Model Mathematics

\frac{d}{d time} (phi_I) = alpha K_T + k1 k2 phi_I (1.0 - (k3 (phi_I + phi_R) + k5 F + k6 C)) - (d1 phi_I)

\frac{d}{d time} (phi_R) = (1.0 - alpha) K_T + k1 k2 phi_R (1.0 - (k3 (phi_I + phi_R) + k5 F + k6 C)) - (d1 phi_R)

\frac{d}{d time} (T) = k4 phi_I + k7 F + Apligraf - (d2 T) Apligraf = \{\begin{matrix} 0.0 if time \geq 0.0 \land time < 28.0 \\ 0.4 if time \geq 28.0 \land time < 29.0 \\ 0.0 if time \geq 29.0 \land time < 35.0 \\ 0.4 if time \geq 35.0 \land time < 36.0 \\ 0.0 if time \geq 36.0 \land time < 42.0 \\ 0.4 if time \geq 42.0 \land time < 43.0 \\ 0.0 if time \geq 43.0 \land time < 49.0 \\ 0.4 if time \geq 49.0 \land time < 50.0 \\ 0.0 if time \geq 50.0 \land time < 56.0 \\ 0.4 if time \geq 56.0 \land time < 57.0 \\ 0.0 if time \geq 57.0 \land time < 63.0 \\ 0.4 if time \geq 63.0 \land time < 64.0 \\ 0.0 if time \geq 64.0 \land time < 70.0 \\ 0.4 if time \geq 70.0 \land time < 71.0 \\ 0.0 if time \geq 71.0 \land time < 77.0 \\ 0.4 if time \geq 77.0 \land time < 78.0 \\ 0.0 otherwise \end{matrix}

\frac{d}{d time} (P) = k8 (phi_I + phi_R) + k9 F + Apligraf - (d3 P) Apligraf = \{\begin{matrix} 0.0 if time \geq 0.0 \land time < 28.0 \\ 1.0 if time \geq 28.0 \land time < 29.0 \\ 0.0 if time \geq 29.0 \land time < 35.0 \\ 1.0 if time \geq 35.0 \land time < 36.0 \\ 0.0 if time \geq 36.0 \land time < 42.0 \\ 1.0 if time \geq 42.0 \land time < 43.0 \\ 0.0 if time \geq 43.0 \land time < 49.0 \\ 1.0 if time \geq 49.0 \land time < 50.0 \\ 0.0 if time \geq 50.0 \land time < 56.0 \\ 1.0 if time \geq 56.0 \land time < 57.0 \\ 0.0 if time \geq 57.0 \land time < 63.0 \\ 1.0 if time \geq 63.0 \land time < 64.0 \\ 0.0 if time \geq 64.0 \land time < 70.0 \\ 1.0 if time \geq 70.0 \land time < 71.0 \\ 0.0 if time \geq 71.0 \land time < 77.0 \\ 1.0 if time \geq 77.0 \land time < 78.0 \\ 0.0 otherwise \end{matrix}

\frac{d}{d time} (F) = M_P + k10 F (1.0 - (k3 (phi_I + phi_R) + k5 F + k6 C)) + Apligraf - (d4 F) Apligraf = \{\begin{matrix} 0.0 if time \geq 0.0 \land time < 28.0 \\ 8000.0 if time \geq 28.0 \land time < 29.0 \\ 0.0 if time \geq 29.0 \land time < 35.0 \\ 8000.0 if time \geq 35.0 \land time < 36.0 \\ 0.0 if time \geq 36.0 \land time < 42.0 \\ 8000.0 if time \geq 42.0 \land time < 43.0 \\ 0.0 if time \geq 43.0 \land time < 49.0 \\ 8000.0 if time \geq 49.0 \land time < 50.0 \\ 0.0 if time \geq 50.0 \land time < 56.0 \\ 8000.0 if time \geq 56.0 \land time < 57.0 \\ 0.0 if time \geq 57.0 \land time < 63.0 \\ 8000.0 if time \geq 63.0 \land time < 64.0 \\ 0.0 if time \geq 64.0 \land time < 70.0 \\ 8000.0 if time \geq 70.0 \land time < 71.0 \\ 0.0 if time \geq 71.0 \land time < 77.0 \\ 8000.0 if time \geq 77.0 \land time < 78.0 \\ 0.0 otherwise \end{matrix}

\frac{d}{d time} (C) = k11 F f_T g_C + Apligraf - (d5 F C) Apligraf = \{\begin{matrix} 0.0 if time \geq 0.0 \land time < 28.0 \\ 18.75 if time \geq 28.0 \land time < 29.0 \\ 0.0 if time \geq 29.0 \land time < 35.0 \\ 18.75 if time \geq 35.0 \land time < 36.0 \\ 0.0 if time \geq 36.0 \land time < 42.0 \\ 18.75 if time \geq 42.0 \land time < 43.0 \\ 0.0 if time \geq 43.0 \land time < 49.0 \\ 18.75 if time \geq 49.0 \land time < 50.0 \\ 0.0 if time \geq 50.0 \land time < 56.0 \\ 18.75 if time \geq 56.0 \land time < 57.0 \\ 0.0 if time \geq 57.0 \land time < 63.0 \\ 18.75 if time \geq 63.0 \land time < 64.0 \\ 0.0 if time \geq 64.0 \land time < 70.0 \\ 18.75 if time \geq 70.0 \land time < 71.0 \\ 0.0 if time \geq 71.0 \land time < 77.0 \\ 18.75 if time \geq 77.0 \land time < 78.0 \\ 0.0 otherwise \end{matrix}

\frac{d}{d time} (H) = k12 F + Apligraf - (d6 H) Apligraf = \{\begin{matrix} 0.0 if time \geq 0.0 \land time < 28.0 \\ 80.0 if time \geq 28.0 \land time < 29.0 \\ 0.0 if time \geq 29.0 \land time < 35.0 \\ 80.0 if time \geq 35.0 \land time < 36.0 \\ 0.0 if time \geq 36.0 \land time < 42.0 \\ 80.0 if time \geq 42.0 \land time < 43.0 \\ 0.0 if time \geq 43.0 \land time < 49.0 \\ 80.0 if time \geq 49.0 \land time < 50.0 \\ 0.0 if time \geq 50.0 \land time < 56.0 \\ 80.0 if time \geq 56.0 \land time < 57.0 \\ 0.0 if time \geq 57.0 \land time < 63.0 \\ 80.0 if time \geq 63.0 \land time < 64.0 \\ 0.0 if time \geq 64.0 \land time < 70.0 \\ 80.0 if time \geq 70.0 \land time < 71.0 \\ 0.0 if time \geq 71.0 \land time < 77.0 \\ 80.0 if time \geq 77.0 \land time < 78.0 \\ 0.0 otherwise \end{matrix}

K_T = tau1 T^{3.0} + tau2 T^{2.0} + tau3 T + tau4

M_P = tau1 P^{3.0} + tau2 P^{2.0} + tau3 P + tau4

f_T = tau1 T^{3.0} + tau2 T^{2.0} + tau3 T + tau4

g_C = tau1 C^{3.0} + tau2 C^{2.0} + tau3 C + tau4

alpha = (- (0.197 \log_{10} H)) + 0.4407