Table 1 Parameters for herd management and population dynamics used in a Mycobacterium avium paratuberculosis infection dynamics model within a structured dairy herd
Notation | Value | Definition | Source |
|---|---|---|---|
σ B | 0.07 | Mortality rate of calves at birth | a, [32] |
σ m | 0.206 | Exit rate of male calves, weeks 2 to 4 (per week) | |
σ C1 | 0.015 | Death rate of female calves, weeks 1 and 2 (individual housing facilities) (per week) | [32] |
σ C2 | 0.0035 | Death rate of female calves, weeks 3 to weaning (collective housing facilities) (per week) | [33] |
σ C3 | 0.00019 | Death rate of heifers from weaning to first calving (per week) | b |
σ h | 0.11 | Sale rate of bred heifers 10 weeks before 1st calving | b |
σ Ai | 27, 25, 31, 31, 62 | Yearly culling rate of cows in parity 1, 2, 3, 4 and above 5 respectively (%) | a, [34] |
m | 2 | Maximal age in individual pen (weeks) | [13] |
w | 10 | Weaning age (weeks) | [13] |
y | 52 | Age when entering the young heifer group (weeks) | |
nb | 2 | Number of neighbours for a calf in an individual pen | b |
h | 91 | Age at first artificial insemination (weeks) | a |
cal | 130 | Age at first calving (weeks) | a,b |
cci | 56.3 | Calving-to-calving interval (weeks) | a,b |
b | 5 | Quantity of colostrum fed to calves (L/day for 3 days) | b |
d | 7 | Quantity of milk fed to calves after 3 days (L/day/calf) | b |
prop | 0.85 | Proportion of lactating cows | a |
ε | 25 | Quantity of milk or colostrum produced (L/day/cow) | a |
f 1 | 0.5 | Quantity of faeces produced by a non-weaned calf (kg/day) | b |
f 2 | 5.5 | Quantity of faeces produced by a weaned calf (kg/day) | b |
f Y | 10 | Quantity of faeces produced by a heifer (kg/day) | b |
f A | 30 | Quantity of faeces produced by a cow (kg/day) | b |
Graz | [14-46] | Grazing period (1 being the first week of the year) | b |
K c | 110 | Number of cows above which the heifer selling rate increases | - |