Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours

In this paper two new mathematical models are proposed that, correspond to a macroscopic model of tissue invasion of solid tumours, in terms of a system of reaction-diffusion-chemotaxis equations. The first model is defined at the micro-scale level of a large number of interacting individual entities, and is in terms of a linear (Markov) equation. The second model refers to the meso-scale level of description of test-entities and is given in terms of a bilinear Boltzmann-type equation. Mathematical relationships among these three possible descriptions are formulated. Explicit error estimates are given.