Mathematical modeling and analysis of a tumor invasion problem with angiogenesis and taxis cascade

In this paper, we propose a mathematical model for tumor invasion supported by angiogenesis and interactions with the surrounding tissue. For the model deduction we employ a multiscale approach starting from lower scales and obtaining by an informal parabolic upscaling a system of reaction–diffusion-taxis equations with a so-called ’taxis cascade’, where one species is performing taxis toward a signal whose production/decay is controlled by the other, for which it also serves as a tactic cue. We prove global existence and uniqueness of solutions to the obtained PDE-ODE system and perform numerical simulations to illustrate the behavior of solutions.