Existence of a traveling wave solution to glioblastoma multiforme model with Gompertz growth function

Abstract

A mathematical model of glioblastoma multiforme with the Gompertz growth function is analyzed. The Fisher-Kolmogorov type model contains a density-dependent diffusion term, taxis and growth function and considers the properties of glioblastoma multiforme. An analytical solution by the traveling wave method is investigated and the condition for its existence is found. Numerical solutions in Matlab to find the optimal values of the model parameters are performed using the simplex Nelder-Mead algorithm.