We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from this framework offers an improvement over existing pair-based models by moving away from edge-centric descriptions while keeping the description concise and relatively simple. For the contagion process, we consider the susceptible–infected–recovered (SIR) model, which is realized on a network with time-varying edges. We show that the shift in perspective from individual-based to pair-based quantities enables exact modelling of Markovian epidemic processes on temporal tree networks. On arbitrary networks, the proposed pair-based model provides a substantial increase in accuracy at a low computational and conceptual cost compared to the individual-based model. From the pair-based model, we analytically find the condition necessary for an epidemic to occur, otherwise known as the epidemic threshold. Due to the fact that the SIR model has only one stable fixed point, which is the global non-infected state, we identify an epidemic by looking at the initial stability of the model.

我们提出了一个流行病在时间网络上传播的建模框架，从中可以恢复基于个人和基于对的模型。从该框架系统派生的建议的基于时间对的模型通过远离边缘中心描述，同时保持描述简洁和相对简单，对现有的基于对的模型进行了改进。对于传染过程，我们考虑了易受感染的恢复（SIR）模型，该模型是在具有时变边缘的网络上实现的。我们表明，从基于个人的数量到基于配对的数量的转变使得可以对时域树网络上的马尔可夫流行过程进行精确建模。在任意网络上，与基于个人的模型相比，所提出的基于对的模型以较低的计算和概念成本显着提高了准确性。从基于配对的模型中，我们分析性地发现发生流行病的必要条件，或者称为流行病阈值。由于SIR模型只有一个稳定的固定点，即全局未感染状态，因此我们通过查看模型的初始稳定性来确定一种流行病。