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

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  • Michael George Roberts
  • Hiroshi Nishiura

Abstract

We analyse data from the early epidemic of H1N1-2009 in New Zealand, and estimate the reproduction number . 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, was estimated to be (95% confidence interval: ). Hence we show that a previous study, which did not account for these factors, overestimated . 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 - 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 , especially when one only has data covering a short time interval during the early growth phase of the epidemic.

Suggested Citation

  • Michael George Roberts & Hiroshi Nishiura, 2011. "Early Estimation of the Reproduction Number in the Presence of Imported Cases: Pandemic Influenza H1N1-2009 in New Zealand," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-9, May.
    • Handle: RePEc:plo:pone00:0017835
    DOI: 10.1371/journal.pone.0017835
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    References listed on IDEAS

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    1. Gabriele Neumann & Takeshi Noda & Yoshihiro Kawaoka, 2009. "Emergence and pandemic potential of swine-origin H1N1 influenza virus," Nature, Nature, vol. 459(7249), pages 931-939, June.
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    1. Pan, Qiuhui & Gao, Ting & He, Mingfeng, 2020. "Influence of isolation measures for patients with mild symptoms on the spread of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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