EXISTENCE OF A TRAVELING WAVE SOLUTION TO GLIOBLASTOMA MULTIFORME MODEL WITH MODIFIED GOMPERTZ GROWTH FUNCTION

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.