A mathematical model of brain tumor

Abstract

Malignant glioma is an aggressive primary brain tumor. Due to its location, the interactions of glioma and the immune system are complex. We start this paper by proposing a simple mathematical model that describes the interaction among glioma cells, microglia and cytotoxic T lymphocytes (CTLs). The existence and stability conditions of the equilibrium points are analyzed. Numerical results showed that neither microglia nor CTLs has the ability to eradicate the tumor. As a result, we extend the model by including the chemotherapeutic agent. The model has six equilibrium points, and one of these points represents a cured state. Through local stability, we found a range of values for the infusion rate that guarantees the elimination of glioma, as well as preventing the glioma from reoccurring.