Model Mathematics

\frac{d}{d time} (P0) = (- p) P0 \frac{d}{d time} (P1) = p P0 - (p P1) - (c P1) \frac{d}{d time} (P2) = p P1 - (p P2) - (2 c P2) \frac{d}{d time} (P3) = p P2 - (p P3) - (3 c P3) \frac{d}{d time} (P4) = p P3 - (p P4) - (4 c P4) \frac{d}{d time} (P5) = p P4 - (p P5) - (5 c P5) \frac{d}{d time} (P6) = p P5 - (p P6) - (6 c P6) \frac{d}{d time} (P7) = p P6 - (p P7) - (7 c P7) \frac{d}{d time} (P8) = p P7 - (p P8) - (8 c P8) \frac{d}{d time} (P9) = p P8 - (p P9) - (9 c P9) A = P0 + P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8 + P9 S = 1 ⅇ^{\frac{p}{c} (1 - (c time) - (ⅇ^{- (c time)}))} D = 1 - (P0 + P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8 + P9)