Nishiura Hiroshi, Chowell Gerardo, Safan Muntaser, Castillo-Chavez Carlos
PRESTO, Japan Science and Technology Agency, Honcho 4-1-8, Kawaguchi, Saitama, 332-0012, Japan.
Theor Biol Med Model. 2010 Jan 7;7:1. doi: 10.1186/1742-4682-7-1.
In many parts of the world, the exponential growth rate of infections during the initial epidemic phase has been used to make statistical inferences on the reproduction number, R, a summary measure of the transmission potential for the novel influenza A (H1N1) 2009. The growth rate at the initial stage of the epidemic in Japan led to estimates for R in the range 2.0 to 2.6, capturing the intensity of the initial outbreak among school-age children in May 2009.
An updated estimate of R that takes into account the epidemic data from 29 May to 14 July is provided. An age-structured renewal process is employed to capture the age-dependent transmission dynamics, jointly estimating the reproduction number, the age-dependent susceptibility and the relative contribution of imported cases to secondary transmission. Pitfalls in estimating epidemic growth rates are identified and used for scrutinizing and re-assessing the results of our earlier estimate of R.
Maximum likelihood estimates of R using the data from 29 May to 14 July ranged from 1.21 to 1.35. The next-generation matrix, based on our age-structured model, predicts that only 17.5% of the population will experience infection by the end of the first pandemic wave. Our earlier estimate of R did not fully capture the population-wide epidemic in quantifying the next-generation matrix from the estimated growth rate during the initial stage of the pandemic in Japan.
In order to quantify R from the growth rate of cases, it is essential that the selected model captures the underlying transmission dynamics embedded in the data. Exploring additional epidemiological information will be useful for assessing the temporal dynamics. Although the simple concept of R is more easily grasped by the general public than that of the next-generation matrix, the matrix incorporating detailed information (e.g., age-specificity) is essential for reducing the levels of uncertainty in predictions and for assisting public health policymaking. Model-based prediction and policymaking are best described by sharing fundamental notions of heterogeneous risks of infection and death with non-experts to avoid potential confusion and/or possible misuse of modelling results.
在世界许多地区，初始流行阶段感染的指数增长率已被用于对基本传染数R进行统计推断，R是2009年甲型H1N1流感传播潜力的一个汇总指标。日本疫情初始阶段的增长率导致R的估计值在2.0至2.6之间，反映了2009年5月学龄儿童中初始疫情的强度。
提供了一个考虑了5月29日至7月14日疫情数据的R的更新估计值。采用年龄结构更新过程来捕捉年龄依赖性传播动态，联合估计基本传染数、年龄依赖性易感性以及输入病例对二代传播的相对贡献。识别了估计疫情增长率时的陷阱，并用于仔细审查和重新评估我们早期对R的估计结果。
使用5月29日至7月14日数据对R的最大似然估计值在1.21至1.35之间。基于我们的年龄结构模型的下一代矩阵预测，在第一波大流行结束时，只有17.5%的人口会感染。我们早期对R的估计在根据日本大流行初始阶段估计的增长率量化下一代矩阵时，没有完全捕捉到全人群的疫情情况。
为了根据病例增长率来量化R，所选模型必须捕捉数据中潜在的传播动态。探索更多的流行病学信息将有助于评估时间动态。尽管R的简单概念比下一代矩阵更容易被公众理解，但包含详细信息（如年龄特异性）的矩阵对于降低预测中的不确定性水平和协助公共卫生决策至关重要。基于模型的预测和决策最好通过与非专家分享感染和死亡的异质风险的基本概念来描述，以避免可能的混淆和/或对建模结果的不当使用。
