Modeling multiple taxis: Tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence

We provide a short review of existing models with multiple taxis performed by (at least) one species and consider new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating proliferating). The migrating cells perform nonlinear diffusion types in response to non-diffusing cues: away from proliferating up the gradient surrounding tissue. Transitions between subpopulations are influenced subcellular (receptor binding) dynamics, thus conferring setting multiscale character. prove global existence weak solutions simplified version numerical simulations full under several phenotype switching motility scenarios. We also compare (via simulations) this corresponding haptotaxis-chemotaxis indirect chemorepellent production discussion about possible extensions challenges.