Centre for Mathematical Biology, Institute of Information and Mathematical Sciences, Massey University, Auckland, New Zealand.
PLoS One. 2011;6(5):e17835. doi: 10.1371/journal.pone.0017835. Epub 2011 May 26.
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.
我们分析了新西兰 2009 年 H1N1 流感早期的疫情数据，并估算了繁殖数 R。我们采用了一种更新过程来考虑输入病例，说明了一些技术陷阱，并提出了一种新的估计方法来解决这些问题。明确考虑了输入病例的感染年龄分布以及国际旅行导致的传播动力学延迟，估计 R 值为（95%置信区间：107，1.47）。因此，我们表明，之前没有考虑这些因素的一项研究高估了 R 值。我们的方法还允许我们检查作为日历时间函数的二次传播发生的感染年龄，表明在疫情早期存在向下偏差。这些技术问题可能会影响到繁殖数 R 的一个著名估计量——给定固有增长率的生成时间的矩母函数的倒数的有用性。明确建模输入病例的感染年龄分布，并检查生成时间的时间依赖性，对于避免对 R 的有偏差估计至关重要，特别是当一个人仅在疫情早期增长阶段覆盖很短的时间间隔的数据时。
