A Mathematical Model of Immune-System-Melanoma Competition

Table 2

Model parameters. The “in vivo’’ label refers to parameters that have been chosen according to in vivo measurements and observations. The “Estimated’’ label refers to free (unknown) parameters that have been tuned.

Param.	Description	Value (estimate)	Ref.
𝛼1	𝐶 growth parameter (Gompertz)	0.2165 Δ(𝑡)^−1	in vivo
𝛼2	𝐶 shrink parameter (Gompertz)	0.01269 Δ(𝑡)^−1	in vivo
𝛼3	𝐶 max killing rate by 𝐸𝑠	0.00000033 Δ(𝑡)^−1	Estimated
𝛼4	𝐴 release rate by Killed 𝐶	0.21 Δ(𝑡)^−1	Estimated
𝛼5	𝐴 natural degradation rate	ln(2)/9 Δ(𝑡)^−1	[19]
𝛼6	Switch rate from 𝑁 to 𝐸𝑠 thanks to 𝐴	0.1 Δ(𝑡)^−1	Estimated
𝛼7	𝐸𝑠 max duplication rate	0.095 Δ(𝑡)^−1	Estimated
𝛼8	E and 𝐸𝑠 nautral death rate	ln(2)/15 Δ(𝑡)^−1	[20]
𝛼9	𝐴𝑏 death rate due to stimulation of 𝐸𝑠	0.000001 Δ(𝑡)^−1	Estimated
𝛼10	𝐴𝑏 and 𝐴𝑠 natural degradation rate	ln(2)/21 Δ(𝑡)^−1	[21, 22]
𝛼11	migration rate from injection to skin compartment	0.009 Δ(𝑡)^−1	Estimated
ℎ	Reinjection rate of N by thymus	0.01 Δ(𝑡)^−1	Estimated
𝑘1	𝐸𝑠 duplication threshold due to 𝐴𝑠	10	Estimated
𝑘2	𝐶-𝐸𝑠 min. killing rate threshold	1	Estimated
𝑘3	𝐶-𝐸𝑠 max. killing rate threshold	50	Estimated
𝑀	Number of N in safe conditions (leukocyte formula)	196000	in vivo
𝐶0	Initial number of C	180000	in vivo
𝑝	No. of injected E by treatment administration	760000	in vivo
𝑞	No. of injected Ab by treatment administration	1000000	in vivo
𝜏	Delay value	1	in vivo