Wastewater surveillance using differentiable Gaussian processes

Abstract Wastewater-based surveillance tracks disease spread within communities by analyzing biological markers in wastewater. A key component of effective wastewater-based surveillance is the reliable inference of underlying viral signals and their changes for accurate interpretation and dissemination. This paper proposes a Bayesian hierarchical modelling framework to jointly estimate wastewater viral signals and their derivatives, while accounting for common features and limitations of wastewater data. Our framework uses differentiable Gaussian processes to model both a common viral trend and deviations at individual stations. Specifically, the common trend is modelled as an Integrated Wiener Process and station-specific signals are smoothed assuming a Matérn covariance function of order 1.5. We demonstrate the framework’s utility by modelling SARS-CoV-2 concentrations across Canada and London, UK, as well as pepper mild mottle virus-normalized respiratory syncytial virus concentrations in Central California. Our results show that this framework reliably estimates both the signal and its derivative in retrospective and surveillance contexts, and show that inference of the signal’s average rates of change is sensitive to the differentiability of the modelling process.