Table 2.

Parameters used in the model

Parameter	Description	Dimensional Value	References
Production rates
r	Growth rate of cancer cells	3.48 × 10−8s−1	42
k	PI3K-mediated growth rate of cancer cell	1*	67
HP	Hill coefficient of cancer cell growth by PI3K	8 × 10−2 μM	Estimated
rT	Supply rate of effector T cells	5.56 × 10−3 cells/cm3s−1	Estimated
χC	Cancer cell carrying capacity	1.0 × 109 cells/cm3	56–59
λP	Source of PI3K	5.56 × 10−7 μMs−1	Estimated
λPF	Stimulation rate of PI3K from CAFs	1.39 × 10−6 μMs−1	Estimated
λr	Recruitment rate of Treg	5.56 cells/cm3s−1	Estimated
λrF	Recruitment rate of Treg by CAFs	27.78 cells/cm3s−1	Estimated
λAT	Injection rate of Treg inhibitor	7.4 × 10−5 μMs−1	Estimated
λAL	Injection rate of PD-L1 inhibitor	5.56 × 10−5 μMs−1	Estimated
λAP	Injection rate of PI3K inhibitor	6.97 × 10−6 μMs−1	Estimated
Degradation/Decay rates
g1	Cancer cells killing rate by activated effector T cell	1.13 × 10−7 s−1	Estimated
g2	Inhibition strength of T cell immune activity by Treg	2*	68
Kr	Inhibition parameter of T cell immune activity	5 × 105 cells/cm3	Estimated
g3	Cancer cells killing rate by CAFs (apoptosis)	2.78 × 10−8 s−1	Estimated
μP	Decay rate of PI3K	8.03 × 10−6s−1	69
μr	Decay rate of Treg	6.03 × 10−6s−1	70
μAT	Decay rate of Treg inhibitor	5.83 × 10−7s−1	71
μAL	Decay rate of PD-L1 inhibitor	5.28 × 10−7s−1	72
μAP	Decay rate of PI3K inhibitor	4.81 × 10−6s−1	73
ω1	Degradation rate of PI3K by inhibitor	1.92 × 10−4 μM−1s−1	Estimated
ω2	Degradation rate of PD-L1 by inhibitor	1.39 × 10−6 μM−1s−1	Estimated
ω3	Degradation rate of Treg by inhibitor	5.24 × 10−5 μM−1s−1	Estimated

Parameters labeled as ‘Estimated’ are not directly measured in experiments but are inferred through simulations to ensure biologically plausible system behavior. These estimations are based on known biological timescales, qualitative observations, or values reported in related literature. Dimensionless values are marked in *.