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Generating and solving the mean field and pair approximation equations in epidemiological models

机译:生成并求解平均场和对近似方程   在流行病学模型中

摘要

The pair approximation is a simple, low-order method to incorporate effectsof local spatial structure in epidemiological models. However, since for Kstate variables in a model there are K(K+1)/2 equations in the pairapproximation, generating these equations, although straightforward, can becometedious. In this paper we describe two programs written in Perl to simplifythis process - one to construct the equations, and the other to generateMatlab/Octave functions to numerically integrate the equations using apositivity-preserving method. A third utility program is also included whichgenerates a Maple file that can be used within the Maple symbolic manipulationprogram to simplify algebraically some of the terms in the generated filedescribing the equations, as well as to check that the usual combination ofequations sum up to zero, which is expected in cases where the total populationsizes are conserved.
机译:对近似是一种简单的低阶方法,可以将局部空间结构的影响纳入流行病学模型中。但是,由于对于模型中的Kstate变量,在对近似中有K(K + 1)/ 2个方程,因此尽管生成这些方程很简单,但可能会变得很麻烦。在本文中,我们描述了两个用Perl编写的程序来简化此过程-一个用于构造方程式,另一个用于生成Matlab / Octave函数以使用正性保留方法对方程进行数值积分。还包括第三个实用程序,该实用程序生成一个Maple文件,该文件可在Maple符号操作程序中使用,以代数形式简化生成的文件中描述方程式的某些项,并检查方程的常规组合总和为零,在保留总人口的情况下可以预期。

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  • 年度 2010
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  • 正文语种 {"code":"en","name":"English","id":9}
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