Neural Posterior Estimation for Spatial Individual-Level Epidemic Models

Abstract

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.