Exact epidemic models on graphs using graph-automorphism driven lumping.
Exact epidemic models on graphs using graph-automorphism driven lumping.
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DOI：
10.1007/s00285-010-0344-x
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发表时间：
2011-04
影响因子：
1.9
通讯作者：
Kiss IZ
中科院分区：
文献类型：
--
作者：
Simon PL;Taylor M;Kiss IZ
疾病传播的动态很大程度上取决于人群接触网络的性质。配对逼近模型和基于个体的网络仿真已被广泛用于模拟具有非平凡性质的接触网络。本文利用连续时间马尔可夫链，从任意接触网络上的简单流行病模型的精确公式出发，严格推导并证明了以前主要基于某些生物学假设来证明的一些已知结果。本文的主要结果是说明图自同构和集总过程之间的联系，从而可以显着减少线性微分方程系统中的方程数量。集总的主要优点是，简化的集总系统不是原始系统的近似值，而是原始系统的精确版本。对于一类特殊的图，我们给出了如何利用图自同构得到集总系统。最后讨论了精确流行病模型和集总法的优点和可能的应用。
The dynamics of disease transmission strongly depends on the properties of the population contact network. Pair-approximation models and individual-based network simulation have been used extensively to model contact networks with non-trivial properties. In this paper, using a continuous time Markov chain, we start from the exact formulation of a simple epidemic model on an arbitrary contact network and rigorously derive and prove some known results that were previously mainly justified based on some biological hypotheses. The main result of the paper is the illustration of the link between graph automorphisms and the process of lumping whereby the number of equations in a system of linear differential equations can be significantly reduced. The main advantage of lumping is that the simplified lumped system is not an approximation of the original system but rather an exact version of this. For a special class of graphs, we show how the lumped system can be obtained by using graph automorphisms. Finally, we discuss the advantages and possible applications of exact epidemic models and lumping.
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影响因子：
1.4
作者：
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通讯作者：
Keeling, M
DOI：
10.1073/pnas.0308344101
发表时间：
2004-10-19
影响因子：
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作者：
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影响因子：
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作者：
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