Research Article

Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions

Table 1

Description and values of patient’s parameters.

Parameter (unit)Description and sourcesFirst patientSecond patient

Tumor growth rate [40, 42].
Half saturation constant of the tumor killing rate [46].
1/b is the tumor carrying capacity [40, 42].
Fractional no ligand-transduced tumor cell kill by natural killer cells [40, 42, 52].
Maximum tumor killing rate by cytokine [44, 46].
Saturation level of fractional tumor cell kill by CD8+T cells. Primed with ligand transduced cells, challenged with ligand transduced [40, 42, 52].
Fraction of circulating lymphocytes that become natural killer cells [40, 42].
Death rate of natural killer cells [40, 42].
Maximum natural killer cells recruitment by ligand transduced tumor cells [40, 42, 52].
Steepness of CD8+T cell recruitment curve by cytokine [40, 42].
Steepness coefficient of the natural killer cell recruitment curve [40, 42].
Maximum CD8+T cell recruitment rate. Primed with ligand transduced cells, challenged with ligand transduced cells [40, 42, 52].
Steepness coefficient of the CD8+T cell recruitment curve [40, 42, 52].
Fractional tumor cells kill by chemotherapy [40, 42].
Fractional natural killer cells kill by chemotherapy [40, 42].
Fractional CD8+T cells kill by chemotherapy [40, 42].
Fractional circulating lymphocytes cells kill by chemotherapy [40, 42].
Exponent of fractional tumor cell kill by CD8+T cells. Primed with ligand transduced cells, challenged with ligand transduced cells [40, 42].
Death rate of CD8+T cells [40, 42].
Natural killer cell inactivation rate by tumor cells [40, 42].
Maximum CD8+T cell recruitment rate by cytokine [40, 42].
CD8+T cell inactivation rate by tumor cells [40, 42].
Rate of which CD8+T cells are stimulated to be produced; as a result, tumor cells killed by natural killer cells [40, 42].
Rate of which CD8+T cells are stimulated to be produced; as a result, tumor cells interaction with circulating lymphocytes [40, 42].
Steepness coefficient of tumor-CD8+T cell lysis term D. Primed with ligand transduced cells, challenged with ligand transduced [40, 42].
Regulatory function by natural killer cells of CD8+T cells [40, 42].
Constant source of circulating lymphocytes [40, 42].
Half saturation constant of the CD4+T cells production rate [46, 53].
Half saturation constant of cytokine production rate [44, 46].
Natural death and differentiation of circulating lymphocytes [40, 42].
Maximum CD4+T cells production rate [44, 46].
Maximum production rate of cytokine [44, 46].
Rate of chemotherapy drug decay [40, 42].
Natural death rate of CD4+T cells [45, 46].
Rate of cytokine decay [40, 42].
Loss rate of CD4+T cells due to interaction with tumor cells [44, 46].