Interdependency and hierarchy of exact and approximate epidemic models on networks
Interdependency and hierarchy of exact and approximate epidemic models on networks
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DOI：
10.1007/s00285-013-0699-x
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发表时间：
2012-12
影响因子：
1.9
通讯作者：
T. Taylor;I. Kiss
中科院分区：
文献类型：
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作者：
T. Taylor;I. Kiss
多年来，$$SIS$$的众多型号 SIS （易感者$$\rightarrow $$ → 已感染$$\rightarrow $$ → 易感）疾病动态在网络上展开。在这里，我们讨论了许多这些模型之间的联系，以及如何将它们视为更一般的基于模体的模型。我们说明了如何不同的模型可以从另一个派生，这是不可能的，讨论扩展到已建立的模型，使这种推导。我们还推导出一个一般结果的精确微分方程的预期数量的任意图案直接从Kolmogorov/主方程，并得出结论，不同的封闭系统的方程网络的不同结构的性能比较。
Over the years numerous models of $$SIS$$ SIS (susceptible $$\rightarrow $$ → infected $$\rightarrow $$ → susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general motif-based models. We illustrate how the different models can be derived from one another and, where this is not possible, discuss extensions to established models that enables this derivation. We also derive a general result for the exact differential equations for the expected number of an arbitrary motif directly from the Kolmogorov/master equations and conclude with a comparison of the performance of the different closed systems of equations on networks of varying structure.