  We propose a multiscale model of the invasion of the extracellular matrix by
two types of cancer cells, the differentiated cancer cells and the cancer stem
cells. We assume that the epithelial mesenchymal-like transition between them
is driven primarily by the epidermal growth factors. We moreover take into
account the transidifferentiation program of the cancer stem cells and the
cancer associated fibroblast cells as well as the fibroblast-driven remodelling
of the extracellular matrix.
  The proposed haptotaxis model combines the macroscopic phenomenon of the
invasion of the extracellular matrix with the microscopic dynamics of the
epidermal growth factors. We analyse our model in a component-wise manner and
compare our findings with the literature. We investigate pathological
situations regarding the epidermal growth factors and accordingly propose
"mathematical-treatment" scenarios to control the aggressiveness of the tumour.
