Parameter | Value | Definition | Units | References |
---|---|---|---|---|
a1 | 4.3992 × 10−2 | Panc02 tumor growth rate | \( \frac{1}{day} \) | Estimated |
Cmax | 1 × 1010 | Maximum sustainable tumor cell population | cell | [19] |
b1 | 3.23 × 10−7 | NK-mediated tumor cell kill rate | \( \frac{1}{cell\times day} \) | [19] |
c1 | 1.1 × 10−7 | CTL-mediated tumor cell kill rate | \( \frac{1}{cell\times day} \) | [19] |
d1 | 2 × 10−34 | Proportional parameter of anti-CD25 treatment for inhibition of anti-immune effects of Treg on CTL-mediated tumor cell killing | \( \frac{1}{cell^3} \) | Estimated |
e1 | 0.345 | Rate of the suppressive effect of Treg on CTL-mediated tumor cell killing | \( \frac{1}{cell} \) | [34] |
f1 | 0.286 | Rate of the suppressive effect of TGF-β on CTL-mediated tumor cell killing | \( \frac{ml}{ng} \) | [34] |
g1 | 3.5 × 10−2 | The apoptosis rate of Panc02 tumor cells by low-dose 5-FU treatment | \( \frac{1}{day} \) | Estimated |
h1 | 2.5 × 105 | Proportional parameter of tumor inhibition rate by Treg depletion through anti-CD25 treatment | \( \frac{cell}{day} \) | Estimated |
k1 | 1 × 10−15 | Proportional parameter of tumor inhibition rate by Treg depletion through anti-CD25 treatment | \( \frac{1}{cell} \) | Estimated |
l1 | 100 | Depth of access of immune cells to the tumor mass | \( {cell}^{\frac{1}{3}} \) | [19] |
a2 | 1.4 × 104 | Constant generation source of NK cells | \( \frac{cell}{day} \) | [19] |
b2 | 4.12 × 10−2 | The exponential death rate of NK cells | \( \frac{1}{day} \) | [19] |
c2 | 0.125 | Maximum of IL-2-mediated NK cell growth | \( \frac{1}{day} \) | [34] |
d2 | 0.3 | Steepness coefficient of the IL-2-mediated NK cell growth rate | \( \frac{ng}{ml} \) | [34] |
e2 | 0.125 | Maximum of IFN-γ mediated NK cell growth rate | \( \frac{1}{day} \) | [34] |
f2 | 0.3 | The steepness coefficient of the IFN-γ-mediated NK cell growth rate | \( \frac{ng}{ml} \) | [34] |
g2 | 1 × 10−9 | Inactivation rate of NK cells by tumor cells | \( \frac{1}{day} \) | Estimated close to the value reported in [19] |
h2 | 1 × 10−10 | Suppression rate of NK cells by Tregs. | \( \frac{1}{cell\times day} \) | [34] |
a3 | 2 × 10−2 | The exponential death rate of CTLs | \( \frac{1}{day} \) | [19] |
b3 | 8 × 10−2 | Maximum tumor-mediated CTL recruitment rate | \( \frac{1}{day} \) | Estimated close to the value reported in [19] |
c3 | 2.02 × 1014 | Steepness coefficient of the tumor-mediated CTL recruitment curve | cell2 | Estimated with regarding the value reported in [19] |
d3 | 1.1 × 10−7 | CTL stimulation rate by tumor-NK cells interactions | \( \frac{1}{cell\times day} \) | [19] |
e3 | 1.5 × 10−10 | Inactivation rate of CTLs by tumor cells | \( \frac{1}{cell\times day} \) | Estimated close to the value reported in [19] |
f3 | 125 × 10−5 | Maximum of IL-2-mediated CTL growth rate | \( \frac{1}{day} \) | Estimated with regarding the value reported in [34] |
g3 | 0.3 | The steepness coefficient of the IL-2-mediated CTL growth rate | \( \frac{ng}{ml} \) | [34] |
h3 | 12.5 × 10−2 | Maximum of IFN-γ-mediated CTL growth rate | \( \frac{1}{day} \) | [34] |
k3 | 0.3 | The steepness coefficient of the IFN-γ-mediated CTL growth rate | \( \frac{ng}{ml} \) | [34] |
l3 | 1 × 10−10 | Suppression rate of CTLs by Tregs | \( \frac{1}{cell\times day} \) | [34] |
p3 | 2.5 × 106 | The normal number of splenic MDSCs in C57/BL6 mice | cell | [19] |
m3 | 18 × 10−2 | Minimal CTL proliferation factor induced by inhibition of MDSCs | --- | [19] |
n3 | 6 × 10−3 | Parameter for MDSC-induced inhibition of CTL proliferation | \( \frac{1}{cell^2} \) | [19] |
a4 | 1.25 × 106 | Normal MDSC production rate | \( \frac{cell}{day} \) | [19] |
b4 | 3.25 × 10−2 | MDSCs normal death rate | \( \frac{1}{day} \) | Estimated with regarding the value reported in [19] |
b4 | 8 × 10−2 | MDSCs death rate during 5-FU treatment | \( \frac{1}{day} \) | Estimated with regarding the value reported in [19] |
c4 | 0.7 × 107 | MDSC expansion coefficient in Panc02 tumor-bearing mice | \( \frac{cell}{day} \) | [19] |
d4 | 1 × 1010 | Steepness coefficient of the tumor-mediated MDSC production curve | cell | [19] |
a5 | 3.6 × 105 | The production rate of T helper cells in the thymus | \( \frac{cell}{day} \) | [34] |
b5 | 1.2 × 10−3 | The exponential death rate of T helper cells based on the half-life | \( \frac{1}{day} \) | [34] |
c5 | 0.125 | Maximum IL-2-mediated T helper cell proliferation rate | \( \frac{1}{day} \) | [34] |
d5 | 0.3 | Steepness coefficient of the IL-2-mediated T helper cell proliferation curve | \( \frac{ng}{ml} \) | [34] |
e5 | 0.125 | Maximum IFN-γ-mediated T helper cell proliferation rate | \( \frac{1}{day} \) | [34] |
f5 | 0.3 | Steepness coefficient of the IFN-γ-mediated T helper cell proliferation curve | \( \frac{ng}{ml} \) | [34] |
g5 | 1 × 10−10 | Suppression rate of T helper cells by Tregs | \( \frac{1}{cell\times day} \) | [34] |
a6 | 5.6 × 105 | The constant production rate of Tregs | \( \frac{cell}{day} \) | [34] |
b6 | 2.3 × 10−2 | The exponential death rate of Tregs based on the half-life | \( \frac{1}{\ day} \) | [34] |
c6 | 2 × 10−4 | Treg origination rate from CTLs | \( \frac{1}{\ day} \) | [34] |
d6 | 4 × 10−4 | Treg origination rate from T helper cells | \( \frac{1}{\ day} \) | [34] |
e6 | 0.125 | Maximum IL-2-mediated growth rate of Tregs | \( \frac{1}{day} \) | [34] |
f6 | 0.3 | Steepness coefficient of the IL-2-mediated Treg growth curve | \( \frac{ng}{ml} \) | [34] |
g6 | 1 × 10−11 | NK-mediated Treg degradation constant rate | \( \frac{1}{cell\times day} \) | [34] |
h6 | 1.5 × 10−11 | Constant inhibition rate of Tregs by anti-CD25 treatment | \( \frac{1}{\ day} \) | [34] |
\( \frac{{\boldsymbol{\tau}}_{\mathbf{1}}}{{\boldsymbol{\alpha}}_{\mathbf{1}}} \) | 2.2483 × 1011 | The natural death rate of IL-2 based on its half-life/ constant production rate of IL-2 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 IFN-γ by CTLs/ Natural death rate of IFN-γ based on its half-life | \( \frac{ng}{ml\times cell} \) | [34] |
\( \frac{{\boldsymbol{\beta}}_{\mathbf{2}}}{{\boldsymbol{\tau}}_{\mathbf{2}}} \) | 4.4691 × 10−13 | The secretion rate of IFN-γ by NK cells/degradation rate of IFN-γ based on its half-life | \( \frac{ng}{ml\times cell} \) | [34] |
\( \frac{{\boldsymbol{\beta}}_{\mathbf{3}}}{{\boldsymbol{\tau}}_{\mathbf{2}}} \) | 4.4691 × 10−13 | The secretion rate of IFN-γ by T helper cells/degradation rate of IFN-γ based on its half-life | \( \frac{ng}{ml\times cell} \) | [34] |
\( \frac{{\boldsymbol{\lambda}}_{\mathbf{1}}}{{\boldsymbol{\tau}}_{\mathbf{3}}} \) | 8.9382 × 10−13 | The constant production rate of TGF-β by tumor cells/death rate of TGF-β based on its half-life | \( \frac{ng}{ml\times cell} \) | [34] |