Aligning SARS-CoV-2 Indicators via an Epidemic Model: Application to Hospital Admissions and RNA Detection in Sewage Sludge

Ascertaining the state of coronavirus outbreaks is crucial for public health decision-making. Absent repeated representative viral test samples in the population, public health officials and researchers alike have relied on lagging indicators of infection to make inferences about the direction of the outbreak and attendant policy decisions. Recently researchers have shown that SARS-CoV-2 RNA can be detected in municipal sewage sludge with measured RNA concentrations rising and falling suggestively in the shape of an epidemic curve while providing an earlier signal of infection than hospital admissions data. The present paper presents a SARS-CoV-2 epidemic model to serve as a basis for estimating the incidence of infection, and shows mathematically how modeled transmission dynamics translate into infection indicators by incorporating probability distributions for indicator-specific time lags from infection. Hospital admissions and SARS-CoV-2 RNA in municipal sewage sludge are simultaneously modeled via maximum likelihood scaling to the underlying transmission model. The results demonstrate that both data series plausibly follow from the transmission model specified and provide a 95% confidence interval estimate of the reproductive number R₀ ≈ 2.4 ±0.2. Sensitivity analysis accounting for alternative lag distributions from infection until hospitalization and sludge RNA concentration respectively suggests that the detection of viral RNA in sewage sludge leads hospital admissions by 3 to 5 days on average. The analysis suggests that stay-at-home restrictions plausibly removed 89% of the population from the risk of infection with the remaining 11% exposed to an unmitigated outbreak that infected 9.3% of the total population.

Highlights

• A maximum likelihood method for aligning observed lagged epidemic indicators via an underlying transmission model is derived and illustrated using observed COVID-19 hospital admissions and SARS-CoV-2 RNA concentrations measured in sewage sludge to model a local SARS-CoV-2 outbreak

• The method enables direct estimation of the reproductive number R₀ from the observed indicators along with the initial prevalence of SARS-CoV-2 infection in the population at risk

• The analysis suggests tracking SARS-CoV-2 RNA concentration in sewage sludge provides a 3 to 5 day lead time over tracking hospital admissions, consistent with purely statistical time series analysis previously reported

• The model enables estimation of the fraction of the population compliant with government-mandated stay-at-home restrictions, the size of the exposed population, and the fraction of the population infected with SARS-CoV-2 over the outbreak