Consistent and fast inference in compartmental models of epidemics using Poisson Approximate Likelihoods

TL;DR

This paper introduces Poisson Approximate Likelihood (PAL) methods for scalable, consistent, and fast inference in complex stochastic epidemic models, outperforming traditional ODE approaches especially for large populations.

Contribution

The paper develops a novel likelihood-based inference framework for stochastic compartmental models, providing theoretical consistency results and practical advantages over existing methods.

Findings

PAL methods are simple, fast, and require no model simulation.

PALs enable fitting complex models like age-structured influenza.

PALs facilitate comparison of over-dispersion mechanisms in rotavirus models.

Abstract

Addressing the challenge of scaling-up epidemiological inference to complex and heterogeneous models, we introduce Poisson Approximate Likelihood (PAL) methods. In contrast to the popular ODE approach to compartmental modelling, in which a large population limit is used to motivate a deterministic model, PALs are derived from approximate filtering equations for finite-population, stochastic compartmental models, and the large population limit drives consistency of maximum PAL estimators. Our theoretical results appear to be the first likelihood-based parameter estimation consistency results which apply to a broad class of partially observed stochastic compartmental models and address the large population limit. PALs are simple to implement, involving only elementary arithmetic operations and no tuning parameters, and fast to evaluate, requiring no simulation from the model and having computational cost independent of population size. Through examples we demonstrate how PALs can be used to: fit an age-structured model of influenza, taking advantage of automatic differentiation in Stan; compare over-dispersion mechanisms in a model of rotavirus by embedding PALs within sequential Monte Carlo; and evaluate the role of unit-specific parameters in a meta-population model of measles.