Table 1.
Definitions and values of parameters for the animals and bacterial ecology. The model was simulated for a 12-month feedlot rearing period.
| Parameter | Definition, units | Base value and distribution | References |
|---|---|---|---|
| Animals, and matter movement | |||
| A | Number of steers | 150 | [35] |
| bw(t) | Body weight (kg) | — | Approximated with a model [38] |
| faeces_dep | Faeces production (ml/kg body weight per h) | 0·992 | Estimated from [46, 47] |
| mCW | Fraction of faeces shed to water | 0·05 | [35] |
| mCF | Fraction of faeces shed to feed | 0·02 | [35] |
| mCE | Fraction of faeces shed to environment | 0·93 | [35] |
| consum_water | Consumption of water (ml/kg bw per h) | 5·11 | Estimated from [48] |
| consum_feed | Consumption of feed (g/kg bw per h) | 1·10 | Estimated from [49] |
| consum_env | Consumption of environment (g/kg bw per h) | 0·08 | Estimated from [35] |
| mWC | Water as fraction of consumption | 0·8124 | Calculated |
| mFC | Feed as fraction of consumption | 0·1749 | Calculated |
| mEC | Environment as fraction of consumption | 0·0127 | Calculated |
| reten_rumen | Ingesta retention time in rumen (h) | 36 | Estimated from [39] |
| reten_rumentolgin | Ingesta retention time from rumen to large intestine (h) | 12 | Estimated from [39] |
| mfrEW | Fractional spillage of environment into water (per h) | 0·0002 | [35] |
| mfrWE | Fractional spillage of water into environment (per h) | 0·0042 | [35] |
| E. coli populations | |||
| υstart | Starting fraction of resistant E. coli in within-pen habitats | 0·02, uniform (0·01, 0·03) | Assumed |
| α | Fitness cost, fractional decrease in net replication rate for resistant E. coli | 0·05, uniform (0·025, 0·075) | Estimated from [9] |
| ζj | Maximum fractional plasmid curing resistant E. coli in habitat j (per h) | 1 | Intervention target |
| τj | Probability of completed conjugation per contact between sensitive cell and plasmid-donor cell in habitat j | 1 | Intervention target |
| E. coli in large intestine | |||
| rC | Net replication rate (per h) | 0·17, uniform (0·085, 0·255) | [34] |
| NmaxC | Maximum E. coli (log c.f.u./ml) | 5·50, log-uniform (4·95, 6·05) | [34] |
| βC | Plasmid transfer term (log/h) | −2·70, log-uniform (−2·97, −2·43) | [34] |
| γ | Fractional in-flow/out-flow (per h) | 0·0100, uniform (0·0050, 0·0150) | [32, 34] |
| E. coli in water | |||
| rW | Net replication rate (per h) | 0·14, uniform (0·07, 0·21) | [35] |
| NmaxW | Maximum E. coli (log c.f.u./ml) | 5·00, log-uniform (4·50, 5·50) | Assumed equal to nmaxE |
| βW | Plasmid transfer term (log/h) | −4·00, log-uniform (−4·40, −3·60) | [37] |
| VW | Volume (l) | 50 | [35] |
| NWfr | Number of E. coli in water supplied (log c.f.u./ml) | 3·00, log-uniform (2·70, 3·30) | [11] |
| υWfr | Fraction of resistant E. coli in water supplied | 0·02, uniform (0·01, 0·03) | Assumed |
| E. coli in feed | |||
| rF | Net replication rate (per h) | 0·02, uniform (0·01, 0·03) | [35] |
| NmaxF | Maximum E. coli (log c.f.u./ml) | 4·00, log-uniform (3·60, 4·40) | [35] |
| βF | Plasmid transfer term (log/h) | −6·00, log-uniform (−6·60, −5·40) | Assumed |
| VF | Volume (l) | 2000 | [35] |
| NFfr | Number of E. coli in feed supplied (log c.f.u./ml) | 3·00, log-uniform (2·70, 3·30) | Assumed equal to NWfr |
| υFfr | Fraction of resistant E. coli in feed supplied | 0·02, uniform (0·01, 0·03) | Assumed |
| E. coli in pen's environment | |||
| rE | Net replication rate (per h) | 0·05, uniform (0·025, 0·075) | [35] |
| NmaxE | Maximum E. coli (log c.f.u./ml) | 5·00, log-uniform (4·5, 5·50) | [35] |
| βE | Plasmid transfer term (log/h) | −4·00, log-uniform (−4·40, −3·60) | Assumed equal to βW |
| VE | Volume (l) | 500 | [35] |