The dependence of the range [θmin,θmax] on model parameters KI, KC, β, and ϕ. In all figures the three shaded areas represent regions describing distinct tumor outcomes: all tumors are eliminated in the (light blue) upper regions; tumor elimination, tumor escape, and long-term tumor dormancy are all possible in the (green) middle regions; and all tumors escape in the (pink) lower regions. The range of θ permitting a long-term dormant cancer state decreases as immune carrying capacity increases (a), and increases as cancer carrying capacity increases (b), for fixed (β,ϕ) in the predation term. The effects of changes in β and ϕ on the range [θmin,θmax] depend on both KI and KC, (c-h). Unless otherwise stated, parameter values are from Table 1.