title: Early estimation of the reproduction number in the presence of imported cases: pandemic influenza H1N1-2009 in New Zealand.
abstract: We analyse data from the early epidemic of H1N1-2009 in New Zealand, and estimate the reproduction number R. 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, R was estimated to be (95% confidence interval: 107,1.47). Hence we show that a previous study, which did not account for these factors, overestimated R. 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 R--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 R, especially when one only has data covering a short time interval during the early growth phase of the epidemic.
authors.affiliation: Centre for Mathematical Biology, Institute of Information and Mathematical Sciences, Massey University, Auckland, New Zealand. m.g.roberts@massey.ac.nz
authors.forename: Michael George
authors.initials: MG
authors.lastname: Roberts
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Nishiura
mesh_terms: D050936:Basic Reproduction Number; D004641:Emigration and Immigration / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D053118:Influenza A Virus, H1N1 Subtype / Q000502:physiology*; D007251:Influenza, Human / Q000453:epidemiology* / Q000635:transmission / Q000821:virology*; D008954:Models, Biological; D009520:New Zealand / Q000453:epidemiology; D058873:Pandemics / Q000706:statistics & numerical data*; D015203:Reproducibility of Results; D012621:Seasons; D013997:Time Factors