Understanding the persistence of measles: reconciling theory, simulation and observation
Understanding the persistence of measles: reconciling theory, simulation and observation
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DOI：
10.1098/rspb.2001.1898
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发表时间：
2002-02-22
影响因子：
4.7
通讯作者：
Grenfell, BT
中科院分区：
文献类型：
--
作者：
Keeling, MJ;Grenfell, BT
自从Bartlett在1957年发现了与麻疹相关的局部灭绝模式以来，已经开发了许多模型试图重现这种现象。最近，使用恒定的感染和潜伏期，而不是更方便的指数形式，已被提出作为一种简单的手段，获得现实的持久性水平。然而，这个结果似乎与严格的数学理论不一致;在这里，我们调和这些差异。使用确定性的方法，我们parameterized各种模型，以适应观察到的两年期吸引子，从而确定的季节性水平的模型的选择。然后，我们可以使用“最佳拟合”参数来比较这些模型的随机版本的持久性。最后，我们考虑观察到的淡出模式和理论上更吸引人的“首次通过时间”之间的差异。
Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'.