Epidemic processes on random graphs or networks are marked by localization of activity that can trap the dynamics into a metastable state, confined to a subextensive part of the network, before visiting an absorbing configuration. Quasistationary (QS) method is a technique to deal with absorbing states for finite sizes and has played a central role in the investigation of epidemic processes on heterogeneous networks where localization is a hallmark. The standard QS method possesses high computer and algorithmic complexity for large systems besides parameters whose choice are not systematic. However, simpler approaches, such as a reflecting boundary condition (RBC), are not able to capture the localization effects as the standard QS method does. In the present work, we propose a QS method that consists of reactivating nodes proportionally to the time they were active along the preceding simulation. The method is compared with the standard QS and RBC methods for the susceptible-infected-susceptible model on complex networks, which is a prototype of a dynamic process with strong localization effects. We verify that the method performs as well the as standard QS in all investigated simulations, providing the same scaling exponents, epidemic thresholds, and localized phases, thus overcoming the limitations of other simpler approaches. We also report that the present method has significant lower computer and algorithmic complexity than the standard QS method. So, this method arises as a simpler and efficient tool to analyze localization on heterogeneous structures through QS simulations.

随机图或网络上的流行过程以活动的本地化为标志，这些活动可以使动态陷入亚稳态，在访问一个吸引人的配置之前，仅限于网络的一个次广泛的部分。准稳态 (QS) 方法是一种处理有限大小的吸收状态的技术，在以定位为标志的异构网络上的流行过程调查中发挥了核心作用。除了参数选择不系统之外，标准QS方法对于大型系统具有很高的计算机和算法复杂度。然而，更简单的方法，例如反射边界条件 (RBC)，无法像标准 QS 方法那样捕捉定位效果。在目前的工作中，我们提出了一种 QS 方法，该方法包括重新激活节点，与它们在之前的模拟中处于活动状态的时间成比例。该方法与复杂网络上的易感-感染-易感模型的标准QS和RBC方法进行了比较，这是具有强大定位效果的动态过程的原型。我们验证该方法在所有研究的模拟中的表现与标准 QS 一样好，提供相同的缩放指数、流行阈值和局部阶段，从而克服其他更简单方法的局限性。我们还报告说，与标准 QS 方法相比，本方法具有显着较低的计算机和算法复杂性。因此，这种方法作为一种更简单有效的工具出现，可以通过 QS 模拟分析异质结构的定位。