The modelling and prediction approaches developed here (see also Chowell et al. [34] for a comparison to other methods) provide tools for real time estimation of epidemiological parameters that are appropriate for emerging infectious diseases. The method is intentionally simple, relying on standard epidemiological population models, in order to be commensurate with the paucity of epidemiological data typically available for emerging infectious diseases. These features are illustrated by the application of the method to H5N1 influenza infection time series in humans. Clearly, the SIR class of models, even when cast in probabilistic terms, relies on several general assumptions, which are simplistic in specific situations. First, these models do not account for contact heterogeneities, resulting from spatial effects, age, and/or the structure of social networks. These effects can be partially addressed by structuring the population compartments in terms of spatial and risk classes [42] . For example, different regions in an affected country may be taken as separate compartments, provided that there are data pertaining to each region. Indeed the method would then allow estimation of correlations between R at different spatial locations. Second, in its present form, the model does not include independent estimation of infectious or incubation periods. It is straightforward to include an incubation period [43] and, given data on the duration of these periods on a case by case basis, these issues can be addressed by including additional Bayesian estimation steps (see [32] ). Notwithstanding these limiting features, the SIR structure allows reliable real time parameter estimation with quantified uncertainty at very low computational overhead, as verified extensively via simulations at varying known input R, and applications to past pandemic outbreaks (Supplementary Material S1 - Fig. S5 and S6 -and Ref [34] ). One feature of the bounds on R derived here is their dependency on the fraction of cases attributed to human transmission, h. Although h is judged to be small from present surveillance [23, 27, 28] , it remains hard to quantify with certainty. Given the paucity of data, we chose in practice to assume independence and use a binomial probability to attribute cases to human transmission vs. infection from the reservoir. However, other procedures to determine h are possible. If enough data were available, an explicit dynamical model of the (animal) reservoir could be built, or an empirical function correlating introductions through time could be used. Indeed, in the optimal scenario, the actual cases of introduction from the reservoir would be known from field work, and the method proposed here could incorporate that information directly. We note that in the most relevant case, when R becomes larger than 1, the effect of h,1 quickly vanishes, as cases multiply exponentially. For R,1, even a choice of h = 1 will lead to estimates of R,1, but different values of h may lead to credible intervals that include the critical threshold. In general, we believe that a suspicion of a possible R<1 should be followed up with careful field investigations.