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.

现实世界中的流行病传播过程取决于人类行为，因此通常是非马尔可夫的，因为传播动力学背后的关键事件不能被描述为泊松随机过程，并且相应的事件时间不是指数分布的。与数学理论已经完善的马尔可夫式传播动力学相比，我们缺乏一个全面的框架来分析和充分理解非马尔可夫式传播过程。在这里，我们开发了一个均值场理论来应对这一挑战，并证明该理论能够在合成和经验网络上准确预测非马尔可夫易感-感染-易感传播动力学的瞬态阶段和稳态。我们进一步发现，非马尔可夫扩展和马尔可夫扩展之间存在等价性取决于特定的边缘激活机制。特别是，当活动边上不存在时间相关性时，可以预期等效性;否则，完全等价不再成立。