Early Estimation of the Reproduction Number in the Presence of Imported Cases: Pandemic Influenza H1N1-2009 in New Zealand

We analyse data from the early epidemic of H1N1-2009 in New Zealand, and estimate the reproduction number [Image: see text]. We employ a renewal process which accounts for imported cases, illustrate some technical pitfalls, and propose a novel estimation method to address these pitfalls. Explicitly accounting for the infection-age distribution of imported cases and for the delay in transmission dynamics due to international travel, [Image: see text] was estimated to be [Image: see text] (95% confidence interval: [Image: see text]). Hence we show that a previous study, which did not account for these factors, overestimated [Image: see text]. Our approach also permitted us to examine the infection-age at which secondary transmission occurs as a function of calendar time, demonstrating the downward bias during the beginning of the epidemic. These technical issues may compromise the usefulness of a well-known estimator of [Image: see text] - the inverse of the moment-generating function of the generation time given the intrinsic growth rate. Explicit modelling of the infection-age distribution among imported cases and the examination of the time dependency of the generation time play key roles in avoiding a biased estimate of [Image: see text], especially when one only has data covering a short time interval during the early growth phase of the epidemic.