Fig 1.
MAP fecal shedding patterns from five seven cows.
Shedding patterns were variable among individuals. The number of samples taken from each cow was also variable, ranging from 2 to 11 samples. The variation in both CFU count and number of samples may be related to disease progression, as animals with high CFU counts may be culled early due to clinical MAP infection related production losses.
Fig 2.
Diagram of hidden Markov model 1.
This diagram represents a hidden Markov model with three hidden states labeled 0, 1, and 2. The model is shown with initial state probabilities, π0, time dependent transition probabilities, P and emissions, E, which have gamma distributions.
Table 1.
Descriptions and initial values of parameters in three hidden state models.
Table 2.
Model comparison using AIC.
Table 3.
Transition and emission probability estimates.
Fig 3.
Transient distributions and emission distributions in two and three hidden state models.
The transient distribution for each Markov chain was calculated for time t = 0,..,300 weeks (A). Fitted emission distributions are shown in (C), and the observed data are shown in grey (B). The number of random samples used to create each plotted state emission distribution was proportional to the stationary distribution value for that hidden state.
Fig 4.
Progression patterns through disease states.
Progression patterns of individual cows through disease states estimated using posterior decoding are shown for both the two state and the three state models (A). The color of the line indicates the state with the highest posterior probability at the last observation. The lines were jittered vertically so that overlapping lines could be distinguished. The empirical and predicted log(CFU) MAP value from seven representative cows shows variability in fecal shedding over the sampling period, with some cows shedding very high CFU counts over the sampling period and others maintaining a lower CFU count (B) The median, and 10–90 percentile range for the predicted log(CFU) distributions are shown as points and bars, respectively. The predicted CFU values are colored according to the fitted state emission distribution for each sample. The empirical log(MAP) CFU counts are shown in black.