Integrating Stochastic Chemotaxis-Haptotaxis Mechanisms in Cancer Invasion: A Multiscale Derivation and Computational Perspective

Abstract

This paper is devoted to multiscale derivation of a nonlinear stochastic chemotaxis-haptotaxis system of cancer invasion of tissue from a new stochastic kinetic theory model based on the micro-macro decomposition technique. We develop a numerical asymptotic preserving scheme to solve numerically the obtained equivalent micro-macro formulation. The aim is to provide an uniformly stable scheme with respect to the small parameter and the consistency with the diffusion limit. The proposed approach is validated by various numerical examples. Finally, we provide some numerical simulation in two-dimensional space obtained from the macroscopic model.

Keywords: Kinetic theory, Stochastic chemotaxishaptotaxis system, multiscale approach, Asymptotic preserving scheme, Finite volume method