Integrating stochastic chemotaxis–haptotaxis mechanisms in cancer invasion: A multiscale derivation and computational perspective

This paper deals with the multiscale derivation of a nonlinear stochastic chemotaxis-haptotaxis system of cancerous tissue invasion from a new stochastic kinetic theory model based on the micro-macro decomposition technique. We show that this approach technically can lead to some systems known in the literature, such as the filling volume effect, and a new system by taking the stochasticity effect and nonlocal diffusion into account. We develop an asymptotic-preserving numerical scheme to solve the obtained equivalent micro-macro formulation numerically. The objective is to provide a uniformly stable scheme regarding the small parameters and consistency with the diffusion limit. Various numerical examples validate the proposed approach. Finally, we provide numerical simulations in the two-dimensional setting obtained by the macroscopic stochastic model.