Model Mathematics

\frac{d}{d time} (y0) = 1.0 g0 + c0 + e0 g0 = h0 r0 h0 = \{\begin{matrix} \frac{a00 y0 + a02 y2}{1.0 + \frac{a00 y0 + a02 y2}{S0} (1.0 - (ⅇ^{- (\frac{a00 y0 + a02 y2}{S0})}))} if a00 y0 + a02 y2 > 0.0 \\ a00 y0 + a02 y2 if a00 y0 + a02 y2 ≦ 0.0 \end{matrix} r0 = \{\begin{matrix} 1.0 - (ⅇ^{\frac{S0 {y0}^{2.0}}{(a00 y0 + a02 y2) {(epsilon - y0)}^{2.0}}}) if y0 < epsilon \land a00 y0 + a02 y2 < 0.0 \\ 1.0 otherwise \end{matrix}

\frac{d}{d time} (y1) = 1.0 g1 + e1 g1 = h1 r1 h1 = \{\begin{matrix} \frac{a10 y0 + a11 y1 + a12 y2}{1.0 + \frac{a10 y0 + a11 y1 + a12 y2}{S1} (1.0 - (ⅇ^{- (\frac{a10 y0 + a11 y1 + a12 y2}{S1})}))} if a10 y0 + a11 y1 + a12 y2 > 0.0 \\ a10 y0 + a11 y1 + a12 y2 if a10 y0 + a11 y1 + a12 y2 ≦ 0.0 \end{matrix} r1 = \{\begin{matrix} 1.0 - (ⅇ^{\frac{S1 {y1}^{2.0}}{(a10 y0 + a11 y1 + a12 y2) {(epsilon - y1)}^{2.0}}}) if y1 < epsilon \land a10 y0 + a11 y1 + a12 y2 < 0.0 \\ 1.0 otherwise \end{matrix}

\frac{d}{d time} (y2) = 1.0 g2 + e2 g2 = h2 r2 h2 = \{\begin{matrix} \frac{a20 y0 + a21 y1 + a22 y2 + a23 y3 + a24 y4}{1.0 + \frac{a20 y0 + a21 y1 + a22 y2 + a23 y3 + a24 y4}{S2} (1.0 - (ⅇ^{- (\frac{a20 y0 + a21 y1 + a22 y2 + a23 y3 + a24 y4}{S2})}))} if a20 y0 + a21 y1 + a22 y2 + a23 y3 + a24 y4 > 0.0 \\ a20 y0 + a21 y1 + a22 y2 + a23 y3 + a24 y4 if a20 y0 + a21 y1 + a22 y2 + a23 y3 + a24 y4 ≦ 0.0 \end{matrix} r2 = \{\begin{matrix} 1.0 - (ⅇ^{\frac{S2 {y2}^{2.0}}{(a20 y0 + a21 y1 + a22 y2 + a23 y3 + a24 y4) {(epsilon - y2)}^{2.0}}}) if y2 < epsilon \land a20 y0 + a21 y1 + a22 y2 + a23 y3 + a24 y4 < 0.0 \\ 1.0 otherwise \end{matrix}

\frac{d}{d time} (y3) = 1.0 g3 g3 = h3 r3 h3 = \{\begin{matrix} \frac{a32 y2 + a33 y3}{1.0 + \frac{a32 y2 + a33 y3}{S3} (1.0 - (ⅇ^{- (\frac{a32 y2 + a33 y3}{S3})}))} if a32 y2 + a33 y3 > 0.0 \\ a32 y2 + a33 y3 if a32 y2 + a33 y3 ≦ 0.0 \end{matrix} r3 = \{\begin{matrix} 1.0 - (ⅇ^{\frac{S3 {y3}^{2.0}}{(a32 y2 + a33 y3) {(epsilon - y3)}^{2.0}}}) if y3 < epsilon \land a32 y2 + a33 y3 < 0.0 \\ 1.0 otherwise \end{matrix}

\frac{d}{d time} (y4) = 1.0 g4 g4 = h4 r4 h4 = \{\begin{matrix} \frac{a42 y2 + a44 y4}{1.0 + \frac{a42 y2 + a44 y4}{S4} (1.0 - (ⅇ^{- (\frac{a42 y2 + a44 y4}{S4})}))} if a42 y2 + a44 y4 > 0.0 \\ a42 y2 + a44 y4 if a42 y2 + a44 y4 ≦ 0.0 \end{matrix} r4 = \{\begin{matrix} 1.0 - (ⅇ^{\frac{S4 {y4}^{2.0}}{(a42 y2 + a44 y4) {(epsilon - y4)}^{2.0}}}) if y4 < epsilon \land a42 y2 + a44 y4 < 0.0 \\ 1.0 otherwise \end{matrix}