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.