Mathematical modeling of the mastitis infection process

Mastitis infection is a biological process with a serial structure and stochastic in nature. A mathematical model for this process was developed from Markov chain theory. The unit of the process was an individual quarter; and four infection processes for first, second, third, fourth or higher lactation were described. Two Markov matrices which probabilistically determine the transitions between seven mutually exclusive states at each stage of the process were defined. After its validation, the model was used to determine the lactational consequences of the mastitis infection by calculating expected milk-yield productivity. Expected milk-yield productivity for an individual quarter was .93, .88, .85, and .84 for first, second, third, and fourth or higher lactation. The expected milk yield productivity of a quarter as a function of its state at the beginning of the process also was calculated. The quarters infected but not clinical have the lowest productivity.