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Table 2 Estimates of parameters providing the best fit of the mathematical model to the shedding data

From: Evaluating contribution of the cellular and humoral immune responses to the control of shedding of Mycobacterium avium spp. paratuberculosis in cattle

cow ID B0, CFU/g r, 10−2/day k C, 10−7/day k H, 10−3/day
C01 6.3 −0.2 0 0
C02 4.7 0.8 −2.55 −571.49
C03 3.6 −0.4 0 −76.32
C04 4.2 0.1 2.17 −189.83
C05 9.2 −0.3 0 0
C06 5 −0.1 0 0
C07 3.9 0.6 0 0
C08 1 1.2 1.69 0
C09 2.2 0.6 0.64 0
C10 4.2 0 0 −76.71
C11 8.3 0 −6.9 76.24
C12 4.1 −0.2 0 −11.27
C13 4.2 −0.2 0 −16.06
C14 8.7 −1.3 −0.99 0
C15 9.7 0.4 1.03 0
C16 6.6 0.1 0 −9.15
C17 0.6 0 4.69 −165.86
C18 6.7 −0.1 0 0
C19 9.1 −0.9 −0.63 0
C20 6.4 −0.4 0 −64.95
  1. The best fit model (the model is shown in Equation 4) was determined by performing F-tests for nested models and using Akaike weights for non-nested models (see Materials and methods for more detail and Additional file 4). Listed parameters are: B 0 is the predicted initial shedding level, r is the rate of exponential change in shedding in the absence of MAP-specific cellular (as measured by LPT) and humoral (as measured by ELISA) immune responses, k C is the predicted rate of reduction in shedding by the cellular immune response, k H is the predicted rate of reduction in shedding by the humoral immune response. Negative values in shedding rate change r indicate predicted decline in shedding in the absence of measurable cellular and antibody responses. Negative values in k C and k H indicate increase in shedding with the presence of corresponding immune responses.