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

• Published in: Biometrics Vol. 78; no. 4; pp. 1530 - 1541
• Main Authors: Fintzi, Jonathan, Wakefield, Jon, Minin, Vladimir N.
• Format: Journal Article
• Language: English
• Published: United States Blackwell Publishing Ltd 01.12.2022
• Subjects: Approximation; Bayes Theorem; Bayesian data augmentation; Coarseness; Computer applications; COVID-19 - epidemiology; Data analysis; Density; Ebola outbreak; Ebola virus; Ebolavirus; elliptical slice sampler; Epidemic models; Epidemics; Hemorrhagic Fever, Ebola - epidemiology; Humans; Incidence; influenza; Markov chain; Markov Chains; Mathematical analysis; monitoring; Monte Carlo Method; noncentered parameterization; Outbreaks; Robustness (mathematics); SARS-CoV-2; Severe acute respiratory syndrome coronavirus 2; Simulation; Statistical methods; Stochastic models; Stochastic Processes; Surveillance; surveillance count data; Viral diseases; Western Africa; Western Africa; elliptical slice sampler; noncentered parameterization; Ebola outbreak; surveillance count data; Bayesian data augmentation
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.13538

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), 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 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 approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large‐population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately 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 applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS‐CoV‐2 dynamics, and apply our method to national surveillance counts from the 2013–2015 West Africa Ebola outbreak.