TARnISHED: Forecasting Emergency Department visits using Wastewater with Multivariate Gaussian Random Walks

Rebeca Cardim Falcao, Michael A Irvine, Hind Sbihi, David A McVea

Keywords: probabilistic time series forecasting, Bayesian inference, multivariate Gaussian random walkers, spatiotemporal modelling, wastewater surveillance

Abstract:

**TARnISHED-WW**

*Forecasting Emergency Department visits using Wastewater with Multivariate Gaussian Random Walkers*

**Approach**

Respiratory emergency department (ED) visits are influenced by many factors, including viruses, bacterias, allergens, and pollutants. Previous work has used weather and air pollution data (e.g., PM2.5), clinical data such as case counts and hospitalizations, and pathogen levels at wastewater, usually focused on a single pathogen in one region. This can be limiting for early-warning and resource allocations when regional signals are co-evolving and pathogens affect ED burden differently.

We propose TARNISHED-WW (Time-series Analysis of Random-walks in WasteWater for Infection Surveillance and Hospital ED visits), a novel framework that integrates multi-pathogen wastewater and clinical data with a latent multivariate Gaussian random walk to capture shared transmission processes across regions, and residual random walkers to represent other drivers of ED visits. We further compare its performance by training a XGBoost model using the same datasets, including multi-pathogen data.

**Results**

Using wastewater, reported cases, and total test counts for Influenza A, RSV, and SARS-CoV-2 across four regions, we evaluated ED visit forecasts with the Continuous Ranked Probability Score (CRPS). TARnISHED achieved lower CRPS than XGBoost (reductions ranging from 12\% to 49\%), with observed data staying within TARnISHED forecast credible intervals

**Impacts**

This work demonstrates improved accuracy by modeling regional correlations and multiple pathogens. Additionally, TARnISHED provides new metrics that can support surveillance strategies and capacity planning. For example, the delay between signals, and the disease relative contribution for ED burden as shown in the figure provided. Thus, this framework provides early warning forecasts with improved accuracy compared to single-pathogen or single-region models, and additional metrics to inform capacity planning and surveillance strategies such as disease relative contribution for ED burden.

Submission Number: 258