Model Mathematics

\frac{d}{d time} (r) = Ir - (k6 r) Ir = \{\begin{matrix} 0.0 if time \geq 0.0 \land time ≦ 90.0 \\ 10.0 if time \geq 91.0 \land time ≦ 92.0 \\ 0.0 if time \geq 93.0 \land time ≦ 113.0 \\ 10.0 if time \geq 114.0 \land time ≦ 115.0 \\ 0.0 if time \geq 116.0 \land time ≦ 136.0 \\ 10.0 if time \geq 137.0 \land time ≦ 138.0 \\ 0.0 if time \geq 139.0 \land time ≦ 159.0 \\ 10.0 if time \geq 160.0 \land time ≦ 161.0 \\ 0.0 if time \geq 162.0 \land time ≦ 252.0 \\ 10.0 if time \geq 253.0 \land time ≦ 254.0 \\ 0.0 if time \geq 255.0 \land time ≦ 275.0 \\ 10.0 if time \geq 276.0 \land time ≦ 277.0 \\ 0.0 if time \geq 278.0 \land time ≦ 298.0 \\ 10.0 if time \geq 299.0 \land time ≦ 300.0 \\ 0.0 if time \geq 301.0 \land time ≦ 321.0 \\ 10.0 if time \geq 322.0 \land time ≦ 323.0 \\ 0.0 otherwise \end{matrix}

\frac{d}{d time} (s) = Is - (k7 s)

\frac{d}{d time} (f) = (- (k1 (r + c) f)) + (k2 + k3 phi_b_s) (1.0 - f) phi_b_s = \frac{1.0}{1.0 + ⅇ^{\frac{- (\log_{10} (1.0 s) - sb)}{delta_b}}}

\frac{d}{d time} (h) = j1 ((k4 + k5 (1.0 - phi_r_s)) (r + c) f - (k8 h)) phi_r_s = \frac{1.0}{1.0 + ⅇ^{\frac{- (\log_{10} (1.0 s) - sr)}{delta_r}}}

Is = \{\begin{matrix} 10.0 if time > 0.0 \land time ≦ 90.0 \\ 0.0 if time > 90.0 \land time ≦ 180.0 \\ 10.0 if time > 180.0 \land time ≦ 270.0 \\ 0.0 if time > 270.0 \land time ≦ 360.0 \\ 0.0 otherwise \end{matrix}