[Paper Review] Inference in Stochastic Epidemic Models via Multinomial Approximations

Nick Whiteley, Lorenzo Rimella|arXiv (Cornell University)|Jun 24, 2020

COVID-19 epidemiological studies25 references4 citations

TL;DR

This paper introduces a computationally efficient method for inference in stochastic epidemic models using recursive multinomial approximations to bypass likelihood intractability, eliminating the need for simulation or tuning parameters. It enables accurate estimation of time-varying reproduction numbers and model parameters in both Ebola and COVID-19 case studies, outperforming ABC and MCMC methods in accuracy and speed.

ABSTRACT

We introduce a new method for inference in stochastic epidemic models which uses recursive multinomial approximations to integrate over unobserved variables and thus circumvent likelihood intractability. The method is applicable to a class of discrete-time, finite-population compartmental models with partial, randomly under-reported or missing count observations. In contrast to state-of-the-art alternatives such as Approximate Bayesian Computation techniques, no forward simulation of the model is required and there are no tuning parameters. Evaluating the approximate marginal likelihood of model parameters is achieved through a computationally simple filtering recursion. The accuracy of the approximation is demonstrated through analysis of real and simulated data using a model of the 1995 Ebola outbreak in the Democratic Republic of Congo. We show how the method can be embedded within a Sequential Monte Carlo approach to estimating the time-varying reproduction number of COVID-19 in Wuhan, China, recently published by Kucharski et al. 2020.

Motivation & Objective

• To address the computational challenge of likelihood intractability in stochastic compartmental epidemic models due to high-dimensional latent state summation.
• To develop a method that avoids stochastic simulation and tuning parameters, unlike ABC or MCMC approaches.
• To enable efficient filtering, smoothing, and likelihood evaluation for partially observed, discrete-time, finite-population epidemic models.
• To extend existing ODE-based inference methods, such as those in Kucharski et al. (2020), to stochastic models for improved realism.
• To demonstrate the method’s accuracy and scalability on real and simulated data, including Ebola and early COVID-19 outbreaks.

Proposed method

• The method uses recursive multinomial approximations to integrate over unobserved compartment counts, replacing intractable likelihood summations with a computationally simple filtering recursion.
• It models transitions between disease states (e.g., S→E, E→I, I→R) using conditionally independent binomial distributions, approximated via multinomial distributions over state transitions.
• The filtering recursion computes approximate marginal likelihoods and smoothing distributions for model parameters and latent states without forward simulation.
• The approach is embedded within a Sequential Monte Carlo (SMC) framework to estimate time-varying reproduction numbers in a stochastic SEIR model.
• It leverages ancestral sampling and resampling to compute posterior distributions over latent states and parameters, enabling full Bayesian inference.
• The method is applied to real Ebola data and extended to the stochastic version of Kucharski et al. (2020)’s COVID-19 model, using observed case counts with reporting uncertainty.

Experimental results

Research questions

• RQ1 Can a likelihood approximation method be developed that avoids stochastic simulation and tuning parameters in stochastic epidemic models?
• RQ2 How accurately can multinomial approximations estimate model parameters and latent states in partially observed, discrete-time epidemic models?
• RQ3 Can the proposed method outperform ABC and MCMC in terms of accuracy and computational efficiency on real-world outbreak data?
• RQ4 To what extent can the method be used to estimate time-varying reproduction numbers in a stochastic epidemic model compared to a deterministic ODE model?
• RQ5 How well does the method handle under-reporting and missing data in real-world surveillance data, such as in the 1995 Ebola outbreak or early COVID-19 in Wuhan?

Key findings

• The method accurately recovers ground truth parameters from synthetic Ebola data, outperforming both Data Augmentation MCMC and ABC in parameter estimation accuracy.
• On real 1995 Ebola outbreak data, the method achieved comparable or better performance than ABC (using ABSEIR R package) and ODE-based models in estimating key epidemiological parameters.
• The effective sample size in the SMC algorithm was comparable to that of Kucharski et al. (2020)’s method, despite using a stochastic model instead of an ODE, indicating robustness and efficiency.
• The estimated time-varying reproduction number $ R_t $ closely matched the true dynamics in the simulated data, with credible intervals covering the true values.
• The method successfully extended the ODE-based model of Kucharski et al. (2020) to a stochastic SEIR framework, maintaining alignment with observed case data while incorporating demographic and reporting uncertainty.
• The approach enabled accurate prediction of new confirmed cases in Wuhan and internationally, with simulated case counts closely matching observed data in both in-sample and out-of-sample periods.