Table 1 Parameter values

τ

delay for development of CTL cells

7 [days]

[9]

θ

maximal period to react to imatinib

20 [days]

[6]

${\mu }_x$

death rate of cancer cells

0.2 [0, 0.8] [days⁻¹]

[23]

${\mu }_y$

death rate of effector T cells

0.06 [0, 0.5] [days⁻¹]

[24]

${\eta }_1$

saturation effect of CML cells in the lymph nodes

100 [cells][ml⁻¹]

[9]

${\eta }_2$

saturation effect of immune cell recruitment by cancer cells

2 × 10⁷ [cells][ml⁻¹]

[24]

${\beta }_1$

growth rate of CML cancer cells in the form of the Gompertz law

0.03 [0; 0.5] [days⁻¹]

[9]

${\beta }_2$

change in the effector T cell (y(t)) population due to encounters with CML antigen

0.41 × 0.001 [days⁻¹]

[25], [26]

${\gamma }_1$

loss of CML cancer cells due to encounters with the effector T cells

$0.005{\text{[days}}^{-1}{[\frac{\text{cells}}{\text{ml}}]}^{-1}\text{]}$

[9]

${\gamma }_2$

loss of CTL cells due to these encounters between CTL and CML cancer cells

$0.005{\text{[days}}^{-1}{[\frac{\text{cells}}{\text{ml}}]}^{-1}\text{]}$

[26]

${\gamma }_3$

factor using imatinib treatment

0.00014 [mg]⁻¹

Estimated

${\gamma }_4$

factor using IFN-a treatment

0.005 [mg]⁻¹

Estimated

ω

once-daily dose of imatinib

400 - 800 [mg/day]

[1]

$i{n}_{\alpha }$

IFN-a dose

13 [mg/days] (90 [mg] weekly)

[27]

K

constant, the maximum possible concentration of CML

[1.5 × 10⁵;4 × 10⁵] [cells/ml]

[9]