a_{1}

4.3992 × 10^{−2}

Panc02 tumor growth rate

\( \frac{1}{day} \)

Estimated

C_{max}

1 × 10^{10}

Maximum sustainable tumor cell population

cell

[19]

b_{1}

3.23 × 10^{−7}

NKmediated tumor cell kill rate

\( \frac{1}{cell\times day} \)

[19]

c_{1}

1.1 × 10^{−7}

CTLmediated tumor cell kill rate

\( \frac{1}{cell\times day} \)

[19]

d_{1}

2 × 10^{−34}

Proportional parameter of antiCD25 treatment for inhibition of antiimmune effects of Treg on CTLmediated tumor cell killing

\( \frac{1}{cell^3} \)

Estimated

e_{1}

0.345

Rate of the suppressive effect of Treg on CTLmediated tumor cell killing

\( \frac{1}{cell} \)

[34]

f_{1}

0.286

Rate of the suppressive effect of TGFβ on CTLmediated tumor cell killing

\( \frac{ml}{ng} \)

[34]

g_{1}

3.5 × 10^{−2}

The apoptosis rate of Panc02 tumor cells by lowdose 5FU treatment

\( \frac{1}{day} \)

Estimated

h_{1}

2.5 × 10^{5}

Proportional parameter of tumor inhibition rate by Treg depletion through antiCD25 treatment

\( \frac{cell}{day} \)

Estimated

k_{1}

1 × 10^{−15}

Proportional parameter of tumor inhibition rate by Treg depletion through antiCD25 treatment

\( \frac{1}{cell} \)

Estimated

l_{1}

100

Depth of access of immune cells to the tumor mass

\( {cell}^{\frac{1}{3}} \)

[19]

a_{2}

1.4 × 10^{4}

Constant generation source of NK cells

\( \frac{cell}{day} \)

[19]

b_{2}

4.12 × 10^{−2}

The exponential death rate of NK cells

\( \frac{1}{day} \)

[19]

c_{2}

0.125

Maximum of IL2mediated NK cell growth

\( \frac{1}{day} \)

[34]

d_{2}

0.3

Steepness coefficient of the IL2mediated NK cell growth rate

\( \frac{ng}{ml} \)

[34]

e_{2}

0.125

Maximum of IFNγ mediated NK cell growth rate

\( \frac{1}{day} \)

[34]

f_{2}

0.3

The steepness coefficient of the IFNγmediated NK cell growth rate

\( \frac{ng}{ml} \)

[34]

g_{2}

1 × 10^{−9}

Inactivation rate of NK cells by tumor cells

\( \frac{1}{day} \)

Estimated close to the value reported in [19]

h_{2}

1 × 10^{−10}

Suppression rate of NK cells by Tregs.

\( \frac{1}{cell\times day} \)

[34]

a_{3}

2 × 10^{−2}

The exponential death rate of CTLs

\( \frac{1}{day} \)

[19]

b_{3}

8 × 10^{−2}

Maximum tumormediated CTL recruitment rate

\( \frac{1}{day} \)

Estimated close to the value reported in [19]

c_{3}

2.02 × 10^{14}

Steepness coefficient of the tumormediated CTL recruitment curve

cell^{2}

Estimated with regarding the value reported in [19]

d_{3}

1.1 × 10^{−7}

CTL stimulation rate by tumorNK cells interactions

\( \frac{1}{cell\times day} \)

[19]

e_{3}

1.5 × 10^{−10}

Inactivation rate of CTLs by tumor cells

\( \frac{1}{cell\times day} \)

Estimated close to the value reported in [19]

f_{3}

125 × 10^{−5}

Maximum of IL2mediated CTL growth rate

\( \frac{1}{day} \)

Estimated with regarding the value reported in [34]

g_{3}

0.3

The steepness coefficient of the IL2mediated CTL growth rate

\( \frac{ng}{ml} \)

[34]

h_{3}

12.5 × 10^{−2}

Maximum of IFNγmediated CTL growth rate

\( \frac{1}{day} \)

[34]

k_{3}

0.3

The steepness coefficient of the IFNγmediated CTL growth rate

\( \frac{ng}{ml} \)

[34]

l_{3}

1 × 10^{−10}

Suppression rate of CTLs by Tregs

\( \frac{1}{cell\times day} \)

[34]

p_{3}

2.5 × 10^{6}

The normal number of splenic MDSCs in C57/BL6 mice

cell

[19]

m_{3}

18 × 10^{−2}

Minimal CTL proliferation factor induced by inhibition of MDSCs



[19]

n_{3}

6 × 10^{−3}

Parameter for MDSCinduced inhibition of CTL proliferation

\( \frac{1}{cell^2} \)

[19]

a_{4}

1.25 × 10^{6}

Normal MDSC production rate

\( \frac{cell}{day} \)

[19]

b_{4}

3.25 × 10^{−2}

MDSCs normal death rate

\( \frac{1}{day} \)

Estimated with regarding the value reported in [19]

b_{4}

8 × 10^{−2}

MDSCs death rate during 5FU treatment

\( \frac{1}{day} \)

Estimated with regarding the value reported in [19]

c_{4}

0.7 × 10^{7}

MDSC expansion coefficient in Panc02 tumorbearing mice

\( \frac{cell}{day} \)

[19]

d_{4}

1 × 10^{10}

Steepness coefficient of the tumormediated MDSC production curve

cell

[19]

a_{5}

3.6 × 10^{5}

The production rate of T helper cells in the thymus

\( \frac{cell}{day} \)

[34]

b_{5}

1.2 × 10^{−3}

The exponential death rate of T helper cells based on the halflife

\( \frac{1}{day} \)

[34]

c_{5}

0.125

Maximum IL2mediated T helper cell proliferation rate

\( \frac{1}{day} \)

[34]

d_{5}

0.3

Steepness coefficient of the IL2mediated T helper cell proliferation curve

\( \frac{ng}{ml} \)

[34]

e_{5}

0.125

Maximum IFNγmediated T helper cell proliferation rate

\( \frac{1}{day} \)

[34]

f_{5}

0.3

Steepness coefficient of the IFNγmediated T helper cell proliferation curve

\( \frac{ng}{ml} \)

[34]

g_{5}

1 × 10^{−10}

Suppression rate of T helper cells by Tregs

\( \frac{1}{cell\times day} \)

[34]

a_{6}

5.6 × 10^{5}

The constant production rate of Tregs

\( \frac{cell}{day} \)

[34]

b_{6}

2.3 × 10^{−2}

The exponential death rate of Tregs based on the halflife

\( \frac{1}{\ day} \)

[34]

c_{6}

2 × 10^{−4}

Treg origination rate from CTLs

\( \frac{1}{\ day} \)

[34]

d_{6}

4 × 10^{−4}

Treg origination rate from T helper cells

\( \frac{1}{\ day} \)

[34]

e_{6}

0.125

Maximum IL2mediated growth rate of Tregs

\( \frac{1}{day} \)

[34]

f_{6}

0.3

Steepness coefficient of the IL2mediated Treg growth curve

\( \frac{ng}{ml} \)

[34]

g_{6}

1 × 10^{−11}

NKmediated Treg degradation constant rate

\( \frac{1}{cell\times day} \)

[34]

h_{6}

1.5 × 10^{−11}

Constant inhibition rate of Tregs by antiCD25 treatment

\( \frac{1}{\ day} \)

[34]

\( \frac{{\boldsymbol{\tau}}_{\mathbf{1}}}{{\boldsymbol{\alpha}}_{\mathbf{1}}} \)

2.2483 × 10^{11}

The natural death rate of IL2 based on its halflife/ constant production rate of IL2 by T helper cells

\( \frac{cell\times ml}{ng} \)

[34]

\( \frac{{\boldsymbol{\beta}}_{\mathbf{1}}}{{\boldsymbol{\tau}}_{\mathbf{2}}} \)

4.4691 × 10^{−13}

constant production rate of IFNγ by CTLs/ Natural death rate of IFNγ based on its halflife

\( \frac{ng}{ml\times cell} \)

[34]

\( \frac{{\boldsymbol{\beta}}_{\mathbf{2}}}{{\boldsymbol{\tau}}_{\mathbf{2}}} \)

4.4691 × 10^{−13}

The secretion rate of IFNγ by NK cells/degradation rate of IFNγ based on its halflife

\( \frac{ng}{ml\times cell} \)

[34]

\( \frac{{\boldsymbol{\beta}}_{\mathbf{3}}}{{\boldsymbol{\tau}}_{\mathbf{2}}} \)

4.4691 × 10^{−13}

The secretion rate of IFNγ by T helper cells/degradation rate of IFNγ based on its halflife

\( \frac{ng}{ml\times cell} \)

[34]

\( \frac{{\boldsymbol{\lambda}}_{\mathbf{1}}}{{\boldsymbol{\tau}}_{\mathbf{3}}} \)

8.9382 × 10^{−13}

The constant production rate of TGFβ by tumor cells/death rate of TGFβ based on its halflife

\( \frac{ng}{ml\times cell} \)

[34]
