Global behavior of B models is discussed. When the source term for new B cells equals zero, the system has a conservation quantity. It implies the structurally unstability. It suggests that lack of the source of new B cells may unstabilize the immune system. When the B model incorporates autoimmunity, it loses symmetry. The asymmetry suggests the transition from a tolerant state to autoimmune state is more likely than the inverse transition. Effect of dose of antigen is also considered.
"Global Dynamics of B Cells and Anti-Idiotipic B Cells and its Application to Autoimmunity." Japan J. Indust. Appl. Math. 24 (1) 105 - 118, February 2007.