The methods presented for the estimation of household reproduction numbers were not affected by this problem in the same way. Analytical approximation were derived which bracketed estimates between a lower and upper bound, and numerical simulations showed the range within these brackets to be narrow. These approximations were shown to be robust, but it is worth noting that assumptions are made about the population mixing randomly out of their households and results are only valid in the scenario of an emerging pathogen where overall prevalence is low.