  The ability to locally degrade the extracellular matrix (ECM) and interact
with the tumour microenvironment is a key process distinguishing cancer from
normal cells, and is a critical step in the metastatic spread of the tumour.
The invasion of the surrounding tissue involves the coordinated action between
cancer cells, the ECM, the matrix degrading enzymes, and the
epithelial-to-mesenchymal transition (EMT). This is a regulatory process
through which epithelial cells (ECs) acquire mesenchymal characteristics and
transform to mesenchymal-like cells (MCs). In this paper, we present a new
mathematical model which describes the transition from a collective invasion
strategy for the ECs to an individual invasion strategy for the MCs. We achieve
this by formulating a coupled hybrid system consisting of partial and
stochastic differential equations that describe the evolution of the ECs and
the MCs, respectively. This approach allows one to reproduce in a very natural
way fundamental qualitative features of the current biomedical understanding of
cancer invasion that are not easily captured by classical modelling approaches,
for example, the invasion of the ECM by self-generated gradients and the
appearance of EC invasion islands outside of the main body of the tumour.
