Spatial individual-level models (ILMs) provide a flexible framework for modelling infectious disease transmission across populations with known locations. Bayesian inference for these models relies on Markov chain Monte Carlo (MCMC), which requires repeated likelihood evaluation and, when parts of the epidemic trajectory are unobserved, data-augmented sampling over high-dimensional latent variables. This computational cost limits the applicability of MCMC to large populations and to settings requiring inference across multiple outbreaks. We propose using neural posterior estimation (NPE) for amortised Bayesian inference in spatial ILMs. NPE trains a conditional normalising flow on simulated data to approximate the posterior directly, bypassing likelihood evaluation at inference time. We compare two embedding architectures: a convolutional neural network (CNN) operating on the population-level incidence curve and a graph neural network (GNN) operating on individual-level infection and location data. In a simulation study under full observation, stochastic removals, and partial observation, both variants produce well-calibrated posteriors, with the GNN embedding yielding lower error and narrower credible intervals for the spatial transmission parameters. We apply the framework to a spatial SEIR model on 1,177 farm locations from the 2001 UK foot-and-mouth disease outbreak. GNN-NPE maintains calibrated coverage and is substantially faster than MCMC on a per-epidemic basis.

翻译：空间个体水平模型（ILM）为已知位置人群间传染病传播建模提供了灵活框架。这些模型的贝叶斯推断依赖马尔可夫链蒙特卡洛方法，需重复计算似然，且在疫情轨迹存在未观测部分时，需对高维隐变量进行数据增强采样。这种计算成本限制了MCMC在大规模人群及需要跨多次暴发进行推断场景中的适用性。我们提出在空间ILM中使用神经后验估计进行摊销贝叶斯推断。NPE通过模拟数据训练条件归一化流直接近似后验，在推断时绕过似然计算。比较两种嵌入架构：处理群体水平发病曲线的卷积神经网络与处理个体水平感染和位置数据的图神经网络。在全观测、随机移除和部分观测模拟研究中，两种变体均产生校准良好的后验，其中GNN嵌入在空间传播参数上获得更低误差和更窄可信区间。我们将该框架应用于2001年英国口蹄疫暴发的1177个农场空间SEIR模型。GNN-NPE维持校准覆盖度，且单次疫情推断速度显著快于MCMC。