Population dynamics in a closed dairy herd and flow diagram of Mycobacterium avium subsp. paratuberculosis (Map) infection dynamics model, representing infection states, transitions between states, and origin of contamination of the local and whole farm environments. Host health states are: S = susceptible; R (in grey square) = resistant; T = transiently infectious; L = latently infected; I
= subclinically infected; I
= clinically affected. Environment states are: E
= indoor environment in housing l, with l = 1 to 6 (1 for calves in individual pens, 2 for calves in collective pens before weaning, 3 for calves in collective pens after weaning before 6 months of age or during winter season, 4 for young heifers during winter season, 5 for heifers during winter season, and 6 for adults during winter season); E
= environment of the whole farm; Eout= outdoor environment of calves when they are grazing. The population dynamics has to be read vertically. Moreover, n = number of individual pens; Z
= transmission functions for horizontal infection; t = time; G = grazing season; Pi = cows in parity i; dotted arrows: contribution to the environment contamination. Exit rates of each compartment are not represented.