A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak transmission dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJP), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is generally impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that replaces the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings. Existing LNA frameworks are inappropriate for incidence data and depend on simulation-based methods or an assumption that disease counts are normally distributed. We demonstrate how to reparameterize a SEM to properly analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and can be applied to a broad class of SEMs. We apply our method to national-level surveillance counts from the 2013--2015 West Africa Ebola outbreak, modeling within-country transmission and importation of infections from neighboring countries.