School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China.
Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, 611731, China.
Nat Commun. 2019 Aug 23;10(1):3748. doi: 10.1038/s41467-019-11763-z.
Epidemic spreading processes in the real world depend on human behaviors and, consequently, are typically non-Markovian in that the key events underlying the spreading dynamics cannot be described as a Poisson random process and the corresponding event time is not exponentially distributed. In contrast to Markovian type of spreading dynamics for which mathematical theories have been well developed, we lack a comprehensive framework to analyze and fully understand non-Markovian spreading processes. Here we develop a mean-field theory to address this challenge, and demonstrate that the theory enables accurate prediction of both the transient phase and the steady states of non-Markovian susceptible-infected-susceptible spreading dynamics on synthetic and empirical networks. We further find that the existence of equivalence between non-Markovian and Markovian spreading depends on a specific edge activation mechanism. In particular, when temporal correlations are absent on active edges, the equivalence can be expected; otherwise, an exact equivalence no longer holds.
在现实世界中，传染病的传播过程取决于人类的行为，因此通常是非马尔可夫的，因为传播动力学的关键事件不能被描述为泊松随机过程，相应的事件时间也不是指数分布。与已发展出完善数学理论的马尔可夫型传播动力学相反，我们缺乏一个全面的框架来分析和充分理解非马尔可夫传播过程。在这里，我们开发了一种平均场理论来应对这一挑战，并证明该理论能够准确预测合成网络和经验网络中非马尔可夫易感染-感染-易感染传播动力学的瞬态相和稳态。我们还发现，非马尔可夫和马尔可夫传播之间的等价性存在取决于特定的边激活机制。具体来说，当活动边上不存在时间相关性时，可以预期等价性；否则，精确的等价性不再成立。
