If the tumour carying capacity is bounded from below, then the breast tumour will eventually reach its carrying capacity due to the effect of an increasing population of tBregs, i.e. $T \nearrow \frac{1}{b}$ when $B \nearrow$ .A model for the mathematical study of immune response to breast cancer is proposed and studied, both analytically and numerically. It is a simplification of a complex one, recently introduced by two of the present authors. It serves for a compact study of the dynamical role in cancer promotion of a relatively recently described subgroup of regulatory B cells, which are evoked by the tumour.