Epidemic propagation on networks represents an important departure from traditional mass-action models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using mean-field models, such as the pairwise model (PWM), the high-dimensionality becomes tractable. While such models have been used extensively for model analysis, there is limited work in the context of statistical inference. In this paper, we explore the extent to which the PWM with the susceptible-infected-recovered (SIR) epidemic can be used to infer disease- and network-related parameters. Data from an epidemics can be loosely categorised as being population level, e.g., daily new cases, or individual level, e.g., recovery times. To understand if and how network inference is influenced by the type of data, we employed the widely-used MLE approach for population-level data and dynamical survival analysis (DSA) for individual-level data. For scenarios in which there is no model mismatch, such as when data are generated via simulations, both methods perform well despite strong dependence between parameters. In contrast, for real-world data, such as foot-and-mouth, H1N1 and COVID19, whereas the DSA method appears fairly robust to potential model mismatch and produces parameter estimates that are epidemiologically plausible, our results with the MLE method revealed several issues pertaining to parameter unidentifiability and a lack of robustness to exact knowledge about key quantities such as population size and/or proportion of under reporting. Taken together, however, our findings suggest that network-based mean-field models can be used to formulate approximate likelihoods which, coupled with an efficient inference scheme, make it possible to not only learn about the parameters of the disease dynamics but also that of the underlying network.

网络上的流行病传播代表了与传统大规模行动模型的重要背离。然而，精确模型的高维性对数学分析和参数推断都提出了挑战。通过使用平均场模型，例如成对模型 (PWM)，高维变得易于处理。虽然此类模型已广泛用于模型分析，但在统计推断方面的工作却很有限。在本文中，我们探讨了易感感染者康复（SIR）流行病的 PWM 在多大程度上可用于推断疾病和网络相关参数。来自流行病的数据可以大致分为人口级别（例如每日新病例）或个人级别（例如恢复时间）。为了了解网络推理是否以及如何受到数据类型的影响，我们对群体级数据采用了广泛使用的 MLE 方法，对个体级数据采用了动态生存分析 (DSA)。对于不存在模型不匹配的场景，例如通过模拟生成数据时，尽管参数之间存在很强的依赖性，但这两种方法都表现良好。相比之下，对于真实世界的数据，例如口蹄疫、H1N1 和 COVID19，虽然 DSA 方法对于潜在的模型不匹配似乎相当稳健，并产生流行病学上合理的参数估计，但我们使用 MLE 方法的结果揭示了几个问题与参数不可识别性以及对关键数量（例如人口规模和/或报告不足的比例）的准确了解缺乏稳健性有关。然而，总而言之，我们的研究结果表明，基于网络的平均场模型可用于制定近似似然性，再加上有效的推理方案，不仅可以了解疾病动态的参数，还可以了解疾病动态的参数。底层网络。