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Table 2 Mathematical model for data generation
From:
Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach
Reactor model equations:
d
X
(
t
)
d
t
=
X
(
t
)
·
μ
(
W
(
t
)
)
+
D
·
X
(
t
)
d
S
(
t
)
d
t
=
−
r
s
(
S
(
t
)
)
·
X
(
t
)
−
D
·
(
S
(
t
)
−
S
F
)
d
P
(
t
)
d
t
=
r
ρ
(
W
(
t
)
)
·
X
(
t
)
−
D
·
P
(
t
)
d
V
(
t
)
d
t
=
F
(
t
)
d
W
d
t
=
Z
−
W
β
d
Z
d
t
=
S
(
t
)
−
Z
β
F
(
t
)
=
(
V
(
t
)
S
F
−
S
(
t
)
)
·
(
r
s
·
X
(
t
)
+
S
s
e
t
−
S
(
t
)
τ
s
e
t
)
D
=
F
V
Cell model equations:
μ
=
K
B
1
·
W
(
t
)
K
s
+
W
(
t
)
−
K
B
2
·
m
A
T
P
r
ρ
=
K
ρ
1
·
μ
+
K
ρ
2
r
S
=
r
S
,
m
a
x
⋅
S
(
t
)
K
s
+
S
(
t
)
W
(
t
)
=
∫
−
∞
t
(
S
(
t
−
τ
)
/
β
2
)
.
τ
·
exp
(
−
τ
/
β
)
·
d
τ
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