Table 2 ∣.

Parameter values

Parameter	Meaning	Value	Model(s)
K	Tumour carrying capacity	2 × 1012	Model 3
K s	Carrying capacity of a fully susceptible tumour	2 × 1012	Model 4
K r	Carrying capacity of a fully resistant tumour	Varied	Model 4
ρ, ρr, ρs	Baseline per-cell growth rate (per day)	0.005928	Models 3 and 4
α	Competition coefficient	1	Model 4
β	Competition coefficient	Varied	Model 4
λ	Treatment sensitivity	1	Models 3 and 4
C max	Maximal instantaneous tolerated dose	2	Models 3 and 4
N 0	Initial tumour size	1010	Models 3 and 4
R 0	Initial resistant cell population size	2.3 × 105	Models 3 and 4
N tol	Tumour size corresponding to treatment failure	7 × 1010	Models 3 and 4
N crit	Lethal tumour size	5 × 1011	Models 3 and 4

Except when otherwise specified, numerical results use the following parameter values. Model 4 is introduced later on. The initial size of the resistant subpopulation is derived through the Goldie–Coldman formula²: $R_0=(1-N_0^{-2\tau })N_0∕2$, where τ=10⁻⁶ is the mutation and back mutation rate of Monro and Gaffney¹⁴ and N₀ is the initial tumour size. The value of N_tol is arbitrary (in log scale, this is almost the average of N₀ and N_crit). The value of C_max is for consistency with the clinical trial results reported by Zhang et al.⁴. On average, the cumulative dose given in that trial was 47% of the MTD, which is consistent with values of C_max between 2 and 2.5 assuming the initial tumour is highly sensitive (higher values otherwise). Since λC_max = 2, it takes as much time for a fully sensitive tumour size to double in the absence of treatment as to be halved under MTD; the dose C = C_max/2 would precisely stabilize a fully sensitive tumour.