Kinetics of the MAP-specific cellular immune response and fits of the mathematical model to these experimental data. We measured MAP-specific cellular immune response using lymphoproliferative assay detecting IFNγ-producing, MAP-specific T cells following infection of calves with MAP (LPT data, Materials and methods for more detail). We fitted a simple, “Ton-Toff” model in which immune response expands to a peak and then contracts (see Equation 1) to the raw LPT data. Results were similar if we fitted log-transformed model predictions to the log-transformed data although some parameter estimates changed (results not shown). Labels for individual cows are shown in the top left corner. Data are shown as points and model predictions are given by lines. Parameters of the best fit model to these data are shown in Additional file 2.