Bacaër Nicolas
IRD (Institut de Recherche pour le Développement), Research Group UMMISCO, 32 avenue Henri Varagnat, 93143, Bondy, France.
J Math Biol. 2012 Feb;64(3):403-22. doi: 10.1007/s00285-011-0417-5. Epub 2011 Mar 15.
The figure showing how the model of Kermack and McKendrick fits the data from the 1906 plague epidemic in Bombay is the most reproduced figure in books discussing mathematical epidemiology. In this paper we show that the assumption of constant parameters in the model leads to quite unrealistic numerical values for these parameters. Moreover the reports published at the time show that plague epidemics in Bombay occurred in fact with a remarkable seasonal pattern every year since 1897 and at least until 1911. So the 1906 epidemic is clearly not a good example of epidemic stopping because the number of susceptible humans has decreased under a threshold, as suggested by Kermack and McKendrick, but an example of epidemic driven by seasonality. We present a seasonal model for the plague in Bombay and compute the type reproduction numbers associated with rats and fleas, thereby extending to periodic models the notion introduced by Roberts and Heesterbeek.
展示克马克和麦肯德里克模型如何拟合1906年孟买鼠疫疫情数据的图表，是讨论数学流行病学的书籍中被引用最多的图表。在本文中，我们表明该模型中参数恒定的假设会导致这些参数出现相当不切实际的数值。此外，当时发表的报告显示，自1897年至少到1911年，孟买的鼠疫疫情实际上每年都呈现出显著的季节性模式。所以1906年的疫情显然不是疫情因易感人群数量降至阈值以下而停止的好例子（如克马克和麦肯德里克所建议的那样），而是季节性驱动疫情的一个例子。我们提出了一个孟买鼠疫的季节性模型，并计算了与老鼠和跳蚤相关的类型繁殖数，从而将罗伯茨和赫斯特贝克引入的概念扩展到周期模型。
