Table 1.

Parameters for the reduced model.

Parameter	Value with unit	Notes and references
C0	106 cells/mL	Maximum PCC density, estimated
P0	105 cells /mL	Maximum PSC density, estimated
kc	7.5 × 10−2 cells1/4mL−1/4day−1	Estimated
μc	20kc /P0	Estimated
Kc	0.1	We assume that the killing rate of cancer increases by a factor of 5, when R increases from 0.1 to 0.9.
λc	10−7 mL per cell per day	In experiments in Seki et al. (2002), 107 CTL cells were found to kill half of the renal cancer cells in about 16 hours. Therefore the maximum rate of CTL in killing cancer cells can be approximated as ln2/16/107 · 24 ≈ 10−7 per cell per day. At the same time, this number is given by λc/(Kc +(1−R)) in a patient. Assume that R is approximately 0.1 in patients, we obtain λc = 10−7 per cell per day.
kp	0.2 per day	Estimated
μp	20 kp	Estimated
Kp	C0/100	Estimated
λp	0.15 per day	The half-life T 1/2 of PSC is 2–5 days. The relation of λp and T1/2 is λp = ln 2/T1/2.
kr	0.2 per day	From the full model, we have kr = α + k1λM/kM. Taking the value that α = 0.2/day, k1 = 40 cells/ml/day (Sichert et al., 2007), kM = 228 cells/ml/day (Sichert et al., 2007; Day et al., 2009), and λM = 0.02/day (Day et al., 2009), we obtain kr ≈ 0.2.
λr	0.22 per day	From the full model, we have λr = λM + α.
γp	0.02λr /Ps	Ps is the PSC density in a healthy person, which satisfies Ps = P0(1−λp/kp).
γc	= γp	Estimated
kt	3300 cells per mL per day	Estimated
Kt	= Kc	Estimated
λt	0.3 per day	Day et al. (2009)