Optimal COVID-19 quarantine and testing strategies

Abstract

As economic woes of the COVID-19 pandemic deepen, strategies are being formulated to avoid the need for prolonged stay-at-home orders, while implementing risk-based quarantine, testing, contact tracing and surveillance protocols. Given limited resources and the significant economic, public health and operational challenges of the current 14-day quarantine recommendation, it is vital to understand if more efficient but equally effective quarantine and testing strategies can be deployed. To this end, we developed a mathematical model to quantify the probability of post-quarantine transmission that varied across a range of possible quarantine durations, timings of molecular testing, and entry uniformly across infection time course or entry as a traced contact. Assuming cases entering quarantine uniformly across infection time course and a one-day delay for testing and, we found that a 13-day quarantine with testing on entry, a seven-day quarantine with testing on exit, and a seven-day quarantine with testing on both entry and exit each provide equivalent or lower probability of post-quarantine transmission compared to a 14-day quarantine with no testing. We found that testing on exit from quarantine is more effective in reducing probability of post-quarantine transmission than testing upon entry. When conducting a single test, testing on exit was most effective for quarantines lasting up to six days. For longer quarantines, the optimal test day was day five or day six. These results differed by no more than one day for cases entering quarantine as traced contacts. Optimal timing of testing during quarantine will reduce the probability of post-quarantine transmission, as false-positive results become less likely, enabling case isolation. Based on 4,040 SARS CoV-2 RT-PCR tests, an exit test 96 hours after the start of quarantine for an offshore oil rig population was demonstrated to identify all known asymptomatic cases that previously tested negative at entry, and—moreover—successfully prevented an expected nine offshore transmission events, each a serious concern for initiating rapid spread and a disabling outbreak in the close quarters of an offshore rig. This successful outcome highlights the importance of context-specific guidelines for the duration of quarantine and timing of testing that can minimize economic impacts, disruptions to operational integrity, and COVID-related public health risks.

Introduction

The COVID-19 pandemic has engendered unprecedented efforts to quell ongoing outbreaks and manage healthcare capacity, including strict travel restrictions and stay-at-home orders. However, these efforts have disrupted workplaces, leading to significant and pervasive socioeconomic costs^1,2. Economic pressures have led many governments and corporations to proceed with plans to reopen their economy and workforce³. Safely reopening in the absence of a vaccine relies on reducing the likelihood of an infectious individual entering a workplace or school⁴. Current strategies include the use of a 14-day quarantine and often with some combination of entry and/or exit testing, coupled with contact tracing should a case arise. These strategies aim to reduce the effective reproduction number R—the average number of secondary infections caused by a primary case—below one.

Quarantining individuals imposes myriad challenges for government workers, military, businesses, universities, and other entities. In many settings, the recommended 14-day quarantine poses a significant strain on the mental and physical health of employees and their families^5,6, coupled with the associated economic toll and potential impacts on operational integrity. For example, during the time of the epidemic with quarantine measures in place, offshore oil and gas employees may be needed to work extended cycles significantly beyond their traditional 14-day on-and-off cycle. This built-in quarantine time into the overall work schedule results in prolonged time periods that crew members are away from their home. Given the impact of long quarantines on mental and physical health^5,6, a priority of our research was to identify a minimal, effective quarantine strategy for close-quarter environments where there is potentially a high risk for the rapid spread of COVID-19 with associated severe outcomes and even mortality.

Previous work has focused on the impact of quarantine and testing on population-level COVID-19 incidence and deaths^7–9, and testing measures that are most appropriate for disease surveillance within a population by examining various testing frequencies¹⁰. Currently, there is no consensus regarding the optimal duration of quarantine or timing of testing that minimizes the risk of outbreaks in workplaces, university campuses, military facilities¹¹. Many institutions are relying on testing at entry into quarantine, and other measures such as symptom screenings, hand sanitizers, and face masks to reduce the risk of an outbreak. Given that over 50% of COVID-19 transmission is attributed to pre-symptomatic and asymptomatic cases¹², screening for symptoms alone is inadequate to prevent or interrupt a COVID-19 outbreak¹². In addition, testing early post-infection could produce a false-negative result¹³. Thus, symptom-based screening and one-time testing could still entail a significant probability of post-quarantine transmission (PQT). Consequently, some jurisdictions have suggested and implemented testing upon exit from a 14-day quarantine¹⁴. Understanding the complementarity of quarantine and testing in reducing PQT would provide vital insight into effective strategies to ensure the safety of civilian and military workers, students returning to classrooms, and international travelers, thereby mitigating disease spread in the wider community.

Here, we evaluate whether an alternative epidemiologically sound, quarantine and testing strategy exists that would be equivalent to the standard 14-day quarantine protocol in reducing PQT. To do so, we developed a mathematical model to calculate the benefits of diverse quarantine and molecular testing strategies in reducing the probability of PQT, accounting for the infectivity profile of an infected individual and the temporal diagnostic sensitivity of RT-PCR testing. We estimated the probability of PQT for an infected individual that has not manifested symptoms but has completed quarantine with undetected infection. In our analysis, we considered different combinations of timing and frequency of testing with quarantine of up to 14 days, with and without contact tracing. In addition, we performed a sensitivity analysis on our results based on the impact of differences in the latent period. We compared the probability of PQT under three scenarios of testing: (i) on entry to quarantine only, (ii) on exit from quarantine only, and (iii) on both entry to and exit from quarantine for an infected individual. Lastly, we analyze the results of the application of guidance from our model regarding the operational processes of quarantine and testing within the oil and gas industry that prevented offshore transmission (Supplementary Information: Narrative).

Results

Using the infectivity profile derived from transmission pairs of COVID-19 infected individuals¹⁵, temporal diagnostic sensitivity of RT-PCR tests¹⁶, and an incubation period of 8.29 days¹⁷, we calculated the probability of PQT for a basic reproduction number of R₀ = 2.5, assuming that secondary infections are distributed through a negative binomial distribution with a dispersion parameter of 0.25¹⁸ (Table S1). From the infectivity profile, assuming that 30.8% of infections are asymptomatic across the disease time course [12], we estimated that the reproduction number reduces to 1.6 under perfect isolation of cases upon symptom onset, with 1.2 secondary cases occurring during the incubation period (Fig. S1A). The expected number of secondary infections still remains above one with a lower asymptomatic proportion of 22.6% or with a reduced R₀ of 2 (Fig. S1B–D). Therefore, perfect isolation of all symptomatic individuals would not be sufficient to interrupt the chain of disease transmission.

Impact of quarantine without testing

To evaluate the effectiveness of quarantine alone, we computed the expected PQT (Fig. S2A) and the probability of PQT after a range of quarantine durations (Fig. 1, Fig. S3). Assuming individuals self-isolate immediately upon symptom onset, we calculated that the probability of PQT declines as the duration of quarantine increases (Fig. 1). This probability is less than 0.25 with a quarantine duration of at least three days, and falls below 0.05 for quarantines of eight days or longer.

Figure 1 :

The probability of post-quarantine transmission for no testing and three testing strategies and durations of quarantine from 1–14 days, with an incubation period of 8.29 days, 30.8% asymptomatic infections and perfect self-isolation of symptomatic infections. Curves for the probability of post-quarantine transmission show the probability of one or more post-quarantine infections when an infected individual enters quarantine uniformly within the incubation or asymptomatic period without testing (red), and with testing upon entry to quarantine (orange), on exit from quarantine (blue), and on both entry to and exit from quarantine (purple). With a delay in sample collection to results, we assumed that testing on exit occurred the day before the end of quarantine.

Testing during quarantine

The effectiveness of quarantine in reducing the probability of PQT can be augmented through testing. We assumed a 24-hour delay between the sample collection and test results, indicating testing on exit occurs a day before the end of quarantine. Under each scenario of testing, individuals who are tested positive or developed symptoms are isolated. We found that any testing during quarantine contributed to a reduction in the probability of PQT across a full range of quarantine durations (Fig. 1 and Fig. S3). However, the magnitude of this reduction was dependent on the duration of quarantine and timing of the test. The largest reduction in the probability of PQT from conducting a single test occurs when it is performed on the last day of quarantine for durations less than seven days; on the day six for a seven-day quarantine; on day five for quarantines lasting between eight and 13 days; and on day six for quarantines that are 14 days or longer (Fig. S4A).

Comparing the three testing strategies, we found that testing on both entry and exit from quarantine provides the greatest return in decreasing the probability of PQT, whereas the benefit of testing in reducing this probability is lowest when conducted only at entry into quarantine (Fig. 1, Fig. S3). Testing on exit consistently outperformed testing on entry across all quarantine durations considered (Fig. 1). For example, a quarantine duration as short as three days with a test on both entry and exit yields a 64.5% reduction in probability of PQT relative to no testing, compared to a 22.8% decrease when the individual is tested on entry only and a 61.4% decline for testing on exit only (Fig. S3).

We compared strategies of quarantine and testing with the widely implemented, World Health Organization-recommended 14-day quarantine without testing¹⁹. We found that a 13-day quarantine with testing on entry, a seven-day quarantine with testing on exit, and a seven-day quarantine with testing on both entry and exit each provide equivalent or lower probability of PQT compared to a 14-day quarantine with no testing (Fig. 1, Fig. S2–S3).

Assessment of quarantine and testing strategies implemented for offshore facilities

We performed an assessment of the practical implications of our analyses based on quarantine and testing protocols in the setting of offshore oil-and-gas platforms (Supplementary Information: Narrative). We stratified the tests into regions A and B based on the location of the lab where the test results were obtained. Among the 4040 RT PCR tests conducted prior to travel offshore, there were 69 positive results (1.7%). Initially, a three-day quarantine with testing only upon entry was implemented. Of the 1792 RT-PCR tests conducted with this strategy, there were 22 positive results (1.2%). Region A deployed a seven-day home quarantine, where testing was performed on both entry and exit (96 h after the first test) starting from August 13, with 50.0% (1/2) of the positive tests occurring on exit (Fig. 2A). Region B expanded to a five-day hotel quarantine with testing on both entry and 96 h after the first test, starting on June 25, 2020. For the period in which the entry and exit testing strategy was implemented in region B, 33.3% (15/45) of the positive tests were obtained upon the exit test, following a negative entry test (Fig. 2B). Further validation of the entry and exit testing protocol was provided through an additional 155 RT-PCR tests performed post-quarantine (11 days after the initial test), all of which were negative.

Figure 2 :

Weekly SARS-CoV-2 testing between April 11 to August 26, 2020 among two regions where crew members were quarantined. The positivity rate of test conducted between April 11 and August 26 for (A) region A (with a seven-day quarantine) where testing on entry and exit was started on August 13 and (B) region B (with a five-day quarantine) where testing on entry and exit was started on June 25. Initially, a three-day quarantine with testing only on entry was conducted in both regions. The vertical dashed line separates the strategy of testing on only entry (left), the strategy of testing on both entry and exit (right), with follow-up post-quarantine tests conducted 11 days after the initial test (i.e., on day 12). Negative and positive sequential symbols − and + indicate the test histories. In these results, negative symbols are always conveying results to tests that were previous to the results quantified by the bar above. The number of positive tests and the number of tests conducted is denoted above the bar in parentheses.

No offshore worker registering negative tests-on-entry-and-exit from quarantine was later diagnosed with COVID-19 during their offshore work. We quantified the probability of PQT for the cases detected by an exit test, as well as the extent to which adding testing on exit to testing on entry reduced this probability, assuming an incubation period of 8.29 days. Individuals who eventually developed symptoms entered quarantine uniformly during their incubation period (prior to symptom onset), whereas asymptomatic individuals entered quarantine over the course of their infection. Compared with a three-day quarantine and testing only on entry, extending the quarantine duration and adding testing on exit (96 h after the first test) reduced the probability of PQT by 98% for the seven-day quarantine and 93% for a five-day quarantine. If the single case identified on the exit test from region A remained undetected within the seven-day quarantine, we estimate an off-shore probability of PQT of 0.13. If the 15 cases that had been ascertained on exit from region B had remained undetected after the five-day quarantine without testing on exit, we estimate that the probability of PQT would have been 0.99, and would have resulted in an expected 9 offshore transmission events—each one a serious concern for initiating rapid spread and a disabling outbreak in the close quarters of an offshore rig. We found that the estimated probability of PQT using the strategy of testing upon entry and exit moderately increased with the proportion of infections being asymptomatic (Fig. S5).

Accounting for prevalence of disease in the community.

We evaluated the impact of disease prevalence in the community on the probability of PQT (Fig. S6). For a cohort of size 40 and a five-day quarantine with prevalence of 1%, we estimated the probability of PQT to be 0.06 for testing only on entry, and 0.005 for testing on both entry and exit (Fig. S6B). For a seven-day quarantine and the same prevalence, the probability of PQT drops from 0.02 for testing only on entry to 0.001 when augmented with testing on exit (Fig. S6C).

Contrasting contact tracing and uniform entry into quarantine

We evaluated the effectiveness of quarantine through contact tracing in reducing the probability of PQT with no delay (Fig. 3, Fig. S7–S8) and with one-day delay in the identification of exposed contacts (Fig. S9–S10). Consistent with practices at remote mining sites, tracing of contacts was assumed to be initiated by the presentation of a worker to the onsite health unit with relevant COVID-19 symptoms. For offshore oil platforms, contact tracing is initiated if there is identification of a positive case either by symptom presentation or by surveillance screening through testing. Rapid contact tracing leads to contacts being quarantined early in the disease time course (if infected), influencing the decline in the probability of PQT as the duration of quarantine increases compared to uniform entry into quarantine over the duration of the incubation period or disease course (Fig. 3 vs Fig. 1).

Figure 3:

The probability of post-quarantine transmission for no testing and three testing strategies and durations of quarantine of 1–14 days, with an incubation period of 8.29 days, 30.8% asymptomatic infections and perfect self-isolation of symptomatic infections. Curves for the probability of post-quarantine transmission show the probability of one or more post-quarantine infections when an infected individual enters quarantine through contact tracing within the incubation period without testing (red), and with testing upon entry to quarantine (orange), on exit from quarantine (blue), and on both entry to and exit from quarantine (purple). With a delay in sample collection to results, we assumed that testing on exit occurred the day before the end of quarantine

Under contact tracing with no testing, the probability of PQT decreases gradually from 0.35 for a quarantine lasting one day to 0.32 for a quarantine of three days, then reduces more rapidly to 0.13 for an eight-day quarantine, and again decreases gradually for longer durations of quarantine (Fig. 3). In contrast, entry into quarantine uniformly over the course of the incubation period or disease period leads to a continuous decline in the probability of PQT from 0.30 for a one-day quarantine to 0.04 for an eight-day quarantine, with the rate of decrease slowing for quarantine durations longer than eight days (Fig. 1).

When testing on entry, the reduction in the probability of PQT as a result of increased duration of quarantine is smaller with contact tracing than with uniform entry into quarantine. For example, the reductions in the probability of PQT from a one-day quarantine to a three-day quarantine with testing on entry are 3.8% and 7.6% for entry into quarantine based on contact tracing and uniformly, respectively.

We found that a seven-day quarantine with testing on exit, and a six-day quarantine with testing on entry and exit result in an equivalent or lower probability of PQT compared to a 14-day quarantine with no testing; testing on entry having only trivial overall benefit (Fig. 3A, Fig. S7–S8). We found that the optimal timing of a single test within quarantine of traced contacts was to test upon the last day of quarantine for durations as long as six days, with testing on day six for quarantines extending beyond six days (Fig. S4B).

Sensitivity analyses

We performed a comparative analysis specifying a latent period that is one day greater or lesser than the reported 2.9 days²⁰. The expected transmission occurring before symptom onset was similar among the different latent periods (1.21 infection for a latent period 2.9 days; 1.24 infections for a latent period of 1.9 days; and 1.27 infections for a latent period of 3.9 days). The infectivity profiles differed among the three latent periods, with a peak infectivity that is higher for both the 1.9-day and 3.9-day latent periods when compared to our baseline (Fig. S11).

When individuals entered quarantine uniformly across the time course of infection (Fig. S12–S15), the probability of PQT was lower for shorter latent periods. For traced contacts entering quarantines of eight days or longer as (Fig. S16–S19), shorter latent periods entailed lower probability of PQT. For traced contacts entering quarantines of fewer than eight days, the relationship of latent period to probability of PQT is more complex. However, one-day changes in the latent period affect the optimal day to conduct a single test by at most one day (Fig. S4). Specifically, we found that a 3.9-day latent period decreased the optimal day of testing estimated for a 2.9-day latent period, whereas a 1.9-day latent period increased the best day to conduct a single test.

Discussion

Here, we developed a modelling framework to calculate the probability of post-quarantine transmission of COVID-19 for a wide range of durations of quarantine, supplemented by testing on entry to quarantine, on exit from quarantine, or both. Evidence suggests that isolation of cases upon symptom onset is insufficient to contain an outbreak of COVID-19¹². However, the likelihood of transmission can be reduced substantially through quarantine and testing⁴. We found that testing on both entry to and exit from quarantine was the most effective strategy in reducing the probability of PQT. Furthermore, the optimal timing of a single test was upon exit for quarantines with durations as short as six days. For a quarantine duration longer than six days, the optimal testing time is on day five or six.

An outbreak can be triggered or sustained within an environment that is monitored only for symptoms of COVID-19. Quarantining individuals before returning to work or school has been a common strategy among many businesses, the military and universities to prevent potential outbreaks. An offshore or military setting is one of numerous close-quarters environments in modern society where an outbreak can seriously impact operational integrity, leading to compromised safety and adverse economic consequences. Hence, minimizing outbreak risk while maintaining staffing is critical. Testing may allow for the quarantine duration to be reduced without increasing the risk of PQT. For example, many universities have implemented plans for quarantining and frequent testing of students and employees, where resources allow^{24, 25}. For businesses and close-quarters environments, the impact of false negatives are a substantially greater issue for operational integrity than false positives. Our results show that testing upon entry to quarantine carries such a risk of false negatives, as infected individuals who enter quarantine very early in the incubation period of disease may not be detected due to low viral loads.

There are benefits to conducting additional tests as prevalence in the general community increases (Fig. S6, blue and purple), because as substantial numbers of infected individuals enter quarantine, larger numbers of individuals may proceed through testing with rare false-negative test results, increasing PQT. Additional tests would further decrease the likelihood of the occurrence of a series of false-negatives and their impact can be quantified with our model framework. We have not quantified more extensive testing strategies here due to the limited availability of testing and the moderate decline in return of additional testing from lower detection rates during the early stages of disease post-infection (Fig. S28) and likely correlations in false-negative test results over time.

Optimal timing of limited testing during quarantine improves the ability to control PQT. Testing several days into quarantine increases the likelihood of an infected case testing positive (Fig. S4). The increasing diagnostic sensitivity of the RT-PCR test is attributable to the rapidly increasing viral load following the less detectable latent stage of infection. If the infected individual remains asymptomatic, testing near the end of a standard 14-day quarantine can also lead to low diagnostic sensitivity due to a declining viral load as they overcome the infection²⁶. Specifying an average incubation period of 8.29 days, our analysis indicates that the lowest probability of PQT is achieved by testing on day six of the standard 14-day quarantine (Fig. S4A, Fig S4B).

Testing was found to result in a smaller reduction of the expected PQT when entering quarantine through contact tracing compared to not. Contact tracing will be more effective in identifying infected individuals than when selecting individuals at random for quarantine, due to the differences in exposure risk, increasing the importance of reducing PQT via testing. For example, if prevalence is 1% and 10 individuals are selected at random for quarantine, then on average 0.1 people would be infected. Alternatively, if an index case is isolated upon symptom onset, there would be on average 1.21 individuals infected (for an R₀ = 2.5) prior to symptom onset and potentially identified through contact tracing. However, individuals entering quarantine because they are identified by contact tracing are likely to do so earlier post-infection (Fig. S31). Therefore, an earlier entry requires a longer quarantine (generally), and makes it more likely that testing occurs during the incubation period, when diagnostic sensitivity of the RT-PCR test is highly limited.

Our results are based on the temporal diagnostic sensitivity of RT-PCR tests, which are currently considered the gold standard test. However, this testing approach is moderately invasive, may be inconsistent during serial testing, and is dependent on the availability of some raw materials that have been scarce^27–30. The use of saliva tests as an alternative could allow for frequent testing of individuals at a decreased cost, while being less invasive and self-administered^31,32. There is also evidence that saliva tests are more sensitive than RT-PCR tests from nasal swabs in COVID-19 patients²⁷but less sensitive for detection in a community setting³³. Thus, the recent innovations to improve access to testing, such as widespread use of saliva tests, could shift optimal decision-making for prevention of COVID-19 transmission via quarantine and testing.

Our study is informative for businesses, military operations and universities, providing quantitative estimation of the residual risk of PQT. The calculated infection risks were used to inform the quarantine and RT-PCR testing strategy deployed by an oil and gas company prior to workers travelling offshore. Of the positive tests obtained under this strategy, 34% were on the exit test, which prevented 16 infected crew members that otherwise would have exited quarantine and entered confined quarters offshore while infectious. The results of the time of testing for a given quarantine duration could be also useful for population-level disease control when quarantine is required for international or even interstate travel.

In summary, prolonged quarantine to reduce PQT leads to increased economic costs and negatively affects mental health and other social aspects of life. However, shortening the duration of quarantine too much can increase the risk of post-quarantine transmission due to false negatives. Furthermore, relying only on symptom onset during quarantine to identify infected cases may not be an effective strategy to prevent post-quarantine transmission, as a sizable proportion of individuals experience asymptomatic infection^22,23. Combining timely testing with a shorter quarantine mitigates both the costs of long quarantine and post-quarantine transmission by asymptomatic casesIt is critical to consider the interplay between diagnostic sensitivity, timing of testing, and quarantine duration when augmenting quarantine with testing.

Our examination of the effects of durations of quarantine and timings of testing is critical to future efforts to balance the risk of PQT with the undue costs associated with prolonged quarantines. As efforts continue for returning to a level of normality, any control strategy will need to account for public safety, commercial and military operational integrity, school reopening and family emotional well-being. Our study indicates that the approach of testing upon entry into quarantine—currently implemented by most administrative bodies—is the least effective strategy. Testing can provide substantially higher dividends in reducing PQT if performed later during quarantine—at exit, or in longer quarantines, at an optimal timing. Defining and comprehending the risk of PQT within each context is essential to effective and transparent balancing of lives and livelihoods in times of a global pandemic.

Conclusion

Our analysis shows a reduced probability of post-quarantine transmission when testing on exit compared to testing on entry. By augmenting quarantine with molecular testing, the quarantine duration can be substantially shortened from the recommended 14-day period, while attaining a similar level of risk. The results from this analysis are supported by data of quarantined crew members of an offshore oil facility.

Methods

Data of SARS CoV-2 tests during quarantine

Between April 11, 2020 and August 26, 2020, there were 4,040 SARS CoV-2 RT-PCR tests conducted among employees of an oil and gas company coming from two regions (stratified by lab location). A third region that was monitored is not included in our data set, as there was low population prevalence entering quarantine and there were no positive tests. During the early stages of the epidemic, both regions used a three-day quarantine with testing on entry. On August 13, employees from region A quarantined at home for seven days, with testing occurring on both entry and exit. While employees were at home, they were asked to practice social distancing in public. Starting on June 25, employees from region B were quarantined in a hotel for five days prior to their departure off-shore and tested on both entry and exit. The requirements of an employee to go off-shore were (1) passing the components of a screening form used to filter out symptomatic cases and those potentially exposed, (2) temperature screenings, and (3) completion of the quarantine with no positive RT-PCR test. Upon a positive test, the employee initiated a 14-day isolation period and followed through the company’s case management process. After the isolation period, individuals were able to return back to work contingent upon two negative RT-PCR tests.

Epidemiological parameters

The average incubation period is 8.29 days¹⁷. The latent period (i.e. infected but low probability of infecting contacts) is 2.9 days²⁰. We consider latent periods of 1.9 days and 3.9 days in a scenario analysis²⁰ (Fig. S11–S19).

For our baseline analysis, we considered a delay of one day between sample collection and result of RT-PCT test. Thus, the sample is taken one day before the end of quarantine when testing on exit. We also conducted the analysis when there was no delay in testing results to examine the impact on the probability of PQT (Fig. S20–S23).

In the baseline analysis, we assumed R₀ = 2.5 and 30.8% of infections are asymptomatic^12,22. We further analyzed the scenario in which 22.6% of infections are asymptomatic (Fig S24–S27)²³. Asymptomatic infections were assumed to be equally as infectious as symptomatic infections. This assumption is based on measurements of viral loads in asymptomatic infections being comparable to those observed in symptomatic cases^34,35.

Infectivity profile

We determined the infectivity profile following the specified latent period using the R code provided by He et al¹⁵. The infectivity during the latent period was expressed as exponentially lower (Supplementary Information: Methods, Infectivity function). Imposing the strict threshold where 20 days after symptom onset infectivity is zero^36,37 made no significant difference to our results.

Temporal diagnostic sensitivity of a SARS CoV-2 RT-PCR assay

We utilized the post-symptom onset temporal diagnostic sensitivity for RT-PCR tests of infected individuals¹⁶, fitting a logistic regression function to the diagnostic sensitivity data from zero to 25 days post-symptom onset through minimization of least squares. To infer the diagnostic sensitivity prior to symptom onset, we first used this function to perform a slight extrapolation of the diagnostic sensitivity back to the peak, which occurred slightly prior to symptom onset. Second, to determine the diagnostic sensitivity for the remaining portion of the incubation period, we specified the interpolation function determined by the infectivity and the diagnostic sensitivity from post-symptom onset, and used that interpolation function on the pre-symptom onset infectivity to determine pre-symptom onset diagnostic sensitivity (Supplementary Information: Methods, Diagnostic sensitivity function). This process provides the diagnostic sensitivity over the entire course of infection (Fig. S28)¹⁰. We assumed that the specificity of the RT-PCR assay was 100%³⁹

Probability of post-quarantine transmission

To calculate the probability of PQT—defined to be the probability of at least one post-quarantine infection—we assumed that the expected post-quarantine transmission is described by a negative binomial distribution with a dispersion parameter of 0.25¹⁸. This value for the dispersion parameter is consistent with numerous published estimates^40–42. For sensitivity analyses, we also computed the probability of PQT given Poisson-distributed post-quarantine transmission (Fig. S29–S30). In our additional analysis accounting for the underlying prevalence within the community, the probability of PQT was defined as the likelihood that at least one infected individual in a cohort became a source of PQT. Similarly, to calculate the probability of PQT given a negative test on entry for N infected individuals, we estimated the probability that at least one of the cases contributed to PQT.

Data availability

The number of positive tests and tests conducted at the two regions quarantining the crew members heading offshore are presented in Fig. 2, with other data used in the analysis referenced in Table S1 and in the Methods.

Code availability

The computational code for the analysis was implemented in MATLAB, and it is available at github.com/WellsRC/Optimizing-COVID19-Quarantine-and-Testing-Strategies.