Last modified: 2014-03-31

#### Abstract

Gliomas form the major class of primary brain tumour and, in their most aggressive form, have a poor prognosis. Treatment is complicated not only due to their critical location, but also by the difficulty of eliminating malignant cells that have infiltrated far beyond the tumour core, leading to their recurrence following surgery. A leading hypothesis (Giese et al. 2003) is that tumour cells switch between proliferating and rapidly migrating phases, a mechanism known as the "go or grow" hypothesis. In this presentation I will propose a simple mathematical model that describes the competition between healthy glial cells and malignant cells, the latter subdivided into invasive and proliferating subpopulations. The model consists of three reaction-diffusion equations, which exhibit travelling wave solutions whose speed of invasion depends on the model parameters. Our analytical and simulations show that increase the probability of migratory state delay the tumour to take over the normal cells. In addition, the wave speed of the tumour increase as the probability of migratory cells increase till the probabilities of migratory state is equal to stationary state then the wave speed start decrease. Moreover, the research showed the influence of the diffusion form on the tumour wave speed and its profile.