Traveling wave speed and profile of a ``go or grow" glioblastoma multiforme model

Glioblastoma (GBM) is considered to be the most aggressive form of brain cancer with the lowest median survival of between 8-12 months. A host of mathematical models in the form of reaction-diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction-diffusion GBM model based on the `go or grow' hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. According to our results, the tumor progresses slower than the simpler Fisher model. Furthermore, following Canosa's method for approximating the traveling wave solution, we consider scenarios for the model with different plausible growth and transition functions.