Ideally, field case tracing should provide a measure of the likelihood that a new case resulted from contact with the (animal) reservoir, DB in Eq. [12] , or was due instead to human contagion. Another possibility is to explicitly model the introductions from the reservoir, K(t) in Eq. [7] . Although some empirical studies start to address this possibility [27, [36] [37] [38] , it is still difficult to calibrate such models and uncertainties remain large. Thus, for the calculations in this study, we choose to use a minimal statistical approach. Formally, assuming statistical independence between different cases, we model each new introduction as a Bernoulli trial with probability h. h is defined as the average probability that a case is attributed to human to human contagion, and 1-h that it is the result of an infection from the reservoir. Note that for emerging infectious diseases this probabilistic model is more appropriate and generalizes (see Supplementary Material S1, Figure S2 ) the more typical modelling of introductions as homogeneous Poisson processes [33] .