Model Mathematics

\frac{d}{d time} (Ip) = f1_G - (E (\frac{Ip}{Vp} - (\frac{Ii}{Vi})) + \frac{Ip}{tp}) Ip_conc = \frac{Ip}{Vp} f1_G = \frac{Rm}{1 + ⅇ^{\frac{C1 - (\frac{G}{Vg})}{a1}}}

\frac{d}{d time} (Ii) = E (\frac{Ip}{Vp} - (\frac{Ii}{Vi})) - (\frac{Ii}{ti}) Ii_conc = \frac{Ii}{Vi}

\frac{d}{d time} (G) = Gin + f5_x3 + (- (f2_G + f3_G f4_Ii)) G_conc = \frac{G}{Vg 10} f2_G = Ub (1 - (ⅇ^{\frac{- G}{C2 Vg}})) f3_G = \frac{G}{C3 Vg} f4_Ii = U0 + \frac{Um - U0}{1 + ⅇ^{(- beta) \ln (\frac{Ii}{C4} (\frac{1}{Vi} + \frac{1}{E ti}))}} f5_x3 = \frac{Rg}{1 + ⅇ^{alpha (\frac{x3 1}{Vp} - C5)}}

\frac{d}{d time} (x1) = \frac{3}{td} (\frac{Ip}{1} - x1) \frac{d}{d time} (x2) = \frac{3}{td} (x1 - x2) \frac{d}{d time} (x3) = \frac{3}{td} (x2 - x3)