Model Mathematics

\frac{d}{d time} (x) = \frac{a1}{k1 + y} - (b1 x)

\frac{d}{d time} (y) = \{\begin{matrix} epsilon (\frac{(a2 + a3 x) y z}{k2 + x^{2.0}} - (b2 y)) if time \geq 0.0 \land time < 10000.0 \\ epsilon (\frac{(a2 + a3 x) y z}{k2 + x^{2.0}} - (b2 y + kc y)) if time \geq 10000.0 \land time < 27280.0 \\ epsilon (\frac{(a2 + a3 x) y z}{k2 + x^{2.0}} - (b2 y)) if time \geq 27280.0 \land time < 50320.0 \\ epsilon (\frac{(a2 + a3 x) y z}{k2 + x^{2.0}} - (b2 y + kc y)) if time \geq 50320.0 \land time < 67600.0 \\ epsilon (\frac{(a2 + a3 x) y z}{k2 + x^{2.0}} - (b2 y)) if time \geq 67600.0 \land time < 90640.0 \\ epsilon (\frac{(a2 + a3 x) y z}{k2 + x^{2.0}} - (b2 y + kc y)) if time \geq 90640.0 \land time < 107920.0 \end{matrix}

\frac{d}{d time} (z) = epsilon delta (a4 x - (\frac{a5 x z}{k3 + x} + b3 z))