Comments from Referee 2 (George Streftaris):

"This is very interesting and challenging work. Rigorous and reliable estimation of epidemiological parameters is in the core of understanding, analysing, predicting and containing the spread of infectious diseases, and has not always been treated in the literature as extensively as it should.

Fitting a Bayesian spatio-temporal model to the 2001 FMD epidemic seems to be the appropriate way to account for the various sources of uncertainty in the observed course of the spread of the disease. The time change-point modelling provides a suitable and viable alternative to continuous time varying parameters, with the model comparison allowing informed assessment of the issue of temporal change in transmission.

In the review of the paper, I highlighted two main issues regarding the modelling of the spread of the disease, which may have an important impact on the drawn inferences. The first issue concerns the infection times being treated as known, taken from clinical evaluation of the age of lesions. The exact infection time, combined with the duration of the latent and infectious period, is critical to modelling the transmission of the disease and deriving good estimates. The virulent (and sometimes asymptomatic) nature of FMD makes the consideration of actual infection times more significant, especially when the estimation of relevant parameters is of primary interest. Earlier work in the analysis of infectious diseases has shown that this should be possible within a Bayesian/MCMC framework.

The second remark in my review referred to the fact that proactively culled premises are assumed to be non-infectious. This is a significant assumption that can lead to over-estimation of transmission parameters. In the original submission of the paper, the authors acknowledge this issue and address it by considering the percentage of potentially infectious proactively culled farms. There are two points here: firstly, even with the small numbers of predicted infectious culled farms, there could be considerable changes in the parameter estimates (although the qualitative conclusions may stay the same) - notice that a number of 159 farms that may have been infected represents about 8% of all IPs; and secondly the estimation of the probability of infection of proactively culled farms relies again on the infection times for IPs being known. This relates to the first comment above, as a more rigorous approach should be taken in estimating the unobserved infection times and the duration of the infectious period in turn. For example, fitting an appropriate probability distribution to the length of infectious period and augmenting the unknown infection times and numbers, should be a possibility within the adopted Bayes/MCMC approach. This could provide more realistic time-windows for weighting the probability of infection, as various quantiles of the infectious period distribution would be available.
An alternative to a full consideration of the possible infectiousness of proactively culled premises could be some sort of sensitivity analysis to the assumption (although it might not be too clear how to do this without having to identify the involved "proactively culled-and-infectious" farms).

The authors addressed the point concerning the assumption of knowledge of the exact infection times by conducting a sensitivity analysis which suggests that the adopted model does not affect significantly the estimates of the epidemiological parameters. This approach is strengthened by an additional analysis which also shows the estimates of the number of infected proactively culled farms not to be sensitive to a suitable randomisation of infection times. On the issue regarding the assumption of non-infectiousness of proactively culled farms, the authors acknowledge the potential effects of the assumption and consider this as an important extension in future work.

The paper makes an important contribution to the estimation of epidemiological parameters of the 2001 FMD outbreak. As emphasised above, the advantages of the Bayesian approach in dealing with the partially observed aspects of the spread of the epidemic (and therefore relaxing the assumptions made in the paper), could be further exploited with the use of an extended model and suitable MCMC methodology. I believe that the authors are currently expanding their work towards this direction, and I look forward to seeing their results published in the near future. "