Descriptions of the different models.
(A) Markov model of disease dynamics with three states: uninfected (H), Sub-clinical (S) and cows showing clinical signs (C). The observations seems to show a unidirectional dynamics, where the empty arrows do not exist in reality or have a very low probability. (B) Deterministic model of bacteria concentration growth (full lines) eventually leading to the transition of a threshold (dashed gray line) and to clinical signs. (C) Dynamic model producing two states with a potential (full line) that has two attractors. The left attractor is the sub-critical stage and the right attractor is the clinical stage (i.e. the stage where clinical signs are exposed). In this case the transition between the two states is through random fluctuations.