(11)
http://plosone.org/article/info:doi/10.1371/journal.pone.0017908#article1.body1.sec2.sec3.p1

There was an error in arguments in equation (11) and later. Equation (10)
applies to an observation in which infection-status of all individuals N is fully observed. In the case of partial observation (e.g. random serological samples) with sample size n, a sampling error is introduced to the standard error, and correct standard error should read: http://www.plosone.org/corrections/pone.0017908.e012.cn.tif

The first term inside square root represents demographic stochasticity and N
corresponds to population size. The second term is equivalent to the standard error of the binomial sampling process with sample size n, corresponding to the measurement of error given an epidemic. It should be noted that n corresponds to the sample size of seroepidemiological survey, while N corresponds to the size of population that the seroepidemiological survey intends to represent. An important implication from this correction is that the above-mentioned demographic stochasticity is negligible as long as serological samples n sufficiently represents infection-status of the total population N. In other words, the 95% confidence interval of final size can be approximately computed by accounting for binomial sampling error only in an ideal condition. However, it may not be frequently the case that the samples less than 0.5% of the total population fully represent infection-status of the entire population. In such an instance, we address the uncertainty by varying the size of population N that we believe the serological samples can represent. For instance, if the samples represent 10,000 individuals in each country, correct 95% CIs of proportion seropositive in Table 2 read (11.5, 20.2), (34.9, 42.2), (2.5, 10.2), (0.8, 20.5), (0.9, 8.2), (11.0, 18.2), (29.3, 36.1), (11.2, 25.5), (3.4, 18.3), (4.5, 11.5) and (1.4, 29.6). As can be seen from the above formula, the confidence intervals are always wider than those of binomial proportion.