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A Mathematical Model of the Brain Tumor Gliobalstoma Multiforme (GBM) and the Immune System (IS) Interaction

Fatma Bozkurt


This paper is devoted to the stability analysis of the interaction of GBM {IS population. GBM is a brain tumor, that has two sub-populations, sensitive and resistant cells. Within a single tumor of monoclonal origin, the sensitive cell produce another population, the resistant cell population, that has more resistance to the drug than the sensitive tumor population. In other words, this self-organism produce mutate cells to protect themselves. The IS cells are also divided into two populations, namely, the macrophages and the activated macrophages. Hence, this model shows two conversions, the conversion from sensitive tumor cells to resistant tumor cells and the conversion from macrophages to active macrophages, and an interaction between the tumor cells and the macrophages. In this work, the local and global stability analysis of the constructed system were analyzed.


differential equations; piecewise constant arguments; local stability; global stability; boundedness.

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