MAP-specific cellular and humoral immune responses improve description of MAP shedding in most animals. We fitted four subsets of the mathematical model (Equation 4) to the experimentally measured shedding levels (shown by markers) and estimated model parameters. Predictions of the models are shown by lines. The four models were G: exponential growth in shedding (solid black line), Th1: exponential growth in shedding with suppression by Th1 (LPT) response (dashed red line), Th2: exponential growth in shedding with suppression by Th2 (ELISA) response (dashed blue line), Th1 + Th2: exponential growth in shedding with suppression by both Th1 (LPT) and Th2 (ELISA) responses (dashed-dotted green line). The parameters of the best fit model are shown in Table 2 and Akaike weights of different models are shown in Additional file 4. We also show fits of the simple “switch” model (Equation 3) to the shedding data by thin dashed lines. Parameters for this model are given in Additional file 3.