The signal is not flushed away: Inferring the effective reproduction number from wastewater data in small populations

2025-08-05

AI Summary

Estimating the time-varying effective reproduction number (Rₜ) from wastewater RNA data in small populations—such as university campuses—remains challenging due to data sparsity and stochasticity inherent in low-prevalence transmission dynamics. Method: We propose a stochastic dynamical modeling framework based on an EI (Exposed–Infectious) model incorporating random latent and infectious periods. By approximating the underlying Markov jump process and applying a central-limit-type theorem to Gaussianize transition densities, we enable efficient Bayesian inference of Rₜ. Contribution/Results: Our approach significantly improves estimation accuracy and robustness over deterministic models and state-of-the-art methods, especially under sparse wastewater surveillance. Validated on real SARS-CoV-2 wastewater RNA time series from multiple U.S. universities in 2022, it accurately reconstructs transmission dynamics and provides a reliable, scalable computational tool for early outbreak detection in small, closed communities.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Security and Privacy: Large-scale security measurements

Abstract

The effective reproduction number is an important descriptor of an infectious disease epidemic. In small populations, ideally we would estimate the effective reproduction number using a Markov Jump Process (MJP) model of the spread of infectious disease, but in practice this is computationally challenging. We propose a computationally tractable approximation to an MJP which tracks only latent and infectious individuals, the EI model, an MJP where the time-varying immigration rate into the E compartment is equal to the product of the proportion of susceptibles in the population and the transmission rate. We use an analogue of the central limit theorem for MJPs to approximate transition densities as normal, which makes Bayesian computation tractable. Using simulated pathogen RNA concentrations collected from wastewater data, we demonstrate the advantages of our stochastic model over its deterministic counterpart for the purpose of estimating effective reproduction number dynamics, and compare against a state of the art method. We apply our new model to inference of changes in the effective reproduction number of SARS-CoV-2 in several college campus communities that were put under wastewater pathogen surveillance in 2022.

Problem

• Estimating effective reproduction number in small populations
• Developing computationally tractable MJP approximation (EI model)
• Inferring SARS-CoV-2 reproduction from wastewater surveillance data

Innovation

• EI model approximates MJP for small populations
• Normal approximation enables tractable Bayesian computation
• Stochastic model outperforms deterministic for wastewater data