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

Abstract

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. Simulationbased 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.

Quantifying invasive pest dynamics through inference of a two-node epidemic network model

“…Similar epidemic models have previously been used to describe the spread of infectious disease within human populations, e.g., for ebola in [18]. In these cases the parameters connecting the nodes represent the rates of the movement of individuals between nodes, e.g., the movement of infected people between geographical locations.…”

“…The transition between the S and I compartments is governed not only by the standard infestation rate parameter β (the rate at which contact of one infested tree with one susceptible tree will result in infestation, referred to as the ‘effective contact rate’), but also an additional infestation ‘pressure’ from the neighbouring node, described by the parameters α ij , where α 12 is the pressure applied by node 1 on node 2, and α 21 the pressure on node 2 by node 1. A similar model has been previously proposed to describe national surveillance counts from the 2013–2015 West Africa Ebola outbreak [18].…”

Inference for epidemic models with time‐varying infection rates: Tracking the dynamics of oak processionary moth in the UK

“…The statistical methodology used is a powerful tool for inferring the parameters of such models from real data and is transferable to other epidemiological and ecological datasets. Previously, similar statistical methodology has been used to describe the spread of infectious diseases (e.g., measles (Cauchemez & Ferguson, 2008) and Ebola (Fintzi et al, 2020)) and the spatial expansion of non-native plants (Cook et al, 2007), but has not yet been applied to the study of invasive insects.…”

A hybrid stochastic model and its Bayesian identification for infectious disease screening in a university campus with application to massive COVID-19 screening at the University of Liège

“…For a Poisson probability distribution, the variance is equal to the mean, so that variations are represented to be relatively more significant for smaller counts. Alternatively, other probability distributions could be used, such as a negative binomial probability distribution which introduces an overdispersion parameter that allows the variance to be larger than the mean [22] . Thus, assuming statistical independence of the variability in the observation process between observation intervals, the observed incidence counts are modeled to be distributed as in which denotes the Poisson probability mass function with mean .…”