Joint Modeling of Two Stochastic Processes, with Application to Learning Hospitalization Dynamics from Wastewater Viral Concentrations

TL;DR

This paper tackles the challenge of learning infection dynamics from aggregated wastewater viral signals and hospitalization data by introducing a latent infection process $s(\cdot)$ that drives both observed outcomes. It develops a flexible, continuous-time multi-state framework for infection, alongside emission models for wastewater load $w(\cdot)$ and hospitalization time-to-event $h(\cdot)$, and combines them with a pseudo-likelihood approach to handle data aggregation and under-reporting. Through simulations, the authors show robust parameter recovery under varying levels of case ascertainment, and a case study of Ottawa COVID-19 data demonstrates coherent recovery of infection prevalence and variant-specific hospitalization risk under different ascertainment scenarios. The proposed approach offers a principled way to exploit environmental surveillance for population-level public health inference when individual-level data are unavailable or incomplete, with broad applicability to emerging pathogens and evolving testing regimes.

Abstract

In the post-pandemic era of COVID-19, hospitalization remains a primary public health concern and wastewater surveillance has become an important tool for monitoring its dynamics at the level of community. However, there is usually no sufficient information to know the infection process that results in both wastewater viral signals and hospital admissions. That key challenge has motived a statistical framework proposed in this paper. We formulate the connection of overtime wastewater viral signals and hospitalization counts through a latent process of infection at the level of individual subject. We provide a strategy for accommodating aggregated data, a typical form of surveillance data. Moreover, we ease the conventional procedure of the statistical learning with the joint modeling using available information on the infection process, which can be under-reporting. A simulation study demonstrates that the proposed approach yields stable inference under different degrees of under-ascertainment. The COVID-19 surveillance data from Ottawa, Canada shows that the framework recovers coherent temporal patterns in infection prevalence and variant-specific hospitalization risk under several reporting assumptions.

Figures (3)

• Figure 1: Wastewater viral signals, daily new COVID-19 hospital admissions, and reported active COVID-19 cases in Ottawa over the study period. Active case counts are rescaled to 1% of their original values to facilitate comparison with wastewater signals and hospital admissions. Dashed segments of the active case curve indicate periods when testing access was limited and reported cases are treated as underreported in the scenario analysis.
• Figure 2: Estimated infection prevalence over time under the three case ascertainment scenarios described in Section \ref{['W3:case:scena']}, together with reported active case counts. Lines are color-coded for the two variant groups, showing periods of co-circulation. Dashed segments of the reported case curve indicate periods treated as under-reporting.
• Figure 3: Observed wastewater viral signals and daily hospital admissions compared with trajectories simulated from the fitted joint model under the policy-informed case ascertainment scenario (Scenario 2). Shaded bands represent the 95% central range of 100 simulated trajectories generated conditional on the fitted parameters, reflecting variability induced by the observation models rather than inferential uncertainty.