is known as Glioblastoma Multiforme (GBM) is modeled, which has two sub-population; the sensitive tumor cell and the resistant tumor cell. Within a single tumor of monoclonal origin, the sensitive cell produces another population, the resistant cell population, that has more resistance to the drug than the sensitive tumor population. In this work, the local and global stability of the positive equilibrium point of the constructed system was investigated based on specific conditions. The boundedness nature and the damped oscillation behavior of the solutions were also analyzed. The obtained stability relations depend to the growth rates of the tumor population and the drug treatment, that was considered in the discussion part of this work.

Index Terms—Difference equations, local stability, global stability, damped oscillation.

F. Bozkurt is with the Erciyes University, Faculty of Education, Department of Mathematics, 38039 Kayseri, Turkey (e-mail: fbozkurt@erciyes.edu.tr).


Cite: F. Bozkurt, "Mathematical Modeling and Stability Analysis of the Brain Tumor Glioblastoma Multiforme (GBM)," International Journal of Modeling and Optimization vol. 4, no. 4, pp. 257-262, 2014.

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