社会技术网络中的传播过程
Spreading Processes over Socio-Technical Networks with Phase-Type Transmissions
摘要：
大多数用于分析网络传播过程的理论工具都假设传输和恢复时间呈指数分布。在实践中，许多真实传播过程的传输时间的经验分布，例如网络内容通过互联网的传播，远远不是指数分布。为了弥合理论与实践之间的差距，我们提出了一种使用相型分布对任意传输时间的传播过程进行建模和分析的方法。相位型分布是一类在正值分布集中稠密的分布族，可以用来近似任何给定的分布。为了说明我们的方法，我们专注于一个流行的模型，通过网络传播：易感染的易感（SIS）网络模型。在这个模型的标准版本中，被告知一条信息的个体会以指数级的速度将这条信息传递给它的邻居。在本文中，我们将这个模型推广到传输率服从相位型分布的情况。使用这个扩展的模型，我们分析的基础上的相位型分布的矢量表示的蔓延的动态。我们说明我们的研究结果通过分析传播过程的网络传输和恢复率遵循威布尔分布。
英文摘要：
Most theoretical tools available for the analysis of spreading processes over networks assume exponentially distributed transmission and recovery times. In practice, the empirical distribution of transmission times for many real spreading processes, such as the spread of web content through the Internet, are far from exponential. To bridge this gap between theory and practice, we propose a methodology to model and analyze spreading processes with arbitrary transmission times using phase-type distributions. Phase-type distributions are a family of distributions that is dense in the set of positive-valued distributions and can be used to approximate any given distributions. To illustrate our methodology, we focus on a popular model of spreading over networks: the susceptible-infected-susceptible (SIS) networked model. In the standard version of this model, individuals informed about a piece of information transmit this piece to its neighbors at an exponential rate. In this paper, we extend this model to the case of transmission rates following a phase-type distribution. Using this extended model, we analyze the dynamics of the spread based on a vectorial representations of phase-type distributions. We illustrate our results by analyzing spreading processes over networks with transmission and recovery rates following a Weibull distribution.
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