Dynamical approach for tumour regression: a cancer stem cell model.

The progression of a population of cancer cells is studied under the assumption that a small sub-population of them co-exists with cells in the usual differentiated state. The evolution of this sub-population will be characterised by the properties of a very peculiar state that all cells experience: the stem state, characterised by high proliferation rate, capacity of self-renewal and strong therapy resistance. Based on recent considerations, transitions between the two co-existing states (stem and differentiated) of cancer cells are assumed to be allowed in both directions. Transitions are mediated by a time-evolving chemical activator. Based on these considerations a model will be presented which will require a sophisticated treatment of population dynamics, admitting three fixed points. This work will focus on dynamical phenomena occurring in such a deterministic model, and will then proceed to a preliminary study of the effects of a noisy environment on it. The hope is that some of the dynamical effects could have optimistic therapeutical implications. These effects will be looked for analytically and/or numerically.