Bayesian inference of heterogeneous epidemic models: Application to COVID-19 spread accounting for long-term care facilities

TL;DR

This paper introduces a high-dimensional Bayesian framework to model and infer the heterogeneous spread and severity of COVID-19, especially within and outside long-term care facilities, using advanced statistical methods and real data from New Jersey and Texas.

Contribution

It develops a novel high-dimensional Bayesian inference approach for complex epidemic models, addressing the curse of dimensionality and demonstrating its application to COVID-19 data.

Findings

Quantified uncertainties in COVID-19 spread within LTC facilities and general population.

Validated forecasting accuracy with empirical posterior samples.

Demonstrated low-dimensional structure in high-dimensional inference problem.

Abstract

We propose a high dimensional Bayesian inference framework for learning heterogeneous dynamics of a COVID-19 model, with a specific application to the dynamics and severity of COVID-19 inside and outside long-term care (LTC) facilities. We develop a heterogeneous compartmental model that accounts for the heterogeneity of the time-varying spread and severity of COVID-19 inside and outside LTC facilities, which is characterized by time-dependent stochastic processes and time-independent parameters in $\sim$1500 dimensions after discretization. To infer these parameters, we use reported data on the number of confirmed, hospitalized, and deceased cases with suitable post-processing in both a deterministic inversion approach with appropriate regularization as a first step, followed by Bayesian inversion with proper prior distributions. To address the curse of dimensionality and the ill-posedness of the high-dimensional inference problem, we propose use of a dimension-independent projected Stein variational gradient descent method, and demonstrate the intrinsic low-dimensionality of the inverse problem. We present inference results with quantified uncertainties for both New Jersey and Texas, which experienced different epidemic phases and patterns. Moreover, we also present forecasting and validation results based on the empirical posterior samples of our inference for the future trajectory of COVID-19.