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The objective of this paper is to present preliminary mathematical models of the interaction between tumor and antibody for the murine BCL1 lymphoma and illustrate how this interaction leads to dormancy of the tumor. We explicitly model the induction by the immune response of cell cycle arrest and apoptosis of the tumor cells. In the absence of large amounts of quantitative data and because the models are preliminary, they are deliberately simple. We neglect, for example, spatial effects on this lymphoid tumor and the synergistic effect of antigen-specific T cells. A comparison of alternative models shows that, although vaccination is necessary to stimulate a sufficient immune response to control tumor growth, boosting of the antibody response by the tumor itself is vital to the mechanisms that maintain dormancy. We determine parameters that control the size of the dormant tumors, and the fraction of proliferating …