Starnini Michele, Pastor-Satorras Romualdo
Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032807. doi: 10.1103/PhysRevE.89.032807. Epub 2014 Mar 14.
We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity-driven-network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework based on a mapping to hidden variables networks, we provide expressions for the percolation time Tp marking the onset of a giant connected component in the integrated network. In particular, we consider both the generating function formalism, valid for degree-uncorrelated networks, and the general case of networks with degree correlations. We discuss the different limits of the two approaches, indicating the parameter regions where the correlated threshold collapses onto the uncorrelated case. Our analytical predictions are confirmed by numerical simulations of the model. The temporal percolation concept can be fruitfully applied to study epidemic spreading on temporal networks. We show in particular how the susceptible-infected-removed model on an activity-driven network can be mapped to the percolation problem up to a time given by the spreading rate of the epidemic process. This mapping allows us to obtain additional information on this process, not available for previous approaches.
我们以最近提出的活动驱动网络模型[N. 佩拉等人，《科学报告》2，469（2012年）]作为代表性例子，研究时间网络的时间渗流特性。基于一种映射到隐藏变量网络的分析框架，我们给出了渗流时间Tp的表达式，它标志着集成网络中巨型连通分量的出现。特别地，我们既考虑了适用于度不相关网络的生成函数形式，也考虑了具有度相关性的网络的一般情况。我们讨论了这两种方法的不同极限情况，指出了相关阈值与不相关情况重合的参数区域。我们的分析预测通过该模型的数值模拟得到了证实。时间渗流概念可有效地应用于研究时间网络上的流行病传播。我们特别展示了活动驱动网络上的易感-感染-移除模型如何在由流行病过程传播速率给出的时间之前映射到渗流问题。这种映射使我们能够获得关于这个过程的额外信息，而这是以前的方法所无法获得的。
