Table 2.

Enterococci Metapopulation Model Equations

Number	Definition	Equation
11	Daily rate of water (W) consumption by pen of cattle (C)	$W_{to}C=\frac{N_c\times W_c}{Trough}$
12	Daily rate of feed (F) consumption by a pen of cattle (C)	$F_{to}C=\frac{N_c\times F_c}{Feed}$
13	Daily consumption of environment (E) (pen surface) by a pen of cattle (C)	$E_{to}C=\frac{N_c\times E_c}{Pen}$
14	Change in Enterococcus number in the cattle large intestine over time (CFU/h)	$\frac{d{C}_j}{dt}=\left(R_C\left(1-\frac{C}{K_C}\right)C_j\times \left(1-{\alpha }_j\right)\times E_j\right)+\tau \times \left(\left(P_{to}C\times P_j\right)+\left(W_{to}C\times W_j\right)+\left(F_{to}C\times F_j\right)\right)-\left(C_{to}P\times C_j\right)\pm \left({\beta }_j\frac{C_{sus}\times C_{res}}{C}\right)$
15	Change in Enterococcus number in water trough over time (CFU/h).	$\frac{d{W}_j}{dt}=\left(P_{to}W\times P_j\right)-\left(R_W{W}_j\left(1+{\alpha }_j\right)\right)-\left(W_{to}C\times W_j\right)-\left(W_{to}P\times W_j\right)\pm \left({\beta }_j\frac{W_{sus}\times W_{res}}{W}\right)$
16	Change in Enterococcus number in feed bunk over time (CFU/h).	$\frac{d{F}_j}{dt}=\left(P_{to}F\times P_j\right)-\left(R_F{F}_j\left(1+{\alpha }_j\right)\right)-\left(F_{to}C\times F_j\right)-\left(F_{to}P\times F_j\right)\pm \left({\beta }_j\frac{F_{sus}\times F_{res}}{F}\right)$
17	Change in Enterococcus number in the pen environment over time (CFU/h).	$\frac{d{P}_j}{dt}=\left(C_{to}P\times C_j\right)+\left(F_{to}P\times F_j\right)+\left(W_{to}P\times W_j\right)-\left(R_P{P}_j\left(1+{\alpha }_j\right)\right)-\left(P_{to}C\times P_j\right)-\left(P_{to}F\times P_j\right)-\left(P_{to}W\times P_j\right)\pm \left({\beta }_j\frac{P_{sus}\times P_{res}}{P}\right)$

M_toN, enterococci move from niche (P, C, W, or F) to niche N (P, C, W, or F).

CFU, colony-forming unit.