Neural posterior estimation for stochastic epidemic modeling

Stochastic infectious disease models capture uncertainty in public health outcomes and have become increasingly popular in epidemiological practice. However, it is hard to calibrate realistic stochastic models to data due to the challenges of likelihood-based inference of unknown parameters. Stochastic epidemic models are nonlinear dynamical systems that may feature massive latent state spaces, resulting in computationally intractable likelihood densities. We develop an approach to calibrating large-scale epidemiological models using Neural Posterior Estimation, an emergent deep learning technique for simulation-based inference. In NPE, a neural network trained on simulated data learns to “invert” a stochastic simulator, returning a parametric approximation to the posterior distribution. Motivated by the problem of understanding transmission of carbapenem-resistant Klebsiella pneumoniae (CRKP), a major healthcare-associated infection, we propose a stochastic, discrete-time susceptible infected model. Through a realistic simulation experiment, we show that NPE produces accurate posterior estimates of unknown infection rates at a computational discount compared to Approximate Bayesian Computation. In an empirical study of CRKP transmission in a Chicago-area hospital, we use NPE to analyze spatial heterogeneity in patient-to-patient transmission risk.