Open Access Open Access  Restricted Access Subscription or Fee Access

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

Fatma Bozkurt

Abstract



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.

Keywords


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

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.