—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.
—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: firstname.lastname@example.org).
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.