Inference for partially observed epidemic dynamics guided by Kalman filtering techniques

TL;DR

This paper introduces a Kalman filtering-based inference method for partially observed epidemic models, providing a practical and general approach to estimate parameters from noisy, incomplete outbreak data, validated on simulated and real influenza data.

Contribution

It develops a Gaussian approximation-based inference method using Kalman filtering for epidemic models, addressing challenges of unobserved coordinates and noisy data.

Findings

The method accurately estimates parameters in simulated SIR epidemic scenarios.

Performance compares favorably with maximum iterated filtering methods.

Applied successfully to real influenza outbreak data from 1978.

Abstract

Despite the recent development of methods dealing with partially observed epidemic dynamics (unobserved model coordinates, discrete and noisy outbreak data), limitations remain in practice, mainly related to the quantity of augmented data and calibration of numerous tuning parameters. In particular, as coordinates of dynamic epidemic models are coupled, the presence of unobserved coordinates leads to a statistically difficult problem. The aim is to propose an easy-to-use and general inference method that is able to tackle these issues. First, using the properties of epidemics in large populations, a two-layer model is constructed. Via a diffusion-based approach, a Gaussian approximation of the epidemic density-dependent Markovian jump process is obtained, representing the state model. The observational model, consisting of noisy observations of certain model coordinates, is approximated by Gaussian distributions. Then, an inference method based on an approximate likelihood using Kalman filtering recursion is developed to estimate parameters of both the state and observational models. The performance of estimators of key model parameters is assessed on simulated data of SIR epidemic dynamics for different scenarios with respect to the population size and the number of observations. This performance is compared with that obtained using the well-known maximum iterated filtering method. Finally, the inference method is applied to a real data set on an influenza outbreak in a British boarding school in 1978.