Monte Carlo Simulation of a Nonlinear Subdiffusion Model of Tumor Invasion

Abstract

The main purpose of this work is to propose a nonlinear non-Markovian model of subdiffusive transportation that involves chemotactic substance affecting the cells’ movement. In this case, both of the random waiting time and the escape rate are affected by a chemotactic gradient. We systematically derive the subdiffusive fractional master equation, then we consider the diffusive limit of the fractional master equation. Finally, a Monte-Carlo simulation is run for the model in order to analys the role of the chemotactic gradient in the diffusion of particles.