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Current biological knowledge supports the existence of a secondary group ofcancer cells within the body of the tumour that exhibits stem cell-likeproperties. These cells are termed Cancer Stem Cells (CSCs}, and as opposed tothe more usual Differentiated Cancer Cells (DCCs), they exhibit highermotility, they are more resilient to therapy, and are able to metastasize tosecondary locations within the organism and produce new tumours. The origin ofthe CSCs is not completely clear; they seem to stem from the DCCs via atransition process related to the Epithelial-Mesenchymal Transition (EMT) thatcan also be found in normal tissue.  In the current work we model and numerically study the transition betweenthese two types of cancer cells, and the resulting "ensemble" invasion of theextracellular matrix. This leads to the derivation and numerical simulation oftwo systems: an algebraic-elliptic system for the transition and anadvection-reaction-diffusion system of Keller-Segel taxis type for theinvasion.

A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix