Scalable calibration of individual-based epidemic models through categorical approximations

TL;DR

This paper introduces a deterministic, scalable method for calibrating individual-based epidemic models using categorical approximations, enabling efficient likelihood estimation and parameter inference for large populations.

Contribution

The authors propose a novel categorical likelihood approximation approach that simplifies and accelerates the calibration of complex individual-based epidemic models.

Findings

Accurate recovery of ground truth parameters.

Comparable marginal log-likelihoods with reduced computational cost.

Successful application to large-scale real-world data with over 160,000 entities.

Abstract

Traditional compartmental models capture population-level dynamics but fail to characterize individual-level risk. The computational cost of exact likelihood evaluation for partially observed individual-based models, however, grows exponentially with the population size, necessitating approximate inference. Existing sampling-based methods usually require multiple simulations of the individuals in the population and rely on bespoke proposal distributions or summary statistics. We propose a deterministic approach to approximating the likelihood using categorical distributions. The approximate likelihood is amenable to automatic differentiation so that parameters can be estimated by maximization or posterior sampling using standard software libraries such as Stan or TensorFlow with little user effort. We prove the consistency of the maximum approximate likelihood estimator. We empirically test our approach on several classes of individual-based models for epidemiology: different sets of disease states, individual-specific transition rates, spatial interactions, under-reporting and misreporting. We demonstrate ground truth recovery and comparable marginal log-likelihood values at substantially reduced cost compared to competitor methods. Finally, we show the scalability and effectiveness of our approach with a real-world application on the 2001 UK Foot-and-Mouth outbreak, where the simplicity of the CAL allows us to include 162775 farms.