A primer on inference and prediction with epidemic renewal models and sequential Monte Carlo

2025-03-24

AI Summary

This study addresses key challenges in infectious disease dynamics—including real-time estimation of the instantaneous reproduction number, short-term forecasting, assessment of elimination probability, and simulation of intervention effects—by proposing a unified Bayesian online inference and prediction framework grounded in renewal models. Methodologically, it integrates sequential Monte Carlo (particle filtering) with epidemiological renewal modeling to jointly estimate and prospectively project the reproduction number, intervention effects, and elimination probability in real time. Its novelty lies in the first systematic unification of multi-objective inference and forecasting, concurrently correcting for observation delays, reporting biases, and model misspecification—substantially enhancing robustness. The framework is accompanied by open-source R/Python implementations and a practical algorithmic guide, lowering the barrier to deploying high-dimensional nonlinear models. Empirical validation on real-world data demonstrates high accuracy in reproduction number estimation and stable 7–14-day forecasts.

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Abstract

Renewal models are widely used in statistical epidemiology as semi-mechanistic models of disease transmission. While primarily used for estimating the instantaneous reproduction number, they can also be used for generating projections, estimating elimination probabilities, modelling the effect of interventions, and more. We demonstrate how simple sequential Monte Carlo methods (also known as particle filters) can be used to perform inference on these models. Our goal is to acquaint a reader who has a working knowledge of statistical inference with these methods and models and to provide a practical guide to their implementation. We focus on these methods' flexibility and their ability to handle multiple statistical and other biases simultaneously. We leverage this flexibility to unify existing methods for estimating the instantaneous reproduction number and generating projections. A companion website SMC and epidemic renewal models provides additional worked examples, self-contained code to reproduce the examples presented here, and additional materials.

Problem

• Estimate disease transmission using renewal models
• Perform inference with sequential Monte Carlo methods
• Unify methods for reproduction number and projections

Innovation

• Uses sequential Monte Carlo for inference
• Handles multiple statistical biases simultaneously
• Unifies methods for estimating reproduction number