Estimating epidemiologic dynamics from cross-sectional viral load distributions

Abstract

Virologic testing for SARS-CoV-2 has been central to the COVID-19 pandemic response, but interpreting changes in incidence and fraction of positive tests towards understanding the epidemic trajectory is confounded by changes in testing practices. Here, we show that the distribution of viral loads, in the form of Cycle thresholds (Ct), from positive surveillance samples at a single point in time can provide accurate estimation of an epidemic's trajectory, subverting the need for repeated case count measurements which are frequently obscured by changes in testing capacity. We identify a relationship between the population-level cross-sectional distribution of Ct values and the growth rate of the epidemic, demonstrating how the skewness and median of detectable Ct values change purely as a mathematical epidemiologic rule without any change in individual level viral load kinetics or testing. Although at the individual level measurement variation can complicate interpretation of Ct values for clinical use, we show that population-level properties reflect underlying epidemic dynamics. In support of these theoretical findings, we observe a strong relationship between the time-varying effective reproductive number, R(t), and the distribution of Cts among positive surveillance specimens, including median and skewness, measured in Massachusetts over time. We use the observed relationships to derive a novel method that allows accurate inference of epidemic growth rate using the distribution of Ct values observed at a single cross-section in time, which, unlike estimates based on case counts, is less susceptible to biases from delays in test results and from changing testing practices. Our findings suggest that instead of discarding individual Ct values from positive specimens, incorporation of viral loads into public health data streams offers a new approach for real-time resource allocation and assessment of outbreak mitigation strategies, even where repeat incidence data is not available. Ct values or similar viral load data should be regularly reported to public health officials by testing centers and incorporated into monitoring programs.

Group testing as a strategy for COVID-19 epidemiological monitoring and community surveillance

“…Results. Based on Eq 9, we find that the viral load distribution for asymptomatic individuals displays two peaks at high and low viral loads, see Fig 3E-in agreement with our analysis of the dataset Lennon et al [55], see Fig 2D. An exponential decrease in the number of new cases favors the proportion of individual at high C t s, see Fig 3E. The distribution of the viral load in symptomatic individuals is less bimodal than the observed asymptomatic distribution, in agreement with our analysis of the symptomatic dataset from Lennon et al [55], see Fig 2E. In [59], a similar results was obtained; a decrease in the incidence rate is shown to be associated to an increase in the proportion of individuals with high C t value.…”

“…In [ 59 ], a similar results was obtained; a decrease in the incidence rate is shown to be associated to an increase in the proportion of individuals with high C t value.…”

“…(C) In the Model 1 context, the distribution of the viral load in asymptomatic individuals is relatively uniform. (D) Model 2 for the evolution of the viral load post-infection distinguishing between symptomatic and asymptomatic (combining [ 58 ] and [ 59 ]). Parameters estimate are provided in Table H in S1 Text .…”

“…We consider the same scaling for the duration of the late infectious phase as the one for the decay time (see parameters in Table 1 ). The piece-wise model considered in [ 59 ] is also nearly flat during the late infectious phase at large time; yet in contrast to Eq 9 , [ 59 ] considers an instantaneous change of slope at the viral load peak.…”

How to detect and reduce potential sources of biases in studies of SARS-CoV-2 and COVID-19

“…As mentioned above, seroprevalence may underestimate cumulative incidence if some individuals who initially have antibody levels sufficient to test positive on a serologic test have waning levels that drop below the threshold for positivity, a phenomenon sometimes called "seroreversion". Low antibody values occur as antibodies are increasing and as they are declining; however, the increase is fast compared to the decline [9,19], so most individuals with low titers will be those on the decline, except perhaps in a very rapidly growing epidemic, where there will be many very recent infections (e.g., [20] but with antibody titers instead of viral load). Antibodies to seasonal coronaviruses have been shown to decline substantially within a period of a few months to a year [21].…”