# Model Mathematics

### Component: environment

### Component: R

$ddtime R = DR \u2062 pi_C - DB pi_C \u2062 R $

### Component: B

$ddtime B = DB pi_C \u2062 R - kB \u2062 B + f f = 0.0001 if time > 20.0 \u2227 time \u2266 80.0 0.0 otherwise$

### Component: C

$ddtime C = DC \u2062 pi_L - DA \u2062 pi_C \u2062 C $

### Component: pi_L

$ pi_L = k3 k4 \u2062 KLP \u2062 pi_P \u2062 B 1.0 + k3 \u2062 K k4 + k1 k2 \u2062 ko \u2062 KOP pi_P \u2062 R + Io \u2062 1.0 + IL rL $

### Component: model_parameters

$ DB = f0 \u2062 dB pi_C = C + f0 \u2062 C_s C + C_s pi_P = P + P_0 P + P_s P = IP kP P_0 = SP kP P_s = k6 k5 $