网络上非马尔可夫流行病的平均场模型：从基于边的房室模型到成对模型
Mean-field models for non-Markovian epidemics on networks: from edge-based compartmental to pairwise models
摘要：
本文提出了一种新的扩展的基于边缘的房室模型的传染病的任意分布的传播和恢复时间。使用消息传递的方法，我们还得到了一个新的两两类传染病模型的马尔可夫传输和任意的恢复期。新的成对的模型允许一个正式证明，消息传递和基于边缘的房室模型是等价的马尔可夫传输和任意恢复过程的情况下。基于边缘和消息传递模型被证明也是等价的任意传输过程，我们展示了这一点的充分证明的第一步。新的成对类模型包含了许多现有的众所周知的模型，可以通过适当的减少。它也适用于相对简单的数值实现。我们测试的理论结果进行比较的各种成对的类似模型的数值解的结果的基础上显式随机网络模拟。
英文摘要：
This paper presents a novel extension of the edge-based compartmental model for epidemics with arbitrary distributions of transmission and recovery times. Using the message passing approach we also derive a new pairwise-like model for epidemics with Markovian transmission and an arbitrary recovery period. The new pairwise-like model allows one to formally prove that the message passing and edge-based compartmental models are equivalent in the case of Markovian transmission and arbitrary recovery processes. The edge-based and message passing models are conjectured to also be equivalent for arbitrary transmission processes; we show the first step of a full proof of this. The new pairwise-like model encompasses many existing well-known models that can be obtained by appropriate reductions. It is also amenable to a relatively straightforward numerical implementation. We test the theoretical results by comparing the numerical solutions of the various pairwise-like models to results based on explicit stochastic network simulations.
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