Nonhomogeneous birth and death models for epidemic outbreak data
Nonhomogeneous birth and death models for epidemic outbreak data
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DOI：
10.1093/biostatistics/kxl023
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发表时间：
2007-04-01
期刊：
影响因子：
2.1
通讯作者：
Heesterbeek, Hans
中科院分区：
文献类型：
--
作者：
van den Broek, Jan;Heesterbeek, Hans
在本文中，广义非线性模型，提出了在建模流行病爆发统计考虑到以下几点。(1)数据的相关性处理与非齐次死亡或非齐次出生过程。(2)第一阶段的爆发是用一个流行病的病原体-传染性-删除（SIR）模型。不久，所采取的控制措施将主导这一进程。这些措施是在自然消除流行病过程之外采取的。患病率与截尾感染时间相关，使得分布函数和生存函数近似满足SIR模型的第一个方程。这就自然地引出了布尔分布族。(3)非齐次出生过程处理的事实是，在实践中，有一些延迟，感染者被登记，但不是合格者。(4)最后，结束所采取的措施所造成的流行病被纳入通过修改的生存函数的最终尺寸参数，以同样的方式在长期生存模型。这些模型被应用于三次爆发：1997年至1998年的荷兰猪瘟爆发，2001年英国口蹄疫爆发，以及2003年荷兰禽流感（H7 N7）爆发。
In this paper, generalized nonlinear models are proposed in order to incorporate the following considerations in modeling an epidemic disease outbreak statistically. (1) The dependence of the data is handled with a nonhomogeneous death or a nonhomogeneous birth process. (2) The first stage of the outbreak is described with an epidemic susceptibles-infectives-removed (SIR) model. Soon the control measures taken will dominate the process. These measures are in addition to the natural epidemic removal process. The prevalence is related to the censored infection times in such a way that the distribution function and thus the survival function satisfy approximately the first equation of the SIR model. This leads in a natural way to the Burr family of distributions. (3) The nonhomogeneous birth process handles the fact that in practice, with some delay, infecteds are registered, but not susceptibles. (4) Finally, the ending of the epidemic caused by the measures taken is incorporated through a modification of the survival function with a final-size parameter, in the same way as is done in long-term survival models. These models are applied to three outbreaks: The Dutch classical swine fever outbreak from 1997 to 1998, the foot- and-mouth disease outbreak in Great Britain from 2001, and the Dutch avian influenza (H7N7) outbreak from 2003.