Spatiotemporal dynamics of epidemics: synchrony in metapopulation models
Spatiotemporal dynamics of epidemics: synchrony in metapopulation models
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DOI：
10.1016/j.mbs.2003.09.003
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发表时间：
2004-03-01
影响因子：
4.3
通讯作者：
Jansen, VAA
中科院分区：
文献类型：
--
作者：
Lloyd, AL;Jansen, VAA
多斑块模型-也称为集合种群模型-提供了一个简单的框架，可以在其中检查空间过程在疾病传播中的作用。考虑了区分k个不同类别个体的n-块模型。使用先前针对个体根据简单线性项在斑块之间迁移的总体设置描述的分析技术的扩展来研究这种模型的空间均匀解的线性稳定性。该技术将nk维线性化系统解耦为n个不同的k维系统，大大简化了分析。空间流行病学模型的一个重要特征是空间耦合可能涉及到非线性项。作为该技术应用的一个例子，对称SIR模型在地方病平衡点附近的动力学行为被分解成空间模式。对于适合于儿童疾病的参数值，得到了对应于同相和异相模式的特征值的表达式，表明系统的主导模式是同相模式。此外，在很大的耦合强度范围内，同相模的衰减比同相模的衰减快得多。(C)2003 Elsevier Inc.保留所有权利。
Multi-patch models - also known as metapopulation models - provide a simple framework within which the role of spatial processes in disease transmission can be examined. An n-patch model which distinguishes between k different classes of individuals is considered. the linear stability of spatially homogeneous solutions of such models is studied using an extension of an analysis technique previously described for a population setting in which individuals migrate between patches according to a simple linear term. The technique considerably simplifies the analysis as it decouples the nk dimensional linearized system into n distinct k-dimensional systems. An important feature of the spatial epidemiological model is that the spatial coupling may involve non-linear terms. As an example of the use of this technique, the dynamical behavior in the vicinity of the endemic equilibrium of a symmetric SIR model is decomposed into spatial modes. For parameter values appropriate for childhood diseases, expressions for the eigenvalues corresponding to in-phase and out-of-phase modes are obtained, and it is shown that the dominant mode of the system is an in-phase mode. Furthermore, the out-of-phase modes are shown to decay much more rapidly than the in-phase mode for a broad range of coupling strengths. (C) 2003 Elsevier Inc. All rights reserved.