CD44 and breast cancer: To highlight the role of the overexpression of the four proteins (EPCAM, CD47, CD44 and MET) in the development of breast cancer and understand the relationship between CTCs (with and without pro-metastatic behaviours) and survival times, we compare simulated overall survival probabilities in the case of CD44, CD47 and MET overexpressions versus the case in which the three CTCs’ markers are underexpressed.