t
_{0}

35

years

minimum time considered by system, in days

t
_{
τ
}

40

years

time in which transplantation occurs, in days

k
_{
e
}

1

μ g/l/year

constant environment antigen entry into the body

k
_{
xec
}

1.5

μ l/cell/year×10^{−3}

second order C dependent E elimination rate constant

k
_{
xsc
}

0.15

μ l/cell/year×10^{−3}

second order C dependent S elimination rate constant

k
_{
xlc
}

0.7

μ l/cell/year×10^{−3}

second order C dependent L elimination rate constant

k
_{
xuc
}

0.5

μ l/cell/year×10^{−3}

second order C dependent U elimination rate constant

k
_{
xyc
}

0.5

μ l/cell/year×10^{−3}

second order C dependent Y elimination rate constant

k
_{
xzc
}

1

μ l/cell/year×10^{−3}

second order C dependent Z elimination rate constant

k
_{
xe
}

1

year^{−1}

first order elimination rate from compartment E

k
_{
xl
}

0.7

year^{−1}

first order elimination rate from compartment L

k
_{
xu
}

0.001

year^{−1}

first order elimination rate from compartment U

k
_{
xy
}

0.001

year^{−1}

first order elimination rate from compartment Y

k
_{
xz
}

1

year^{−1}

first order elimination rate from compartment Z

k
_{
ls
}

1.5

year^{−1}

first order transfer rate from compartment S to L

k
_{
zy
}

6

year^{−1}

first order transfer rate from compartment Y to Z

k
_{
xc
}

1

year^{−1}

first order elimination rate from compartment C

k
_{
xce
}

1

l/μ g/year

second order E dependent C_{
e
} elimination rate constant

k
_{
xcs
}

0.02

l/μ g/year

second order S dependent C_{
l
} elimination rate constant

k
_{
xcl
}

0.02

l/μ g/year

second order L dependent C_{
l
} elimination rate constant

k
_{
xcu
}

0.02

l/μ g/year

second order U dependent C_{
u
} elimination rate constant

k
_{
xcy
}

0.02

l/μ g/year

second order Y dependent C_{
z
} elimination rate constant

k
_{
xcz
}

0.02

l/μ g/year

second order Z dependent C_{
z
} elimination rate constant

k
_{
c
}

0.3

cell/μ l/year×10^{3}

basal lymphocyte production

k
_{
s
}

2

1/year

first order S dependent S production and elimination rate

  
constant

S
^{∗}

7

μ g/l

allograft maximum regeneration rate

κf

0

ng/ml/year

drug delivery rate  scenario 1 (no drug treatment)

κf

36500

ng/ml/year

drug delivery rate  scenario 2 (moderate drug treatment)

κf

127750

ng/ml/year

drug delivery rate  scenario 3 (high drug treatment)

k
_{
xf
}

365

1/year

first order elimination rate from compartment F

k
_{
cacF
}

2.92

l/μ g/year

Tcells production rate (Tcells clonal expansion), A and c

  
dependent

S
_{
τ
}

1000

μ g/l

antigen S concentration at time t_{
τ
}

U
_{
τ
}

1000

μ g/l

antigen U concentration at time t_{
τ
}

Y
_{
τ
}

1000

μ g/l

antigen Y concentration at time t_{
τ
}

λ

0.01

ml/ng

k_{
cac
} decreasing coefficient, F dependent

E
_{0}

1.38

μ g/l

E initial condition

S
_{0}

0

μ g/l

S initial condition

L
_{0}

0

μ g/l

L initial condition

U
_{0}

0

μ g/l

U initial condition

Y
_{0}

0

μ g/l

Y initial condition

Z
_{0}

0

μ g/l

Z initial condition

F
_{0}

0

ng/ml

F initial condition

C
_{e 0}

1.1

cell/μ l×10^{3}

C_{
E
} value at t=t_{0}

C
_{l 0}

0.3

cell/μ l×10^{3}

C_{
L
} value at t=t_{0}

C
_{u 0}

0.3

cell/μ l×10^{3}

C_{
U
} value at t=t_{0}

C
_{z 0}

0.3

cell/μ l×10^{3}

C_{
Z
} value at t=t_{0}
