a, Relative benefit, in terms of time to treatment failure, for ideal containment (at size Ntol) versus ideal MTD, for varied values of Kr and β. This figure is based on approximate formulas that are highly accurate for the selected parameter values (Supplementary Information, section 5.2). Extended Data Fig. 8 shows an alternative version of this plot based on simulations. Contour lines are at the power of 2. b, Eventual outcomes of ideal containment (idCont) and ideal MTD (idMTD) treatment strategies based on exact formulas (Supplementary Information, section 5.1). The ‘infinite’ region in a corresponds to the ‘TI’ region in b. Fixed parameter values are as in Table 2.