Research Article

Estimating epidemiologic dynamics from cross-sectional viral load distributions

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Science  16 Jul 2021:
Vol. 373, Issue 6552, eabh0635
DOI: 10.1126/science.abh0635

Added value of PCR testing for COVID-19

During the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic, polymerase chain reaction (PCR) tests were generally reported only as binary positive or negative outcomes. However, these test results contain a great deal more information than that. As viral load declines exponentially, the PCR cycle threshold (Ct) increases linearly. Hay et al. developed an approach for extracting epidemiological information out of the Ct values obtained from PCR tests used in surveillance for a variety of settings (see the Perspective by Lopman and McQuade). Although there are challenges to relying on single Ct values for individual-level decision-making, even a limited aggregation of data from a population can inform on the trajectory of the pandemic. Therefore, across a population, an increase in aggregated Ct values indicates that a decline in cases is occurring.

Science, abh0635, this issue p. eabh0635; see also abj4185, p. 280

Structured Abstract


Current approaches to epidemic monitoring rely on case counts, test positivity rates, and reported deaths or hospitalizations. These metrics, however, provide a limited and often biased picture as a result of testing constraints, unrepresentative sampling, and reporting delays. Random cross-sectional virologic surveys can overcome some of these biases by providing snapshots of infection prevalence but currently offer little information on the epidemic trajectory without sampling across multiple time points.


We develop a new method that uses information inherent in cycle threshold (Ct) values from reverse transcription quantitative polymerase chain reaction (RT-qPCR) tests to robustly estimate the epidemic trajectory from multiple or even a single cross section of positive samples. Ct values are related to viral loads, which depend on the time since infection; Ct values are generally lower when the time between infection and sample collection is short. Despite variation across individuals, samples, and testing platforms, Ct values provide a probabilistic measure of time since infection. We find that the distribution of Ct values across positive specimens at a single time point reflects the epidemic trajectory: A growing epidemic will necessarily have a high proportion of recently infected individuals with high viral loads, whereas a declining epidemic will have more individuals with older infections and thus lower viral loads. Because of these changing proportions, the epidemic trajectory or growth rate should be inferable from the distribution of Ct values collected in a single cross section, and multiple successive cross sections should enable identification of the longer-term incidence curve. Moreover, understanding the relationship between sample viral loads and epidemic dynamics provides additional insights into why viral loads from surveillance testing may appear higher for emerging viruses or variants and lower for outbreaks that are slowing, even absent changes in individual-level viral kinetics.


Using a mathematical model for population-level viral load distributions calibrated to known features of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral load kinetics, we show that the median and skewness of Ct values in a random sample change over the course of an epidemic. By formalizing this relationship, we demonstrate that Ct values from a single random cross section of virologic testing can estimate the time-varying reproductive number of the virus in a population, which we validate using data collected from comprehensive SARS-CoV-2 testing in long-term care facilities. Using a more flexible approach to modeling infection incidence, we also develop a method that can reliably estimate the epidemic trajectory in even more-complex populations, where interventions may be implemented and relaxed over time. This method performed well in estimating the epidemic trajectory in the state of Massachusetts using routine hospital admissions RT-qPCR testing data—accurately replicating estimates from other sources for the entire state.


This work provides a new method for estimating the epidemic growth rate and a framework for robust epidemic monitoring using RT-qPCR Ct values that are often simply discarded. By deploying single or repeated (but small) random surveillance samples and making the best use of the semiquantitative testing data, we can estimate epidemic trajectories in real time and avoid biases arising from nonrandom samples or changes in testing practices over time. Understanding the relationship between population-level viral loads and the state of an epidemic reveals important implications and opportunities for interpreting virologic surveillance data. It also highlights the need for such surveillance, as these results show how to use it most informatively.

Ct values reflect the epidemic trajectory and can be used to estimate incidence.

(A and B) Whether an epidemic has rising or falling incidence will be reflected in the distribution of times since infection (A), which in turn affects the distribution of Ct values in a surveillance sample (B). (C) These values can be used to assess whether the epidemic is rising or falling and estimate the incidence curve.


Estimating an epidemic’s trajectory is crucial for developing public health responses to infectious diseases, but case data used for such estimation are confounded by variable testing practices. We show that the population distribution of viral loads observed under random or symptom-based surveillance—in the form of cycle threshold (Ct) values obtained from reverse transcription quantitative polymerase chain reaction testing—changes during an epidemic. Thus, Ct values from even limited numbers of random samples can provide improved estimates of an epidemic’s trajectory. Combining data from multiple such samples improves the precision and robustness of this estimation. We apply our methods to Ct values from surveillance conducted during the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic in a variety of settings and offer alternative approaches for real-time estimates of epidemic trajectories for outbreak management and response.

This is an open-access article distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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