Model Mathematics

\frac{d}{d time} (R) = f1 - (delta_R R) logR = \log_{10} R

\frac{d}{d time} (U) = f2 + d01 B1 + d12 B2 - (delta_U U + alpha0 P U + alpha1 B1 U) logU = \log_{10} U

\frac{d}{d time} (B1) = alpha0 P U + d12 B2 - (d01 B1 + delta_b1 B1 + alpha1 B1 U) logB1 = \log_{10} B1

\frac{d}{d time} (B2) = alpha1 B1 U - (d12 B2 + delta_b2 B2) logB2 = \log_{10} B2

P = P0 + PE q q = \{\begin{matrix} 0.0 if time < ti \\ 1.0 - (ⅇ^{(- G) (time - ti)}) if time < T + ti \land time \geq ti \\ ⅇ^{G T - 1.0} ⅇ^{G (time - ti)} otherwise \end{matrix}

f1 = a0 (1.0 - (\frac{B2}{b + B2})) + \frac{x (1.0 - (ⅇ^{\frac{- x}{a}})) B2}{b0 + B2}

\frac{d}{d time} (x) = \frac{s (P - P0)}{P + P1} - (delta_x x)

f2 = \frac{kappa R}{kappa0 + R}