Table S4.

The parameters of the model.

Parameter	Description	Value	Units	Ref.
a w	Tumor growth rate (colorectal cancer)	2.31 × 10−1	day−1	[32]
c	Rate of NK cell-induced tumor death	5.156 × 10−14	L cell−1 day−1	[32]
d	Immune strength coefficient	{1.3, 1.6, 2.1}	day−1	[32]
1	Immune system strength scaling coefficient	{1.1, 1.4, 2}	unitless	[32]
s	Value describing how quickly CD8+ T cells respond to the presence of a tumor	{5×10−3, 8×10−3, 4×10−2}	L	[32]
ξ	Rate of NK cell-induced tumor death through antibody-dependent cellular cytotoxicity (ADCC)	6.5 × 10−6 (0 for panitumumab)	L cell−1 day−1	[32]
h 1	Concentration of mAbs necessary for half-maximal increase in ADCC activity	1.25 × 10−6 (0 for panitumumab)	mg L−1	[32]
X	Determines the percent level of the maximum rate of chemotherapy-induced tumor death of wild-type and mutant cells	0.75	unitless	[32]
K T	Death rate of wild-type and mutant tumor cells due to chemotherapy	(8.1 × 10−1)· X	day−1	[25], [32]
K AT	Chemotherapy-induced death rate of wild-type and mutant tumors due to mAbs cetuximab and panitumumab	4 × 10−4	L mg−1 day−1	[32]
δ T	Chemotherapy efficacy coefficient on wild-type and mutant cancer cells	2 × 10−1	L mg−1	[32]
Y	Determines the percent level of the maximum rate of mAb-induced tumor death of wild-type and mutant cells	0.75	unitless	[32]
ψ	Rate of mAb-induced wild-type and mutant tumor cell death	(2.28 × 10−2)· Y for cetuximab (3.125 × 10−2)· Y for panitumumab	L mg−1 day−1	[32]
f	Rate of NK cell turnover	1 × 10−2	day−1	[32]
e	Rate of NK synthesis from circulating lymphocytes	$\frac{1}{9}\cdot f$	day−1	[32]
g N	IL-2 concentration needed for half-maximal NK cell proliferation	2.5036 × 105	IU L−1	[32]
p N	Rate of IL-2-induced NK cell proliferation	5.13 × 10−2	day−1	[32]
p	Rate of NK cell death due to interaction with the tumor	5.156 × 10−14	cell−1 day−1	[32]
p A	Rate of NK cell death due to interaction with mAbs complexes	6.5 × 10−10 (0 for panitumumab)	cell−1 day−1	[32]
K N	Rate of NK cell depletion due to chemotherapy toxicity	9.048 × 10−1	day−1	[32]
δ N	Coefficient of chemotherapy toxicity on NK cells	2 × 10−1	L mg−1	[32]
m	Rate of turnover of activated CD8+ T cells	5 × 10−3	day−1	[32]
θ	IL-2 concentration required to halve the CD8+ T cell turnover rate	2.5036 × 10−3	IU L−1	[32]
q	Rate of CD8+ T cell death due to interaction with the tumor	5.156 × 10−17	cell−1 day−1	[32]
r 1	Rate of activation of CD8+ T cell due to NK cell-lysed tumor cell debris	5.156 × 10−12	cell−1 day−1	[32]
r 2	Rate of CD8+ T cell production from circulating lymphocytes	1 × 10−15	cell−1 day−1	[32]
p I2	Rate of CD8+ T cell activation induced by IL-2	2.4036	day−1	[32]
g I2	Concentration of IL-2 necessary for half-maximal CD8+ T cell activation	2.5036 × 103	IU L−1	[32]
u	Rate of inhibition of surplus CD8+ T cells induced by Treg cells in the presence of IL-2	2.3085 × 10−13	L2 cell−2 day−1	[49]
κ	Concentration of IL-2 required to halve the immunosuppressive effect of Treg cells on CD8+ T cells	2.5036 × 103	IU L−1	[49]
j	Rate of activation of CD8+ T cells due to CD8+ T cell-lysed tumor cell debris	1.245 × 10−4	day−1	[32]
k	Tumor size required for half-maximal CD8+ T cell activation by CD8+ T cell-lysed tumor cell debris	2.019 × 107	cells	[32]
K L	Rate of CD8+ T cell depletion from chemotherapy toxicity	4.524 × 10−1	day−1	[32]
δ L	Coefficient of chemotherapy toxicity on CD8+ T cells	2 × 10−1	L mg−1	[32]
β	Rate of circulating lymphocyte turnover	6.3 × 10−3	day−1	[32]
α	Rate of circulating lymphocyte production	(3 × 109)·β	cells L−1 day−1	[32]
K C	Rate of lymphocyte depletion from chemotherapy toxicity	5.7 × 10−1	day−1	[32]
δ C	Coefficient of chemotherapy toxicity on circulating lymphocytes	2 × 10−1	L mg−1	[32]
μ I2	Rate of excretion and elimination of IL-2	11.7427	day−1	[32]
ω	Rate of IL-2 production from CD8+ T cells	7.88 × 10−2	IU cell−1 day−1	[32]
ϕ	Rate of IL-2 production from circulating CD4+ and naive CD8+ T cells	1.788 × 10−7	IU cell−1 day−1	[32]
ζ	Concentration of IL-2 for half-maximal CD8+ T cell IL-2 production	2.5036 × 103	IU L−1	[32]
γ 1	The rate of excretion and elimination of irinotecan	4.077 × 10−1	day−1	[32]
η	Rate of cetuximab and panitumumab turnover and excretion	1.386 × 10−1 for cetuximab 9.242 × 10−2 for panitumumab	day−1	[32]
λ	Rate of mAb-tumor cell complex formation	8.9 × 10−14 for cetuximab 8.6 × 10−14 for panitumumab	mg cell−1 L−1 day−1	[32]
h 2	Concentration of cetuximab or panitumumab for half-maximal EGFR binding	4.45 × 10−5 for cetuximab 4.3 × 10−5 for panitumumab	mg L−1	[32]
T K	Carrying capacity of wild-type and mutant tumor cells combined in the absence of tumor angiogenesis	1 × 106	cells	[50]
g 2	Conversion factor from number of activated endothelial cells to the increase in tumor carrying capacity	1	$\frac{\text{tumor cells}}{\text{endothelial cell}}$	Est.
p 1	Maximum rate of production of TGF-β by hypoxic tumor cells	1 × 105	IU L−1 day−1	Est. from [50]
b 1	Critical tumor size at which the angiogenic switch occurs	1 × 106	cells	[50]
S 1	Concentration of TGF-β necessary to reduce the CD8+ T cell killing rate of tumor cells by half	7 × 104	IU L−1	[51]
u 1	Decay rate of TGF-β	10	day−1	[50]
b K	Proliferation rate of angiogenic endothelial cells	0.198	day−1	[52]
K max	Maximum carrying capacity for blood vessel growth stimulated by TGF-β secreted by tumor cells	5 × 109	cells	Est.
g 1	TGF-β concentration that gives a half-maximal proliferation rate of endothelial cells	1 × 104	IU L−1	Est.
d K	Growth inhibition coefficient of endothelial cells by tumor cells	5 × 10−8	cell−2/3 day−1	Est. from [53]
λ T	Suppressive effect of Treg cells on wild-type and mutant tumor cell kill rate by NK cells	1.59 × 10−9	L cell−1	[45]
w	Rate of Treg cell production from circulating lymphocytes	4.698 × 10−4	day−1	[45]
u R	Rate of Treg cell turnover	3.851 × 10−2	day−1	[54]
p R	Rate of IL-2-induced Treg cell proliferation	3.598 × 10−2	day−1	[49]
g R	Concentration of IL-2 necessary for half-maximal activation of Treg cells	11.027	IU L−1	[49]
h R	Rate of Treg cell inhibition by Sunitinib	0.227	day−1	[45]
K R	Rate of Treg cell depletion from chemotherapy toxicity	5.7 × 10−1	day−1	[45]
α 1	Determines the scope of influence of KRAS-mutant tumor cells Tcp in making tumor cells resistant to chemotherapy and in reducing the sensitizing role of Cetuximab and Panitumumab to chemotherapy	1 × 107	unitless	[25]
λ R	Efficacy of Sunitinib in inhibiting the immunosuppressive activity of Tregs	50.02	L mg−1	[45]
δ R	Chemotherapy toxicity on Tregs	2 × 10−1	L mg−1	[32]
η s	Rate of excretion and elimination of Sunitinib	0.277	day−1	[45]
a m	Growth rate of mutant tumor cells (colorectal cancer)	2.31 × 10−1	day−1	[32]
μ	Maximum mutation rate of wild-type tumor cells	4 × 10−5	day−1	[55]
K M	Concentration of Irinotecan chemotherapy that leads to a half-maximal rate of mutation of wild-type tumor cells Tw into irinotecan-resistant tumor cells Ti	1 × 103	mg L−1	Est.
δ TR	Efficacy of the second type of chemotherapy drug of killing irinotecan-resistant tumor cells	2 × 10−1	L mg−1	[32]
γ 2	Rate of excretion and elimination of the hypothetical chemotherapy drug	4.077 × 10−1	day−1	[32]
η F	Degradation rate of anti-TGF-beta (Fresolimumab)	0.033	day−1	Est. from [56]
b 2	Rate of loss of free TGF-β due to binding with anti-TGF-β	100	L mg−1 day−1	Est. from [56]
b 3	Rate of loss of free anti-TGF-β due to binding with TGF-β	2.5 × 10−13	L IU−1 day−1	Est. from [56]
λ M 0	Differentiation rate of M0 macrophages into an M1 or M2 macrophage	1 × 10−4	day−1	Est. from [31]
λ M 1	Maximal rate at which M2 macrophages switch phenotype to become M1 macrophages	6 × 10−3	day−1	[31]
λ M 2	Maximal rate at which M1 macrophages switch phenotype to become M2 macrophages	6 × 10−3	day−1	Est. from [31]
λ MI 4	Production rate of M2 macrophages due to IL-4	1 × 10−3	day−1	[31]
λ MIγ	Production rate of M1 macrophages due to IFN-γ	1 × 10−3	day−1	[31]
λ MIα	Production rate of M1 macrophages due to TNF-α	1 × 10−3	day−1	[31]
λ T1M1	Production rate of Th1 cells by M1 macrophages and IL-12	0.23	day−1	[31]
λ TI2	Production rate of Th1 cells by IL-2	1	day−1	[31]
λ T2	Production rate of Th2 cells	0.8	day−1	[31]
λ IγT1	Production rate of IFN-γ by Th1 cells	3.731 × 10−3	IU cell−1 day−1	[31]
λ I12M1	Production rate of IL-12 by M1 macrophages	0.13	IU cell−1 day−1	Est. from [31]
λ I2T1	Production rate of IL-2 by Th1 cells	0.0672	IU cell−1 day−1	[31]
λ TαM1	Production rate of TNF-α by M1 macrophages	13.91	IU cell−1 day−1	[31]
λ I1βM1	Production rate of IL-1β by M1 macrophages	0.1022	IU cell−1 day−1	Est. from [31]
λ I10M 2	Production rate of IL-10 by M2 macrophages	0.02	IU cell−1 day−1	[31]
λ I4T 2	Production rate of IL-4 by Th2 cells	0.0775	IU cell−1 day−1	[31]
λ I4M 2	Production rate of IL-4 by M2 macrophages	0.3094	IU cell−1 day−1	[31]
λ IαM 2	Production rate of IFN-alpha by M2 macrophages	1 × 10−5	IU cell−1 day−1	[31]
λ Treg	Production rate of Tregs from Th0 cells due to TGF-β	0.001	day−1	Est.
λ MI10	Production rate of M2 macrophages due to IL-10	1 × 10−3	day−1	Est. from [31]
λ I1βT1	Production rate of IL-1beta by Th1 cells	0.1022	IU cell−1 day−1	Est. from [31]
λ TαT1	Production rate of TNF-alpha by Th1 cells	13.91	IU cell−1 day−1	Est. from [31]
λ I10T2	Production rate of IL-10 by Th2 cells	0.02	IU cell−1 day−1	Est. from [31]
λ I12T1	Production rate of IL-12 by Th1 cells	0.13	IU cell−1 day−1	Est. from [31]
d M1	Death rate of M1 macrophages	0.02	day−1	[31]
d M 2	Death rate of M2 macrophages	0.008	day−1	[31]
d T1	Death rate of Th1 cells	1.97 × 10−1	day−1	[31]
d T2	Death rate of Th2 cells	1.97 × 10−1	day−1	[31]
d Iγ	Degradation rate of IFN-γ	2.16	day−1	[31]
d Tα	Degradation rate of TNF-α	55.45	day−1	[31]
d I1β	Degradation rate of IL-1β	6.65	day−1	[31]
d I 4	Degradation rate of IL-4	50	day−1	[31]
d I10	Degradation rate of Il-10	8.32	day−1	[31]
d I12	Degradation rate of IL-12	1.38	day−1	[31]
d Iα	Degradation rate of IFN-α	2.16	day−1	Est. from [31]
M 0	Constant source of monocytes	5 × 1010	cells L−1	[31]
T 0	Constant source of naïve T cells	2 × 1010	cells L−1	[31]
K T1	Th1 cell saturation	1 × 1010	cells L−1	[31]
K Iγ	IFN-γ saturation	2.6 × 106	IU L−1	[31]
K I 2	IL-2 saturation	8 × 106	IU L−1	[31]
K I 4	IL-4 saturation	2.6 × 106	IU L−1	[31]
K I10	IL-10 saturation	3 × 104	IU L−1	Est. from [31]
K I12	IL-12 saturation	1.95 × 108	IU L−1	[31]
K M1	M1 saturation	5 × 1010	cells L−1	[31]
K M 2	M2 saturation	1 × 1011	cells L−1	[31]
K I1β	IL-1β saturation	1.3 × 105	IU L−1	[31]
K Iα	IFN-α saturation	2.6 × 106	IU L−1	Est. from [31]
K Tα	TNF-α saturation	1.3 × 107	IU L−1	[31]
K TGF β	TGF-beta saturation	2600	IU L−1	Est. from [31]
g TGF β	Concentration of TGF-β for half-maximal activation of Tregs	7 × 104	IU L−1	Est.
δ M1	Death rate of cancer cells by M1 macrophages	1 × 10−9	L cell−1 day−1	Est. from [32]
δ T1	Death rate of cancer cells by Th1 cells.	1 × 10−9	L cell−1 day−1	Est. from [32]
T I10	IL-10 concentration that reduces CTL anti-tumor response by half	3 × 104	IU L−1	Est.
η AI10	Degradation rate of anti-IL-10	3.3 × 10−2	day−1	Est. from [56]
b 4	Rate of loss of free IL-10 due to binding with anti-IL-10	15	L mg−1 day−1	Est. from [56]
b 5	Rate of loss of free anti-IL-10 due to binding with IL-10	1.665 × 10−12	L IU−1 day−1	Est. from [56]