Viral dynamics of acute SARS-CoV-2 infection and applications to diagnostic and public health strategies

SARS-CoV-2 infections are characterized by viral proliferation and clearance phases and can be followed by low-level persistent viral RNA shedding. The dynamics of viral RNA concentration, particularly in the early stages of infection, can inform clinical measures and interventions such as test-based screening. We used prospective longitudinal quantitative reverse transcription PCR testing to measure the viral RNA trajectories for 68 individuals during the resumption of the 2019–2020 National Basketball Association season. For 46 individuals with acute infections, we inferred the peak viral concentration and the duration of the viral proliferation and clearance phases. According to our mathematical model, we found that viral RNA concentrations peaked an average of 3.3 days (95% credible interval [CI] 2.5, 4.2) after first possible detectability at a cycle threshold value of 22.3 (95% CI 20.5, 23.9). The viral clearance phase lasted longer for symptomatic individuals (10.9 days [95% CI 7.9, 14.4]) than for asymptomatic individuals (7.8 days [95% CI 6.1, 9.7]). A second test within 2 days after an initial positive PCR test substantially improves certainty about a patient’s infection stage. The effective sensitivity of a test intended to identify infectious individuals declines substantially with test turnaround time. These findings indicate that SARS-CoV-2 viral concentrations peak rapidly regardless of symptoms. Sequential tests can help reveal a patient’s progress through infection stages. Frequent, rapid-turnaround testing is needed to effectively screen individuals before they become infectious.

sensitivity of a test intended to identify infectious individuals declines substantially with test turnaround 48 time.

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Conclusions. SARS-CoV-2 viral concentrations peak rapidly regardless of symptoms. Sequential tests can 51 help reveal a patient's progress through infection stages. Frequent rapid-turnaround testing is needed to 52 effectively screen individuals before they become infectious.

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A critical strategy to curb the spread of SARS-CoV-2 is to rapidly identify and isolate infectious individuals. 56 Because symptoms are an unreliable indicator of infectiousness and infections are frequently 57 asymptomatic 1 , testing is key to determining whether a person is infected and may be contagious. Real time 58 quantitative reverse transcriptase polymerase chain reaction (RT-qPCR) tests are the gold standard for 59 detecting SARS-CoV-2 infection. Normally, these tests yield a binary positive/negative diagnosis based on 60 detection of viral RNA. However, they can also quantify the viral titer via the cycle threshold (Ct). The Ct 61 is the number of thermal cycles needed to amplify sampled viral RNA to a detectable level: the higher the 62 sampled viral RNA concentration, the lower the Ct. This inverse correlation between Ct and viral 63 concentration makes RT-qPCR tests far more valuable than a binary diagnostic, as they can be used to 64 reveal a person's progress through key stages of infection 2 , with the potential to assist clinical and public 65 health decision-making. However, the dynamics of the Ct during the earliest stages of infection, when 66 contagiousness is rapidly increasing, have been unclear, because diagnostic testing is usually performed 67 after the onset of symptoms, when viral RNA concentration has peaked and already begun to decline, and 68 performed only once 3,4 . Without a clear picture of the course of SARS-CoV-2 viral concentrations across 69 the full duration of acute infection, it has been impossible to specify key elements of testing algorithms 70 such as the frequency of rapid at-home testing 5 that will be needed to reliably screen infectious individuals 71 before they transmit infection. Here, we fill this gap by analyzing the prospective longitudinal SARS-CoV-72 2 RT-qPCR testing performed for players, staff, and vendors during the resumption of the 2019-20 National 73 Basketball Association (NBA) season.

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Methods. 76 Data collection. 77 The study period began in teams' local cities from June 23 rd through July 9 th , 2020, and testing continued 78 for all teams as they transitioned to Orlando, Florida through September 7 th , 2020. A total of 68 individuals 79 (90% male) were tested at least five times during the study period and recorded at least one positive test 80 with Ct value <40. Most (85%) of consecutive tests were recorded within one day of each other and fewer 81 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted June 6, 2021. ;https://doi.org/10.1101https://doi.org/10. /2020 than 3% of the intervals between consecutive tests exceeded 4 days (Supplemental Figure 1). Many 82 individuals were being tested daily as part of Orlando campus monitoring. Due to a lack of new infections 83 among players and team staff after clearing quarantine in Orlando, all players and team staff included in 84 the results pre-date the Orlando phase of the restart. A diagnosis of "acute" or "persistent" infection was 85 abstracted from physician records. "Acute" denoted a likely new infection. "Persistent" indicated the 86 presence of virus in a clinically recovered individual, likely due to infection that developed prior to the 87 onset of the study. There were 46 acute infections; the remaining 22 individuals were assumed to be 88 persistently shedding SARS-CoV-2 RNA due to a known infection that occurred prior to the study period 6 .  Due to imperfect sampling, persistent viral shedding, and test uncertainty near the limit of detection, a 97 straightforward analysis of the data would be insufficient to reveal the duration and peak magnitude of the 98 viral trajectory. Imperfect sampling would bias estimates of the peak viral concentration towards lower 99 concentrations/higher Ct values since the moment of peak viral concentration is unlikely to be captured.

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Persistent shedding and test uncertainty would bias estimates of the trajectory duration towards longer 101 durations of infection. To address these problems, we used a Bayesian statistical model to infer the peak Ct 102 value and the durations of the proliferation and clearance stages for the 46 acute infections (Figure 1; 103 Supplemental Methods). We assumed that the viral concentration trajectories consisted of a proliferation 104 phase, with exponential growth in viral RNA concentration, followed by a clearance phase characterized 105 by exponential decay in viral RNA concentration 8 . Since Ct values are roughly proportional to the negative 106 logarithm of viral concentration 2 , this corresponds to a linear decrease in Ct followed by a linear increase. 107 We therefore constructed a piecewise-linear regression model to estimate the peak Ct value, the time from 108 infection onset to peak (i.e., the duration of the proliferation stage), and the time from peak to infection 109 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted June 6, 2021. ; https://doi.org/10.1101/2020.10.21.20217042 doi: medRxiv preprint resolution (i.e., the duration of the clearance stage). This allowed us to separate the viral trajectories into 110 the three distinct phases of proliferation (from the onset of detectability to the peak viral concentration, or  we extracted all observed Ct values within a 5-unit window (e.g., between 30 and 35 Ct) and measured how 125 frequently these values sat within the proliferation stage, the clearance stage, or the persistent stage. We 126 measured these frequencies across 10,000 posterior parameter draws to account for that fact that Ct values 127 near stage transitions (e.g., near the end of the clearance stage) could be assigned to different infection 128 stages depending on the parameter values (see Figure 1, bottom-right). We did this for 23 windows with 129 midpoint spanning from Ct = 37.5 to Ct = 15.5 in increments of 1 Ct.

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To calculate the probability that a Ct value sitting within the 5-unit window corresponded to an acute 132 infection (i.e., either the proliferation or the clearance stage), we summed the proliferation and clearance 133 frequencies for all samples within that window and divided by the total number of samples in the window. 134 We similarly calculated the probability that a Ct sitting within the 5-unit window corresponded to just the 135 proliferation phase. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted June 6, 2021. ; https://doi.org/10. 1101 To assess the information gained by conducting a second test within two days of an initial positive, we 138 restricted our attention to all samples that had a subsequent sample taken within two days. We repeated the 139 above calculations for (a) consecutive tests with decreasing Ct and (b) consecutive tests with increasing Ct.

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That is, we measured the frequency with which a given Ct value sitting within a 5-unit window, followed 141 by a second test with either lower or higher Ct, sat within with the proliferation, clearance, or persistence 142 stages.

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Measuring the effective sensitivity of screening tests.

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The sensitivity of a test is defined as the probability that the test correctly identifies an individual who is 146 positive for some criterion of interest. For clinical diagnostic SARS-CoV-2 tests, the criterion of interest is 147 current infection with SARS-CoV-2. Alternatively, a common goal is to predict infectiousness at some 148 point in the future, as in the context of test-based screening prior to a social gathering. The 'effective 149 sensitivity' of a test in this context (i.e., its ability to predict future infectiousness) may differ substantially 150 from its clinical sensitivity (i.e., its ability to detect current infection). A test's effective sensitivity depends 151 on its inherent characteristics, such as its limit of detection and sampling error rate, as well as the viral 152 dynamics of infected individuals.

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To illustrate this, we estimated the effective sensitivity of (a) a test with limit of detection of 40 Ct and a 155 1% sampling error probability (akin to RT-qPCR), and (b) a test with limit of detection of 35 Ct and a 5% 156 sampling error probability (akin to some rapid antigen tests). We measured the frequency with which such 157 tests would successfully screen an individual who would be infectious at the time of a gathering when the 158 test was administered between 0 and 3 days prior to the gathering, given viral trajectories informed by the 159 longitudinal testing data (see schematic in Figure 1). To accomplish this, we drew 1,000 individual-level 160 viral concentration trajectories from the fitted model, restricting to trajectories with peak viral concentration 161 above a given infectiousness threshold (any samples with peak viral concentration below the infectiousness 162 threshold would never be infectious and so would not factor into the sensitivity calculation). For the main 163 analysis, we assumed that the infectiousness threshold was at 30 Ct 10 . In a supplementary analysis, we also 164 assessed infectiousness thresholds of 35 and 20 Ct. We drew onset-of-detectability times (i.e., the onset of 165 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted June 6, 2021. ; https://doi.org/10.1101/2020.10.21.20217042 doi: medRxiv preprint the proliferation stage) according to a random uniform distribution so that each person would have a Ct   Table 1. There was a substantial amount of individual-level variation in the peak 204 Ct value and the proliferation and clearance stage durations (Supplemental Figures 9-14).

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Using the full dataset of 68 individuals, we estimated the frequency with which a given Ct value was 207 associated with an acute infection (i.e., the proliferation or clearance phase, but not the persistence phase), 208 and if so, the probability that it was associated with the proliferation stage alone. The probability of an acute 209 infection increased rapidly with decreasing Ct (increasing viral load), with Ct < 30 virtually guaranteeing 210 an acute infection in this dataset ( Figure 4A). However, a single Ct value provided little information about 211 whether an acute infection was in the proliferation or the clearance stage ( Figure 4B). This is unsurprising 212 since the viral trajectory must pass through any given value during both the proliferation and the clearance 213 stage. With roughly uniform sampling over time, a given Ct value is more likely to correspond to the 214 clearance stage simply because the clearance stage is longer.

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We assessed whether a second test within two days of the first could improve these predictions. A positive 217 test followed by a second test with lower Ct (higher viral RNA concentration) was slightly more likely to 218 be associated with an active infection than a positive test alone (Figure 4C). Similarly, a positive test 219 followed by a second test with lower Ct (higher viral RNA concentration) was much more likely to be 220 associated with the proliferation phase than with the clearance phase ( Figure 4D).

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The copyright holder for this preprint this version posted June 6, 2021. ; https://doi.org/10.1101/2020.10.21.20217042 doi: medRxiv preprint We next estimated how the effective sensitivity of a pre-event screening test declines with increasing time 223 to the event. For a test with limit of detection of 40 Ct and a 1% chance of sampling error, the effective 224 sensitivity declines from 99% when the test coincides with the start of the event to 76% when the test is 225 administered two days prior to the event (Figure 5A), assuming a threshold of infectiousness at 30 Ct 10 .

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This two-day-ahead sensitivity is slightly lower than the effective sensitivity of a test with a limit of 227 detection at 35 Ct and a 5% sampling error administered one day before the event (82%), demonstrating 228 that limitations in testing technology can be compensated for by reducing turnaround time. Using these 229 effective sensitivities, we estimated the number of infectious individuals who would be expected to arrive 230 at a gathering with 1,000 people given a pre-gathering screening test and a 2% prevalence of infectiousness 231 in the population. Just as the effective sensitivity declines with time to the gathering, the predicted number 232 of infectious individuals rises with time to the gathering ( Figure 5B) since longer delays between the 233 screening test and the gathering make it more likely that an individual will be undetectable at the time of 234 testing but infectious at the time of the event. Changing the infectiousness threshold modulates the 235 magnitude of the decline in effective sensitivity associated with longer testing delays; however, the overall 236 trend is consistent (Supplemental Figure 18).

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Discussion. 239 We provide the first comprehensive data on the early-infection RT-qPCR Ct dynamics associated with 240 SARS-CoV-2 infection. We found that viral titers peak quickly, normally within 3 days of the first possible 241 RT-qPCR detection, regardless of symptoms. Our findings highlight that repeated PCR tests can be used to  If a patient is at risk for complications, closer monitoring and more proactive treatment may be preferred 247 for patients near the start of infection than for those who are already nearing its resolution. We also show 248 that the effective sensitivity of pre-event screening tests declines rapidly with test turnaround time due to 249 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted June 6, 2021. ; https://doi. org/10.1101org/10. /2020 the rapid progression from detectability to peak viral titers. Due to the transmission risk posed by large 250 gatherings 11 , the trade-off between test speed and sensitivity must be weighed carefully. Our data offer the 251 first direct measurements capable of informing such decisions.  CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted June 6, 2021. ; https://doi.org/10.1101/2020.10.21.20217042 doi: medRxiv preprint that the central patterns will hold across populations: first, that low Cts (<30) strongly predict acute 278 infection, and second, that a follow-up test collected within two days of an initial positive test can 279 substantially help to discern whether a person is closer to the beginning or the end of their infection. Our 280 study did not test for the presence of infectious virus, though previous studies have documented a close 281 inverse correlation between Ct values and culturable virus 10 . Our assessment of pre-event testing assumed 282 that individuals become infectious immediately upon passing a threshold and that this threshold is the same 283 for the proliferation and for the clearance phase. In reality, the threshold for infectiousness is unlikely to be 284 at a fixed viral concentration for all individuals and may be at a higher Ct/lower viral concentration during 285 the proliferation stage than during the clearance stage. Further studies that measure culturable virus during 286 the various stages of infection and that infer infectiousness based on contact tracing combined with 287 prospective longitudinal testing will help to clarify the relationship between viral concentration and 288 infectiousness.

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To manage the spread of SARS-CoV-2, we must develop novel technologies and find new ways to extract 291 more value from the tools that are already available. Our results suggest that integrating the quantitative 292 viral RNA trajectory into algorithms for clinical management could offer benefits. The ability to chart a 293 patient's progress through their infection underpins our ability to provide appropriate clinical care and to 294 institute effective measures to reduce the risk of onward transmission. Marginally more sophisticated 295 diagnostic and screening algorithms may greatly enhance our ability to manage the spread of SARS-CoV-296 2 using tests that are already available.

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The copyright holder for this preprint this version posted June 6, 2021. ;https://doi.org/10.1101https://doi.org/10. /2020 298 299 300  infectious. One day prior to the gathering, the individual could be detected by either a rapid test or a PCR test. Two days prior to 313 the event, the individual could be detected by a PCR test but not by a rapid test. Three days prior to the event, neither test would 314 detect the individual.

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Effective sensitivity for a test with limit of detection of 40 Ct and 1% sampling error probability (red) and 35 Ct and 5% sampling 351 error probability (blue). B: Number of infectious individuals expected to attend an event of size 1,000 assuming a population 352 prevalence of 2% infectious individuals for a test with limit of detection of 40 Ct and 1% sampling error probability (red) and 35

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Ct and 5% sampling error probability (blue). Shaded bands represent 90% prediction intervals generated from the quantiles of

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