key: cord-0703122-oav3286j
authors: Quilty, B. J.; Clifford, S.; Flasche, S.; Kucharski, A. J.; CMMID COVID-19 Working Group,; Edmunds, W. J.
title: Quarantine and testing strategies in contact tracing for SARS-CoV-2
date: 2020-08-24
journal: nan
DOI: 10.1101/2020.08.21.20177808
sha: 6a44b577f846eae8e62f83f122f0f787aaefafe3
doc_id: 703122
cord_uid: oav3286j

Previous work has indicated that contact tracing and isolation of index case and quarantine of potential secondary cases can, in concert with physical distancing measures, be an effective strategy for reducing transmission of SARS-CoV-2. Currently, contacts traced manually through the NHS Test and Trace scheme in the UK are asked to self-isolate for 14 days from the day they were exposed to the index case, which represents the upper bound for the incubation period. However, following previous work on screening strategies for air travellers it may be possible that this quarantine period could be reduced if combined with PCR testing. Adapting the simulation model for contact tracing, we find that quarantine periods of at least 10 days combined with a PCR test on day 9 may largely emulate the results from a 14-day quarantine period in terms of the averted transmission potential from secondary cases (72% (95%UI: 3%, 100%) vs 75% (4%, 100%), respectively). These results assume the delays from testing index cases' and tracing their contacts are minimised (no longer than 4.5 days on average). If secondary cases are traced and quarantined 1 day earlier on average, shorter quarantine periods of 8 days with a test on day 7 (76% (7%, 100%)) approach parity with the 14 day quarantine period with a 1 day longer delay to the index cases' test. However, the risk of false-negative PCR tests early in a traced case's infectious period likely prevents the use of testing to reduce quarantine periods further than this, and testing immediately upon tracing, with release if negative, will avert just 17% of transmission potential on average. In conclusion, the use of PCR testing is an effective strategy for reducing quarantine periods for secondary cases, while still reducing transmission of SARS-CoV-2, especially if delays in the test and trace system can be reduced, and may improve quarantine compliance rates.

Following the notation of Kretzschmar et al. (2020) (5) , we consider the following events to be relevant to the tracing of the contacts of an index case -an individual assumed to be newly-symptomatic with COVID-19 and seeking a test (Figure 1 ). Each of the following variables are specific to an individual, but we omit a subscript, , for brevity. An individual is exposed and becomes infected at time

We assume the i . T 0 index case has onset of symptoms at time , lasting until time . For asymptomatic cases, no symptoms T 2 T 2 ′ are ever displayed and hence both and are undefined. For sensitivity, we assume testing of the index T 2 T 2 ′ case occurs at time , 1, 2 or 3 days after symptom onset , with the results of the test available at time ;

those testing positive will go on to isolate for 10 days from their symptom onset (6) . We assume that positive cases are immediately referred to contact tracers, with the index case's contacts' information sourced at , T 4 and these contacts are then traced and quarantined at time For comparison, we consider the baseline for . T 4 ′ index case testing delay to be 2 days. Figure 1 -Example schematic of the contact tracing process and associated timings where an index case causes two secondary cases, one of which is symptomatic and one of which is asymptomatic. Darker shaded regions of each cases' timeline indicate periods of increased infectivity. Arrows indicate transmission events, with red crosses indicating transmission prevented through quarantine of traced contacts. As the asymptomatic secondary case is quarantined (dashed red line) before they become infectious, they never spend any time infectious in the community.

Rather than assuming a specific time at which infectivity begins ( in Kretzschmar's notation) we consider T 1 the infectivity profile, i.e, a distribution of times at which transmission is likely to occur. This distribution is derived by considering the incubation period (time from exposure to onset of symptoms), , and T 2 − T 0 delay from infectiousness to onset of symptoms , and using the corrections by Ashcroft et al. (2020) T 2 − T 1 (7) to the method of He et al. (2020) (8) with incubation periods sampled from the distribution in (9) .

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For the index case we parameterise the delays associated with the contact tracing system (having a test to receiving the results ( ), sourcing contact information ( ), and tracing ( )) according

to the latest NHS Test and Trace data from the week 16 July 2020 to 22 July 2020 (Table 1 ) (10) . These times are reported as 24 hour intervals ( days), which we used to derive a 0 , , ,

Gamma distribution considering the delay in each index case's awaiting a test result, sourcing of contacts and tracing of contacts as doubly-censored observations on the specified time intervals using the fitdistcens function from the fitdistrplus package in R (11) .

We consider the same quarantine stringency settings as in our previous work (3) , namely: low, moderate, high and maximum stringencies, based on the expected reduction of onwards transmission potential (Table  S1 ). Any secondary case displaying symptoms during their quarantine period will continue to isolate until 10 days have passed since onset of symptoms (6) . Low stringency quarantine consists of a test at time of tracing and release from quarantine a day later if negative. Moderate stringency consists of mandatory quarantine periods of 3, 5 or 7 days, releasing on that day if no testing is considered or, if testing is considered, T 3 ′ − T 3 days later if the test is negative. The high stringency scenarios consider double testing in order to minimise the amount of time spent in quarantine; a 14 day maximum quarantine period is in effect, but individuals returning two negative tests in this time are granted early release. We consider delays until first test of days from initial time of quarantine and then delays from first to second test of days,

which results in the potential for early release after days of quarantine, accounting for a 1-day 3, , 0} { 4 . . . , 1 turnaround for test results. The maximum stringency setting, 14 days of quarantine, represents the time by which it is expected that 95% of ever-symptomatic cases will display symptoms and continue to self-isolate. As in the moderate stringency setting, release is at the end of the mandatory quarantine period if no test is considered, or after when the test is negative.

Further details on the testing scenarios, infection history generation, and test sensitivity are provided in Tables S1 and S2 in the Supplementary Appendix, adapted from Tables 2 and 3 in Clifford and Quilty et al. (3) .

For each secondary case we calculate the mass of the infectivity profile distribution from exposure to post-tracing isolation as a measure of transmission potential prior to quarantine. Similarly, the mass of the infectivity after release is a measure of transmission potential after quarantine. We assume that infectivity is zero 14 days after the incubation period, effectively truncating the infectivity distribution to the right, parameterised in terms of number of days from onset (7) . We also truncate on the left for each secondary case's exposure time on the left (here, ) and rescale the mass of the distribution to account for these − t = T 2 truncations. We therefore calculate the transmission potential prior to tracing, after release, and the amount of transmission potential which is averted by quarantine. We report the median and 95% uncertainty interval of these simulated values based on 1000 simulated index cases each with 1000 secondary cases generated.

Model code is available at https://github.com/cmmid/pcr_track_trace . CC-BY 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 August 24, 2020. .

The summary statistics of the fitted distributions of return of index cases' test results, and subsequent sourcing and tracing of contacts, are given in Table 1 and Figure S1 . A majority of all activities relevant to contact tracing are completed within 24 hours of their beginning. The average modelled contact tracing takes approximately 2.5 days from time of initial test to completion of tracing. Here we have assumed that the duration of each of these activities are independent. 

The longer the delay to the index case's seeking a test, the more potential for transmission from as yet untraced secondary cases there is. This is independent of the stringency scenarios as transmission occurs prior to tracing. If the delay from symptom onset of the index case to having a test is 2 days, 25% (95% UI: 0%, 95%) of the secondary cases' maximum transmission potential occurs prior to tracing. If this is reduced to a 1 day delay, the pre-quarantine transmission potential is 15% (0%, 91%); for an increase to 3 days' delay, the transmission potential increases to 38% (0%, 98%).

Longer quarantine periods decrease the proportion of the transmission potential spent in the community after release ( Figure 2 ). If the delay from symptom onset of the index case to having a test is 2 days, and no testing or quarantine is conducted, 75% (4%, 100%) of transmission potential occurs after tracing. For a 14 day quarantine with no testing, the transmission potential after release is reduced to less than 0.02% (0%, 17%). However at 8 days quarantine with a single test on day 7, the median transmission potential after release decreases to 1%, albeit with a long tail (upper 97.5% quantile: 82%).

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The copyright holder for this preprint this version posted August 24, 2020. . Figure 2 -Transmission potential after release (integral of infectivity curve over times after quarantined) in each quarantine and testing scenario. Row facets indicate delay from symptom onset to having a PCR test for the index case. Scenarios with no testing are denoted by orange bars; single tests with purple bars, and two tests with blue bars. Labels in the High stringency scenario indicate the different combinations of days of first and second test relative to entering quarantine. We assume that test results are delayed by 1 day and hence persons leave quarantine 1 day after their final test. Central bar = median; light bar = 95% uncertainty interval; dark bar = 50% uncertainty interval.

We find that the transmission potential averted, i.e, the proportion of transmission potential spent in quarantine and isolation instead of in the community, increases as the quarantine period increases. The transmission potential averted can be increased further if PCR testing is conducted on the final day of . CC-BY 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.

The copyright holder for this preprint this version posted August 24, 2020. . quarantine. We see that, assuming a delay to index case test of 2 days, the introduction in the low stringency setting of a test with a single day's turnaround (effectively a one day quarantine) is to avert 17% (0%, 100%) of infectivity (Figure 2 , low). However as the quarantine period increases, the relative contribution of a test is lessened. In the maximum stringency scenarios, with 14 days of mandatory quarantine, 75% of transmission potential is averted (95% UI: (4%, 100%)) both with and without a test (Figure 2 , max). PCR testing can be used to achieve a modest reduction in quarantine duration. For all index case test delays considered, the 14 day quarantine averted transmission potential can be achieved by testing on day 9 and releasing on day 10 if negative (2 day index test delay, 72% (3%, 100%), Figure 3 , mod.). The additional benefit of a second test -0, 1, 2, or 3 days into quarantine -is negligible for longer quarantine periods ( Figure  3 , high, Table 2 ). Varying the day of the first test in double testing scenarios also had little effect.

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The copyright holder for this preprint this version posted August 24, 2020. . Figure 3 : Transmission potential averted (integral of infectivity curve over times quarantined). Row facets indicate delay from symptom onset to having a PCR test for the index case. Scenarios with no testing are denoted by orange bars; single tests with purple bars, and two tests with blue bars. Labels in the High stringency scenario indicate the different combinations of days of first and second test relative to entering quarantine. We assume that test results are delayed by 1 day and hence persons leave quarantine 1 day after their final test. Central bar = median; light bar = 95% uncertainty interval; dark bar = 50% uncertainty interval.

While the inclusion of a test or the lengthening of quarantine can reduce the transmission potential, efforts to reduce the delay in the index case's seeking of a test (and subsequently isolating) can lead to a reduction in quarantine period while averting the same amount of transmission potential. If the current delay to index case testing is 3 days, the same averted transmission potential for a 14 day quarantine (62%, (2%, 99%)) is . CC-BY 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.

The copyright holder for this preprint this version posted August 24, 2020. . https://doi.org/10.1101/2020.08.21.20177808 doi: medRxiv preprint achieved at a 2 day delay with a quarantine lasting 6 days with a test on day 5 (62%, (4%, 100%) ). Similarly, if the current delay is 2 days, reducing the delay to 1 day could replace a 14 day quarantine (transmission potential averted 74% (5%, 100%)) with one lasting 8 days with a test on day 7 (76% (7%, 100%) ). In effect, decreasing index cases' delay to a test by 1 day and adopting PCR testing at the end of the quarantine period may reduce length of quarantine by 1 week.

Much of the uncertainty in transmission potential for a given index case testing delay and quarantine scenario is due to the variation in onset of symptoms in secondary cases relative to the time of exposure of the index case. The overall transmission potential is a combination of that of the symptomatic and asymptomatic cases. In the low stringency scenarios, we see that asymptomatic cases are unlikely to be detected by a test at day 0 and that the ability to reduce transmission potential in the ever-symptomatic cases is dependent on the index case's delay to testing and isolation ( Figure 4 , Table 3 ). For both the high (double testing) and maximum (14 day quarantine) scenarios, the averted transmission potential for the ever-symptomatic cases is approximately the same within each index case testing delay ( Figure 4 , Table 3 ) as conducting multiple tests during the quarantine period gives a greater chance of detecting the infection. For a delay of 1 day, 86% (8%, 100%) of the transmission is averted, decreasing to 76% (4%, 100%) and 63% (2%, 100%) for 2 and 3 days respectively. For the asymptomatic cases in the high testing scenario, earlier testing returns false negative tests and some asymptomatics are released too early and may go on to cause additional cases. In both the moderate and high scenarios, the averted transmission potential for symptomatic and asymptomatic cases converge the longer the quarantine lasts. Table 3 : Averted transmission potential stratified by number of days and testing in quarantine, delay to index cases' test and isolation, and type of infection (asymptomatic = never symptomatic, pre-symptomatic = ever symptomatic and released from quarantine prior to the detected onset of symptoms). . CC-BY 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.

The copyright holder for this preprint this version posted August 24, 2020. . CC-BY 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.

The copyright holder for this preprint this version posted August 24, 2020. . Figure 4 : Averted transmission potential stratified by type of infection (asymptomatic = never symptomatic, pre-symptomatic = ever symptomatic and released from quarantine prior to the detected onset of symptoms). Row facets indicate delay from symptom onset to having a PCR test for the index case. Scenarios with no testing are denoted by orange bars; single tests with purple bars, and two tests with blue bars. Labels in the High stringency scenario indicate the different combinations of days of first and second test relative to entering quarantine. We assume that test results are delayed by 1 day and hence persons leave quarantine 1 day after their final test. Central bar = median; light bar = 95% uncertainty interval; dark bar = 50% uncertainty interval.

The number of days secondary cases spend infectious prior to testing of the index case and tracing of contacts is dependent on the delays from the onset of symptoms of the index case to tracing of the secondary case, some of which can be reduced by more effective sensitisation of the public to COVID-19 symptoms, and more effective tracing systems.

We find that, provided the time from the index case's symptom onset to tracing of secondary contacts are moderately short ( 4.5 days on average, comprising 2 days for onset to a test and 2.5 days on average for all ≤ subsequent tracing), a quarantine period of at least 10 days may largely emulate the 14 day quarantine period in the reduction of traced infectious individuals entering the community. If this can be reduced to 3.5 days, the quarantine period could be shortened further to 9 days, as currently-infectious individuals are in quarantine or isolation for longer overall. In our analysis we assumed that delays in test result return, sourcing of contacts and contacting them to encourage quarantine are all independent. The delays may be positively correlated, however, with common structural causes, which could lead to a total delay distribution with a smaller median and larger variance. This would have the effect of getting more people into quarantine quicker, but those who are delayed in being quarantined are delayed longer. Longer delays to quarantining reduce the relative effectiveness of shorter quarantine periods in comparison to a 14 day quarantine period, as individuals spend less of their infectious period in quarantine after initial tracing and may exit prior to onset of symptoms. Longer delays also result in a predictable increase in the number of days individuals . CC-BY 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.

The copyright holder for this preprint this version posted August 24, 2020. . spend infectious prior to being traced. Notably, even a 14-day quarantine period does not eliminate the risk of individuals spending time infectious after release. However, this represents individuals who are late in their infectious period and largely asymptomatic, where their true transmission potential is likely minimal, according to the infectivity profile as detailed in Ashcroft et al. 2020 (7) .

Inclusion of a PCR test provides some benefit with shorter quarantine periods. This additional benefit diminishes with longer quarantine duration, as infectious persons have a higher probability of developing symptoms (if ever-symptomatic) and self-isolating. The high probability of a false-negative test result early on in a person's infection prevents their use from fully replacing long quarantine periods. Having two tests has a negligible effect on reducing the transmission potential above that of a single test, and the additional benefit is again lessened with longer quarantine periods.

We find considerable uncertainty in our estimates of secondary cases' transmission potential primarily due to variation in the simulated incubation period of index cases, which infectivity is dependent on, leading to a wide spread in the time of exposure of secondary cases. This is then compounded by the variation in infectivity of secondary cases, as well as variation in testing and tracing delays.

Due to a lack of currently available data, we have assumed that index cases effectively self-isolate (and hence cease generating secondary cases) once their symptoms develop to the point that they seek out and take a PCR test, with a central assumption of 2 days. However, if this period can be reduced through sensitisation of the public to COVID-19 symptoms and the importance of early action, shorter quarantine periods with testing at the end of the period becomes more viable. If digital contact tracing were introduced, it is estimated that great advances could be made in improving the effectiveness of contact tracing through a reduction in the delays associated with sourcing and quarantining contacts (2,3), a process which we estimate currently takes an average of 2.5 days.

In this analysis we consider only the performance of quarantine and testing strategies with respect to infection history timings and tracing delays, and as such we do not consider other aspects of the test and trace system which may result in poor outcomes, such as the fraction of index cases that do not engage with the service (12) , variation in the number of cases generated by each index case (13) , the proportion of secondary cases missed by tracers (14) , or the non-adherence or evasion of quarantine by secondary cases. A survey by Smith et al. found, in UK households with a person exhibiting COVID-19 symptoms, 75.1% of households had a member leave the premises within the past 24 hours, indicating a worrying lack of compliance with quarantine rules (15) . It is likely that longer quarantine periods result in a decrease in both the proportion of individuals adhering to quarantine requirements and the degree to which they comply, and throughout this work we have assumed perfect compliance that does not wane. It may be possible to derive a waning function through a meta-analysis of previous studies of quarantine compliance, yet these are likely to show large heterogeneity due to the factors identified by Webster et al. (16) . If shorter quarantine periods with PCR testing can maintain the averted transmission potential from the current 14 day quarantine policy and do indeed increase the degree of compliance, as well as reduce evasion, then the risk of transmission from secondary cases will be lower than under the current quarantine policy. As such, while we have shown that PCR testing combined with 10 days of quarantine can reduce the transmission potential from secondary cases to similar levels produced by a 14 day quarantine, addressing other structural issues in contact tracing such as testing delays and non-adherence would provide a synergistic effect, further reducing risk.

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The copyright holder for this preprint this version posted August 24, 2020. . https://doi.org/10.1101/2020.08.21.20177808 doi: medRxiv preprint

Table S1 -Strategies for risk mitigation. Where one of the described lines contains "or", we consider all combinations contained within.

Description of screening policy given but no distribution described, the parameter is derived from other distributions in the table and has no closed-form.^Parameters are location and scale for log-Normal distribution, not summary statistics of observed incubation period.

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The copyright holder for this preprint this version posted August 24, 2020. Scaling factor derived from (22) Figure S1 : Observed delays (green bars) and modelled probability distributions (dark green curves) for the delays in the test and trace system. The total time delay is a kernel-smoothed empirical density based on the sum of 10,000 independent samples from the

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CMMID nCoV working group. Effectiveness of airport screening at detecting travellers infected with novel coronavirus (2019-nCoV)

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COVID-19 infectivity profile correction. ArXiv200706602 Q-Bio Stat

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fitdistrplus: An R Package for Fitting Distributions

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Role of testing in COVID-19 control

Asymptomatic SARS-CoV-2 infections: a living systematic review and meta-analysis

The Natural History and Transmission Potential of Asymptomatic Severe Acute Respiratory Syndrome Coronavirus 2 Infection

This research was partly funded by the National Institute for Health Research (NIHR) (Billy Quilty is funded by 16