Table 1 Values of the biological and pathophysiological parameters for the tumour system

Therapeutic parameters

p _I

1.25 × 10^-1

Interleukin 2-induced CD8+T-cell recruitment rate (maximum value)

Kirschner et al.[10]

per day (rate value)

g _I

2.00 × 10⁷

Interleukin 2-induced CD8+T-cell recruitment (steepness value of the curve)

Kirschner et al.[10]

cell² (cell-cell interaction)

μ_I

1.0 × 10¹

Decay rate of Interleukin-2 drug

Kirschner et al.[10]

per day

Birth/death parameters

α

7.5 × 10⁸

Circulating lymphocyte birth rate (constant source)

de Pillis et al.[18]

cells per day

β

1.20 × 10^-2

Lymphocyte death and differentiation rate

de Pillis et al.[18]

per day

γ

9.0 × 10^-1

Chemotherapy drug decay rate

Calabresi et al.[20]

per day

k _T

9.0 × 10^-1

Chemotherapy-induced tumour cell lysis

Perry [1]

per day

k _N , k _L , k _C

6.0 × 10^-1

Chemotherapy-induced lysis of NK cells, CD8+T-cells, and Circulating lymphocytes, respectively

Perry [1]

per day

r ₁

1.1 × 10^-7

CD8+T cell generation rate, induced by tumour cell lysis by NK cell

Yates et al.[21]; Lanzavecchia et al. [22]

per cell per day

r ₂

6.5 × 10^-11

CD8+T cell generation rate, induced by tumour cell - circulating lymphocyte lysis

de Pillis et al.[18]

per cell per day

Pathophysiological parameters

a

4.31 × 10^-1 (high grade tumour); 3.01x10^-1 (low grade tumour)

Rate of tumour growth

Calabresi et al.[20]; Stein [23]

per day

b

2.17 × 10^-8 (high grade tumour); 1.02 × 10^-8 (low grade tumour)

Deceleration effect of logistic growth of tumour

Calabresi et al.[20]; Stein [23]

per cell

c

6.41 × 10^-11

NK cell-induced lysis of (non)-ligand-transduced tumour cell

Diefenbach et al.[24]

per cell per day

d

2.34

CD8+T cell-induced fractional tumour cell lysis (saturation value); priming by ligand-transduced cell

Dudley et al.[25]

per day

e

2.08 × 10^-3

Lymphocyte fraction converting to NK cells

Kuznetsov et al.[9]

per day

f

4.12 × 10^-2

NK cell death rate

Kuznetsov [9]

per day

g

4.98 × 10^-1

Ligand-transduced tumour cell-induced NK cell recruitment rate (maximum value)

Dudley et al.[25]

per day

h

2.02 × 10⁷

NK cell recruitment by tumour cell (steepness index of recruitment curve)

Kuznetsov et al.[9]

cell² (cell-cell interaction)

l

2.09

CD8+T cell-induced tumour cell lysis (exponent value)

Dudley et al.[25]

Dimensionless (exponent)

s

8.39 × 10^-2

CD8+T cell-induced tumour cell lysis (Value of Steepness index of term D denoting lysis)

Dudley et al.[25]

Dimensionless (exponent)

p

3.42 × 10^-7

Tumour-cell induced inactivation of NK cell

Diefenbach et al.[24]

per cell per day

m

2.04 × 10^-1

CD8+T cell death rate

Yates et al.[21]

per day

j

2.49 × 10^-2

Recruitment rate of CD8+T cells (max. value), cells primed with ligand-transduced tumour cells

Diefenbach et al.[24]

per day

k

3.66 × 10⁷

CD8+Tcell recruitment curve (steepness index), cells primed with ligand-transduced tumour cells

Diefenbach et al.[24]

cell² (cell-cell interaction)

q

1.42 × 10^-6

Tumour cell-induced CD8+T cell inactivation rate

Kuznetsov et al.[9]

per cell per day

u

3.00 × 10^-10

CD8+T-cell regulation by NK-cell

de Pillis et al.[18]

per cell² per day (cell-cell interaction rate)