Model Mathematics

\frac{d}{d time} (Rs) = (kr + ksyn) Cs + Vs - (kf L Rs + kt Rs)

\frac{d}{d time} (Cs) = kf L Rs - ((kr + ke) Cs)

\frac{d}{d time} (Ri) = kre Ci + kt Rs - (kfe Li Ri + kh Ri)

\frac{d}{d time} (Ci) = kfe Li Ri + ke Cs - ((kre + kh) Ci)

\frac{d}{d time} (Li) = \frac{kre Ci - (kfe Li Ri)}{Ve NA} - (kx Li)

\frac{d}{d time} (Ld) = kh Ci

\frac{d}{d time} (L) = \frac{(kr Cs + kx Li Ve NA - (kf L Rs)) Y}{NA}

\frac{d}{d time} (Y) = \{\begin{matrix} (\frac{600 Cs}{250 + Cs} - 200) 1 e 3 if \frac{600 Cs}{250 + Cs} - 200 > 0 \\ 0 otherwise \end{matrix}

kf = \{\begin{matrix} \frac{kr}{11.1} if IL2 = 1 \\ \frac{kr}{8.2} otherwise \end{matrix} kre = \{\begin{matrix} kr 8 if IL2 = 1 \\ kr 5 otherwise \end{matrix} kfe = \{\begin{matrix} \frac{kre}{1000} if IL2 = 1 \\ \frac{kre}{3000} otherwise \end{matrix}