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Table 2 Summary of parameter values
| Notation | Description | Value used | References |
|---|---|---|---|
| δ D | Diffusion coefficient of DCs | 8.64×10−7 cm2 day−1 | [65] |
| δ T | Diffusion coefficient of T cells | 8.64×10−7 cm2 day−1 | [65] |
| δ M | Diffusion coefficient of MDSCs | 8.64×10−7 cm2 day−1 | [65] |
| δ C | Diffusion coefficient of tumor cells | 8.64×10−7 cm2 day−1 | [65] |
| \(\delta _{I_{12}}\) | Diffusion coefficient of IL-12 | 6.05×10−2 cm2 day−1 | Estimated |
| \(\delta _{I_{2}}\) | Diffusion coefficient of IL-2 | 9.58×10−2 cm2 day−1 | Estimated |
| \(\delta _{T_{\beta }}\) | Diffusion coefficient of TGF- β | 8.52×10−2 cm2 day−1 | Estimated |
| \(\delta _{I_{6}}\) | Diffusion coefficient of IL-6 | 9.03×10−2 cm2 day−1 | Estimated |
| \(\delta _{I_{10}}\) | Diffusion coefficient of IL-10 | 9.11×10−2 cm2 day−1 | Estimated |
| δ A | Diffusion coefficient of anti-PD-1 | 7.85×10−2 cm2 day−1 | Estimated |
| δ B | Diffusion coefficient of BRAF/MEKi | 3.16×10−1 cm2 day−1 | Estimated |
| σ 0 | Flux rate of T 1 and T 8 cells at the boundary | 1 cm−1 | [65] |
| χ | Chemoattraction coefficient of IL-6 | 10 cm5/g·day | [90, 91] |
| λ DC | Activation rate of DCs by tumor cells | 4 g/cm3·day | [65] |
| \(\lambda _{T_{1}I_{12}}\) | Activation rate of CD 4+ T cells by IL-12 | 18.64 day−1 | Estimated |
| \(\lambda _{T_{1}I_{2}}\) | Activation rate of CD 4+ T cells by IL-2 | 0.25 day−1 | [65] |
| \(\lambda _{T_{8}I_{12}}\) | Activation rate of CD 8+ T cells by IL-12 | 16.6 day−1 | Estimated |
| \(\lambda _{T_{8}I_{2}}\) | Activation rate of CD 8+ T cells by IL-2 | 0.25 day−1 | [65] |
| \(\lambda _{T_{r}T_{\beta }}\) | Activation rate of Tregs by TGF- β | 0.415 day−1 | Estimated |
| \(\lambda _{T_{r}Q}\) | Activation rate of Tregs by PD-1-PD-L1 | 0.083 day−1 | Estimated |
| λ M | Activation rate of MDSCs | 1.05 day−1 | [40] |
| λ C | Growth rate of cancer cells | 0.616 day−1 | Estimated |
| λ 0 | Growth rate of cancer cells uninhibited (by immune cells) | 0.069 day−1 | Estimated |
| \(\lambda _{I_{12}D}\) | Production rate of IL-12 by DCs | 2.76×10−6 day−1 | Estimated |
| \(\lambda _{I_{12}B}\) | Promotion of IL-12 production by BRAF/MEKi | 1 | Estimated |
| \(\lambda _{I_{2}T_{1}}\) | Production rate of IL-2 by CD 4+ T cells | 2.82×10−8 day−1 | Estimated |
| \(\lambda _{T_{\beta } C}\) | Production rate of TGF- β by cancer cells | 2.18×10−10 day−1 | Estimated |
| \(\lambda _{T_{\beta } T_{r}}\) | Production rate of TGF- β by Tregs | 5.57×10−9 day−1 | [75] |
| \(\lambda _{T_{\beta } M}\) | Production rate of TGF- β by MDSCs | 2.18×10−10 day−1 | Estimated |
| \(\lambda _{I_{6} C}\) | Production rate of IL-6 by cancer cells | 3.54×10−10 day−1 | Estimated |
| \(\lambda _{I_{10} C}\) | Production rate of IL-10 by cancer cells | 9.10×10−10 day−1 | Estimated |
| \(\lambda _{I_{10} M}\) | Production rate of IL-10 by MDSCs | 1.82×10−9 day−1 | Estimated |
| η 1 | Killing rate of tumor cells by CD 4+ T cells | 11.5 day−1·cm3/g | Estimated |
| η 8 | Killing rate of tumor cells by CD 8+ T cells | 46 day−1·cm3/g | Estimated |
| μ PA | Blocking rate of PD-1 by anti-PD-1 | 6.04×106 cm3/g·day | Estimated |
| μ BC | Absorbtion rate of BRAF/MEKi by cancer cells | 6.17×10−10 day−1 | Estimated |
| ρ P | Expression of PD-1 in T cells | 2.49×10−7 | Estimated |
| ρ L | Expression of PD-L1 in T cells | 5.22×10−7 | Estimated |
| ε C | Expression of PD-L1 in tumor cells | 0.01 | [84] |
| ε M | Expression of PD-L1 in MDSCs | 0.005 | Estimated |
| d D | Death rate of DCs | 0.1 day−1 | [65] |
| \(d_{T_{1}}\) | Death rate of CD 4+ T cells | 0.197 day−1 | [65] |
| \(d_{T_{8}}\) | Death rate of CD 8+ T cells | 0.18 day−1 | [65] |
| \(d_{T_{r}}\) | Death rate of Tregs | 0.2 day−1 | [75] |
| d M | Death rate of MDSCs | 0.03 day−1 | [40] |
| d C | Death rate of tumor cells | 0.17 day−1 | [65] |
| \(d_{I_{12}}\) | Degradation rate of IL-12 | 1.38 day−1 | [65] |
| \(d_{I_{2}}\) | Degradation rate of IL-2 | 2.376 day−1 | [65] |
| \(d_{T_{\beta }}\) | Degradation rate of TGF- β | 499.066 day−1 | Estimated |
| \(d_{I_{6}}\) | Degradation rate of IL-6 | 4.16 day−1 | Estimated |
| \(d_{I_{10}}\) | Degradation rate of IL-10 | 8.32 day−1 | Estimated |
| d A | Degradation rate of anti-PD-1 | 0.046 day−1 | [87] |
| d B | Degradation rate of BRAF/MEKi | 1.66day−1 | Estimated |
| D 0 | Density of inactive DCs | 2×10−5 g/cm3 | [65] |
| T 10 | Density of naive CD 4+ T cells in tumor | 4×10−4 g/cm3 | Estimated |
| T 80 | Density of naive CD 8+ T cells in tumor | 2×10−4 g/cm3 | Estimated |
| C M | Carrying capacity of cancer cells | 0.8 g/cm3 | [65] |
| \(\hat T_{1}\) | Density of CD 4+ T cells from lymph node | 4×10−3 g/cm3 | Estimated |
| \(\hat T_{8}\) | Density of CD 8+ T cells from lymph node | 2×10−3 g/cm3 | Estimated |
