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.

中文翻译：

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非马尔可夫传输和恢复网络中SIS扩展过程的稳定性

尽管通常使用马尔可夫模型来分析网络中发生的病毒传播过程，其中 传播 和 复苏时间遵循指数分布，经验研究表明，在许多实际情况下，这些时间的分布不一定是指数分布。为了克服这个限制，我们首先引入一个广义的易感性-易感性传播模型，该模型允许遵循传播和恢复时间相型分布。在这种情况下，我们在不依赖均值场近似的情况下，朝着传播模型的无感染平衡导出了指数衰减率的下限。基于我们的结果，我们说明了传输/恢复分布的特定形状如何影响收敛到平衡的指数速率。