
354 Modeling and Inverse Problems in the Presence of Uncertainty
CTMCs {X
M
(t) : t ≥ 0} with transition rates and corresponding state change
vectors defined in Table 8.6 is density dependent.
Based on Kurtz’s limit theorem, we know that the corresponding determin-
istic model for the stochastic pork production network model with transition
rates λ
j
and corresponding state change vectors v
j
given in Table 8.6 is
˙x
M
1
(t) = −k
1
x
M
1
(t)(L
2
− x
M
2
(t))
+
+ k
4
min(x
M
4
(t), S
m
)
˙x
M
2
(t) = −k
2
x
M
2
(t)(L
3
− x
M
3
(t))
+
+ k
1
x
M
1
(t)(L
2
− x
M
2
(t))
+
˙x
M
3
(t) = −k
3
x
M
3
(t)(L
4
− x
M
4
(t))
+
+ k
2
x
M
2
(t)(L
3
− x
M
3
(t))
+
˙x
M
4
(t) = −k
4
min(x
M
4
(t), S
m
) + k
3
x
M
3
(t)(L
4
− x
M
4
(t))
+
x
M
(0) = x
M
0
.
(8.45)
8.6.3 Numerical ...