Model Mathematics

\frac{d}{d time} (P) = k1_Ca + k2_Ci + D - (k1 Ra P + k2 Ri P + kcl P)

\frac{d}{d time} (Ra) = k1_Ca + k3 Ri - (k1 Ra P + k3_Ra)

\frac{d}{d time} (Ri) = k2_Ci + k3_Ra - (k2 Ri P + k3 Ri)

\frac{d}{d time} (Ca) = k1 Ra P + k4 Ci - (k1_Ca + k4_Ca)

\frac{d}{d time} (Ci) = k2 Ri P + k4_Ca - (k2_Ci + k4 Ci)

rho = \frac{Ra + Ca}{Ra + Ca + Ri + Ci}

D = De + Dd cycle_length = tau_on + tau_off time_hour = \frac{time 1}{3600} Dd = \{\begin{matrix} dmin if \frac{time_hour}{cycle_length} \geq j \\ dmax if time_hour - (⌊ \frac{time_hour}{cycle_length} ⌋ cycle_length) \geq 0 \land time_hour - (⌊ \frac{time_hour}{cycle_length} ⌋ cycle_length) < tau_on \\ dmin if time_hour - (⌊ \frac{time_hour}{cycle_length} ⌋ cycle_length) \geq tau_on \land time_hour - (⌊ \frac{time_hour}{cycle_length} ⌋ cycle_length) < cycle_length \end{matrix}