Stability of SIS Spreading Processes in Networks With Non-Markovian Transmission and Recovery
Stability of SIS Spreading Processes in Networks With Non-Markovian Transmission and Recovery
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DOI：
10.1109/tcns.2019.2905131
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发表时间：
2016-06
影响因子：
4.2
通讯作者：
Masaki Ogura;V. Preciado
中科院分区：
文献类型：
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作者：
Masaki Ogura;V. Preciado
虽然网络中发生的病毒传播过程通常使用马尔可夫模型进行分析，其中传输和恢复时间都遵循指数分布，但实证研究表明，在许多真实的场景中，这些时间的分布不一定是指数分布。为了克服这一限制，我们首先引入了一个广义的易感-感染-易感传播模型，该模型允许传播和恢复时间遵循相型分布。在这种情况下，我们推导出一个下界的指数衰减率对无感染的平衡的传播模型，而不依赖于平均场近似。基于我们的研究结果，我们说明了传输/恢复分布的特定形状如何影响向平衡收敛的指数速度。
Although viral spreading processes taking place in networks are often analyzed using Markovian models, in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real scenarios, the distribution of these times is not necessarily exponential. To overcome this limitation, we first introduce a generalized susceptible–infected–susceptible spreading model that allows transmission and recovery times to follow phase-type distributions. In this context, we derive a lower bound on the exponential decay rate toward the infection-free equilibrium of the spreading model without relying on mean-field approximations. Based on our results, we illustrate how the particular shape of the transmission/recovery distribution influences the exponential rate of convergence toward the equilibrium.