Use of a nonlinear model to estimate milk losses due to subclinical mastitis in Holstein-Zebu cows

Abstract

The objective of this observational study was to estimate milk loss from subclinical mastitis (SCM) using a nonlinear one-phase exponential decay function fitted to the relationship between the sum of the California mastitis test scores of productive quarters (x1, 0 to 16) and daily milk production per cow (y, kg/day). The function was y = (a – b)e^−c1*x1 + b, where a is the predicted y when x is zero, b is the y when x1 tends to infinity, and c1 is a rate constant. The fitted function was y = (10.02 – 5.76)e^{−0.06137*x1} + 5.76, with an adjusted coefficient of determination (R²_adj) of 0.0692, a standard deviation of the residual (S_y.x) equal to 13.49, and an Akaike’s information criterion corrected (AIC_C) of 3902.8. To this function, we added the multiplicative factors test day (x2, 1 to 12), the number of productive quarters (x3, 2, 3 or 4), months of age of cow (x4, 25 to 209), and days in milk (x5, 2 to 196), to adjust the decay function for their effects. The fitted model was y = [(9.65 – 3.95)e^{−0.03415*x1} + 3.95] (x2^–0.1081) (x3^0.1049) (x4^0.1589) (x5^–0.1972) with R² of 0.3166, S_y.x = 11.38, and AIC_C = 3821.9. We used the adjusted decay function parameters to compute a conversion factor (CF, 0 to 1) each x1 integer value from 0 to 16 to project its actual y to that of an SCM-free udder (x = 0). Then, the CF for a x1 of 0 equals to 9.65/9.65 = 1, and for a x1 of 8 equals 8.28, so its CF would be 8.29/9.65 = 0.8588. A cow with a 5.5 kg/day milk production at an x1 score of 8 would have an SCM-free production of 5.5/0.8588 = 6.4 kg/day, and its daily milk loss would be 6.4-5.5 = 0.9 kg/day. The difference, multiplied by MX$ 5.50 (US$ 0.275), would result in an economic loss of 4.95 Mexican pesos per day. This procedure makes possible the timely on-site estimation of economic losses due to subclinical mastitis.