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Model Mathematics

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Component: environment

Component: Py

\frac{d}{d time} (Py) = r4 Py1 - (r3 {Zn}^{2} Py)

Component: Py1

\frac{d}{d time} (Py1) = r3 {Zn}^{2} Py + k_1 Qw2 - (r4 Py1 + k1a Dw Py1)

Component: Dw

\frac{d}{d time} (Dw) = k_1 Qw2 + k3 Qw1 + k_2 Qw1 - (k1a Dw Py1 + k2 Dw Rw)

Component: Rw

\frac{d}{d time} (Rw) = k3 Qw1 + k_2 Qw1 - (k2 Dw Rw)

Component: Qw1

\frac{d}{d time} (Qw1) = k2 Dw Rw - (k3 Qw1 + k_2 Qw1)

Component: Qw2

\frac{d}{d time} (Qw2) = k1a Dw Py1 - (k_1 Qw2)

Component: Mw

\frac{d}{d time} (Mw) = k3 Qw1

Component: Px

\frac{d}{d time} (Px) = r2 Px1 + k_1 Qz4 - (r1 Zn Px + k1b Dz Px)

Component: Px1

\frac{d}{d time} (Px1) = r1 Zn Px + k_1 Qz2 - (r2 Px1 + k1 Dz Px1)

Component: Dz

\frac{d}{d time} (Dz) = k_1 Qz2 + k3 Qz1 + k_2 Qz1 + k_1 Qz4 - (k1b Dz Px + k1 Dz Px1 + k2a Dz Rz)

Component: Rz

\frac{d}{d time} (Rz) = k3 Qz1 + k_2 Qz1 + k3 Qz3 + k_2 Qz3 + k3 Qz5 + k_2 Qz5 - (k2a Dz Rz + k2b Qz4 Rz + k2c Qz2 Rz)

Component: Qz1

\frac{d}{d time} (Qz1) = k2a Dz Rz - (k3 Qz1 + k_2 Qz1)

Component: Qz2

\frac{d}{d time} (Qz2) = k1 Dz Px1 + k3 Qz3 + k_2 Qz3 - (k_1 Qz2 + k2c Qz2 Rz)

Component: Qz3

\frac{d}{d time} (Qz3) = k2c Qz2 Rz - (k3 Qz3 + k_2 Qz3)

Component: Qz4

\frac{d}{d time} (Qz4) = k1b Dz Px + k3 Qz5 + k_2 Qz5 - (k_1 Qz4 + k2b Qz4 Rz)

Component: Qz5

\frac{d}{d time} (Qz5) = k2b Qz4 Rz - (k3 Qz5 + k_2 Qz5)

Component: Mz

\frac{d}{d time} (Mz) = k3 Qz1 + k3 Qz3 + k3 Qz5

Component: model_parameters

k3 = \{\begin{matrix} 0.0 if time \geq 0.0 \land time < td0 \\ 0.011 if time \geq td0 \land time < td \end{matrix}

Source: Derived from workspace Cui, Kaandorp, Lloyd, 2008 at changeset edffca194968.

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