While there is a large literature on the form of epidemic waves in the time domain, models of their structure and shape in the spatial domain remain poorly developed. This paper concentrates on the changing spatial distribution of an epidemic wave over time and presents a simple method for identifying the leading and trailing edges of the spatial advance and retreat of such waves. Analysis of edge characteristics is used to (a) disaggregate waves into 'swash' and 'backwash' stages, (b) measure the phase transitions of areas from susceptible, S, through infective, I, to recovered, R, status (S --> I --> R) as dimensionless integrals and (c) estimate a spatial version of the basic reproduction number, R(0). The methods used are illustrated by application to measles waves in Iceland over a 60-year period from 1915 to 1974. Extensions of the methods for use with more complex waves are possible through modifying the threshold values used to define the start and end points of an event.

中文翻译：

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单个流行病波的反冲模型。

尽管在时域中流行病波的形式已有大量文献，但在时域中其结构和形状的模型仍然欠发达。本文着眼于流行病波随时间变化的空间分布，并提出了一种简单的方法来识别流行病波的空间前进和后退的前沿和后沿。边缘特征分析用于（a）将波分解为“冲刷”和“反洗”阶段，（b）测量区域从易感S到感染I到恢复R状态的相变（S- -> I-> R）作为无量纲积分，并且（c）估算基本再现数R（0）的空间形式。在1915年至1974年的60年中，将这些方法应用于冰岛的麻疹浪潮进行了说明。