Gunther, N. and Hoffmann, G.W. "Qualitative Dynamics of a Network Model of Regulation of the Immune System: A Rationale for the IgM to IgG Switch", Journal of Theoretical Biology, 94, 815-855 (1982).

This is an extensive analysis of the properties of a two-variable mathematical model that simulates the interactions deemed to be operative in four stable steady states of the system. Terms in the equations denoting both IgM and IgG killing are both necessary for these steady states to exist and be stable. IgM is important in the virgin state, while IgG is important in the immune (memory) state, in agreement with experimental observations.