Lloyd Alun L
Program in Theoretical Biology, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA.
Theor Popul Biol. 2004 Feb;65(1):49-65. doi: 10.1016/j.tpb.2003.07.002.
The major role played by demographic stochasticity in determining the dynamics and persistence of childhood diseases, such as measles, chickenpox and pertussis, has long been realized. Techniques which can be used to estimate the magnitude of this stochastic effect are of clear importance. In this study, we assess and compare the use of two moment closure approximations to estimate the variability seen about the average behavior of stochastic models for the recurrent epidemics seen in childhood diseases. The performance of the approximations are assessed using analytic techniques available for the simplest epidemiological model and using numerical simulations in more complex settings. We also present epidemiologically important extensions of previous work, considering variability in the SEIR model and in situations for which there is seasonal variation in disease transmission. Important implications of stochastic effects for the dynamics of childhood diseases are highlighted, including serious deficiencies of deterministic descriptions of dynamical behavior.
人口统计学随机性在决定儿童疾病（如麻疹、水痘和百日咳）的动态变化和持续存在方面所起的主要作用早已为人所知。可用于估计这种随机效应大小的技术显然很重要。在本研究中，我们评估并比较了两种矩封闭近似方法的使用情况，以估计儿童疾病中反复出现的流行病随机模型平均行为的变异性。使用适用于最简单流行病学模型的分析技术以及在更复杂环境中的数值模拟来评估近似方法的性能。我们还提出了先前工作在流行病学方面的重要扩展，考虑了SEIR模型中的变异性以及疾病传播存在季节性变化的情况。强调了随机效应对儿童疾病动态变化的重要影响，包括动力学行为确定性描述的严重不足。
