Ball Frank, Lyne Owen
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
Stat Methods Med Res. 2006 Oct;15(5):481-97. doi: 10.1177/0962280206071643.
This paper is concerned with stochastic models for the spread of an epidemic among a community of households, in which individuals mix uniformly within households and, in addition, uniformly at a much lower rate within the population at large. This two-level mixing structure has important implications for the threshold behaviour of the epidemic and, consequently, for both the effectiveness of vaccination strategies for controlling an outbreak and the form of optimal vaccination schemes. A brief introduction to optimal vaccination schemes in this setting is provided by presenting a unified treatment of the simplest and most-studied case, viz. the single-type SIR (susceptible -->infective --> removed) epidemic. A reproduction number R*, which determines whether a trace of initial infection can give rise to a major epidemic, is derived and the effect of a vaccination scheme on R* is studied using a general model for vaccine action. In particular, optimal vaccination schemes which reduce R* to its threshold value of one with minimum vaccination coverage are considered. The theory is illustrated by application to data on a variola minor outbreak in São Paulo, which, together with other examples, is used to highlight key issues related to vaccination schemes.
本文关注的是一种流行病在家庭群体中传播的随机模型，在该模型中，个体在家庭内部均匀混合，此外，在整个总体人群中以低得多的速率均匀混合。这种两级混合结构对流行病的阈值行为具有重要影响，因此，对控制疫情爆发的疫苗接种策略的有效性以及最优疫苗接种方案的形式都有重要影响。通过对最简单且研究最多的情况，即单类型SIR（易感者→感染者→康复者）流行病进行统一处理，给出了这种情况下最优疫苗接种方案的简要介绍。推导出一个繁殖数R*，它决定了初始感染的痕迹是否会引发大规模疫情，并使用疫苗作用的一般模型研究了疫苗接种方案对R的影响。特别地，考虑了以最小疫苗接种覆盖率将R降低到其阈值1的最优疫苗接种方案。通过将该理论应用于圣保罗一场小型天花疫情的数据进行说明，该数据与其他例子一起用于突出与疫苗接种方案相关的关键问题。
