Latin Hypercube Sampling (LHS) allows an efficient sampling of the parameter space which requires a smaller sample size than simple sampling to achieve the same accuracy [41] . LHS was used to build n Q~1 000 sets of parameters Q:fq 1 , . . . ,q nQ g (uniform sampling was used to determine the n Q values of each model parameter) and thus, through model simulations, n Q time series of predicted notified cases fz t (q)g q[Q . The optimal parameter set q ? was chosen as the one minimizing the score function, i.e. q ?~a rg min q[Q F (q). We repeated the above described procedure 100 times. This allowed us to estimate distributions of model parameters and, consequently, of the other quantities of interest (e.g. R 0 , probability of major outbreak, attack rate). The index case was recorded on June 23 2007 (a man who had arrived in Italy from India on June 21, [1] ) and thus we initialized all simulations with 1 infected individual on June 23. Results of the optimization procedure are shown in Fig. S1. Fig. S2 shows that 100 simulations are sufficient to obtain meaningful distributions of parameters and quantities of interest.