Abstract:
This thesis explores a model for aggressive brain cancer - glioblastoma multiforme,
with modified gompertzian growth function. Density-dependent diffusion term, taxis,
and growth functions are included in the model that considers the glioblastoma mul tiforme properties. The experimental data of Stein et al. [58] has been used in this
work. The given model is solved both analytically and numerically by using the Mat lab program. The analytical method finds the condition for existing a traveling wave
solution of the given glioblastoma model and numerical computations are done by
using the Nelder-Mead simplex algorithm that minimizes the function through which
it finds the optimal parameters of the model. The simulation results confirm the
analytical predictions.