Optimal COVID-19 quarantine and testing strategies

Coronavirus; quarantine; viral shedding; disease control; testing; contact tracing 28 29 *contributed equally to this research 30 31 †corresponding author: [email protected] 32 . CC-BY-NC-ND 4.0 International licenseIt 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under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.(which was not certified by peer review)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. 2

33 As economic woes of the COVID-19 pandemic deepen, strategies are being formulated to avoid 34 the need for prolonged stay-at-home orders, while implementing risk-based quarantine, testing, 35 contact tracing and surveillance protocols. Given limited resources and the significant economic, 36 public health, and operational challenges of the current 14-day quarantine recommendation, it is 37 vital to understand if shorter but equally effective quarantine and testing strategies can be 38 deployed. To quantify the probability of post-quarantine transmission upon isolation of a positive 39 test, we developed a mathematical model in which we varied quarantine duration and the timing 40 of molecular tests for three scenarios of entry into quarantine. Specifically, we consider travel 41 quarantine, quarantine of traced contacts with an unknown time if infection, and quarantine of 42 cases with a known time of exposure. With a one-day delay between test and result, we found 43 that testing on exit (or entry and exit) can reduce the duration of a 14-day quarantine by 50%, 44 while testing on entry shortened quarantine by at most one day. Testing on exit more effectively 45 reduces post-quarantine transmission than testing upon entry. Furthermore, we identified the 46 optimal testing date within quarantines of varying duration, finding that testing on exit was most 47 effective for quarantines lasting up to seven days. As a real-world validation of these principles, 48 we analyzed the results of 4,040 SARS CoV-2 RT-PCR tests administered to offshore oil rig 49 employees. Among the 47 positives obtained with a testing on entry and exit strategy, 16 cases 50 that previously tested negative at entry were identified, with no further cases detected among 51 employees following quarantine exit. Moreover, this strategy successfully prevented an expected 52 nine offshore transmission events stemming from cases who had tested negative on the entry test, 53 each one a serious concern for initiating rapid spread and a disabling outbreak in the close 54 quarters of an offshore rig. This successful outcome highlights that appropriately timed testing 55 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 3 can make shorter quarantines more effective, thereby minimizing economic impacts, disruptions 56 to operational integrity, and COVID-related public health risks. 57 58 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 4

59 The COVID-19 pandemic has engendered unprecedented efforts to quell ongoing outbreaks and 60 manage healthcare capacity, including strict travel restrictions and stay-at-home orders. These 61 efforts have disrupted workplaces, leading to significant and pervasive socioeconomic costs 1,2. 62 In turn, these economic pressures have led many governments and corporations to lift 63 restrictions3. Safely reopening in the absence of a vaccine relies on reducing the likelihood of an 64 infectious individual entering a workplace, school, or other social gathering 4. Current strategies 65 to ensure safety often include a 14-day quarantine—either as a consequence of travel or 66 following exposure to an infected person, as recommended by the World Health Organization 67 (WHO).5 These quarantines are sometimes combined with entry and/or exit testing, in which a 68 positive test prompts isolation until recovery. 69 70 Quarantine imposes myriad challenges for institutions of government, militaries, businesses, 71 universities, and other entities. At the individual level, the recommended 14-day quarantine 72 causes strain on mental health. 6,7 This burden is coupled with the associated economic toll and 73 potential impacts on operational integrity. For example, the typical 14-day on-and-off cycle for 74 offshore oil and gas employees is substantially disrupted when quarantine measures are required. 75 These quarantines result in prolonged time periods that crew members are away from their home. 76 Given the impact of long quarantines on mental health 6,7, we evaluated the potential that a 77 shorter quarantine combined with testing optimization could achieve reduced transmission of 78 COVID-19 within close-quarter environments where there is potentially a high risk for rapid 79 spread. 80 81 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 5 Evidence suggests that isolation of cases upon symptom onset is insufficient to contain an 82 outbreak of COVID-19 8. The likelihood of transmission can be reduced substantially through 83 quarantine and testing 4. Previous work has focused on the impact of quarantine and testing on 84 population-level COVID-19 incidence and deaths 9–11, shortened quarantines upon negative RT-85 PCR test at entry from contact tracing or seven days after exposure 12 and testing measures that 86 are most appropriate for disease surveillance within a high-risk population (e.g. healthcare 87 workers) by examining various testing frequencies and their reduction of secondary infections13. 88 Currently, there is no consensus regarding the optimal duration of quarantine or timing of testing 89 that minimizes the probability of post-quarantine transmission (PQT), defined as one or more 90 infections observed after the quarantine period. Many institutions are relying on testing at entry 91 into quarantine combined with other measures such as symptom screenings, hand sanitizers, and 92 face masks to reduce the risk of an outbreak. However, the majority of COVID-19 transmission 93 is attributable to pre-symptomatic and asymptomatic cases screening for symptoms alone is 94 inadequate to prevent or interrupt a COVID-19 outbreak 8. In addition, testing too early post-95 infection is likely to produce a false-negative result 14. Thus, symptom-based screening and one-96 time testing could still entail a significant probability of PQT. 97 98 Some jurisdictions have suggested and implemented testing upon exit from a 14-day 99 quarantine15. For example, Australia has implemented a compulsory 14-day quarantine, with 100 testing within 48 hours after arrival and between day 10 and 12 of quarantine, to reduce 101 transmission from imported cases 16. Although these multiple tests aid in case identification, this 102 strategy does not include any reduction of the burden of long quarantine. Understanding the 103 complementarity of quarantine and testing in reducing PQT would provide vital insight into 104 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 6 effective strategies that mitigate disease spread in travel-based and contact-tracing based 105 contexts. 106 107 We applied a mathematical modeling approach to evaluate whether a less burdensome quarantine 108 and testing strategy exists that would be epidemiologically equivalent to the standard 14-day 109 quarantine protocol in reducing PQT. This model accounts for the infectivity profile of an 110 infected individual as well as the temporal diagnostic sensitivity of RT-PCR testing. Across a 111 variety of quarantine and testing scenarios, we estimated the probability of PQT for an infected 112 individual who has not manifested symptoms by the end of the quarantine period. We considered 113 three applications: (i) quarantine for travel, initiated at random times across the infectious course, 114 (ii) quarantine prompted by contact-tracing and therefore initiated early in the infectious course, 115 and (iii) quarantine when the time of exposure is known. We compared the probability of PQT 116 under three testing scenarios: (i) on entry to quarantine only, (ii) on exit from quarantine only, 117 and (iii) on both entry to and exit from quarantine for an infected individual. Across these 118 scenarios, we varied the duration of quarantine and identified the optimal testing date based on 119 that duration. As validation of our recommendations, we analyzed the real-world application of 120 our model-based findings to protocols within the oil and gas industry that prevented offshore 121 transmission. 122 123

124 We derived an infectivity profile based on transmission pairs of COVID-19 infected 125 individuals 17, a basic reproduction number of R0 = 2.5, and an incubation period of 8.29 days 18, 126 and estimated the temporal diagnostic sensitivity of RT-PCR tests 19 (Table S1). Specifying 127 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 7 30.8% of infections as remaining asymptomatic across the disease course 20,21, we estimated that 128 perfect isolation of cases upon symptom onset would reduce the reproduction number to 1.6, 129 with 1.2 secondary cases occurring during the incubation period (Fig. S1A). The reproductive 130 number remained above one even when we lowered the asymptomatic proportion to 22.6% or 131 reduced R0 to 2 (Fig. S1B–D). Therefore, perfect isolation of all symptomatic individuals would 132 not be sufficient to interrupt the chain of disease transmission. 133 134 Entry into quarantine when the time of exposure is unknown 135 For settings where there is no administrative knowledge of the time of exposure such as travel 136 quarantine, we computed the expected PQT (Fig. S2) and the probability of PQT after a range of 137 quarantine durations without testing (Fig. 1A, Fig. S3A). Assuming individuals self-isolate 138 immediately upon symptom onset, the probability of PQT declines as the duration of quarantine 139 increases (Fig. 1A). This probability is less than 0.25 with a quarantine duration of at least three 140 days, and falls below 0.05 for quarantines of eight days or longer. 141 142 The impact of quarantine can be augmented through testing. We assumed a 24-hour delay 143 between the sample collection and test results, so that testing on exit occurred one day before the 144 end of quarantine. Individuals who tested positive or developed symptoms were isolated until 145 recovery. We found that any testing during quarantine contributed to a reduction in the 146 probability of PQT across the full range of quarantine duration (Fig. 1A and Fig. S3A). The 147 magnitude of this reduction was dependent on both the duration of quarantine and the timing of 148 the testing. 149 150 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 8 The largest reduction in the probability of PQT from conducting a single test occurred when it 151 was performed on exit for quarantines of seven days or less; on day five for quarantines lasting 152 between eight and 13 days; and on day six for quarantines that are 14 days or longer (Fig. 1B). 153 As quarantined (asymptomatic) cases proceed through their quarantine, they simultaneously 154 progress through their infectious course. Symptom onset will send a substantial fraction of 155 infected individuals to isolation and diagnostic sensitivity decreases for the remainder19, leading 156 to slightly diminishing benefits of “exit” tests performed later than day six. 157 158 Comparing the three testing strategies, we found that testing on both entry and exit from 159 quarantine provides the greatest reduction in PQT, whereas the benefit of testing at entry is 160 minimal (Fig. 1A, Fig. S3A). Testing on exit consistently and substantially outperformed testing 161 on entry across all quarantine durations considered (Fig. 1A). 162 163 We specifically compared strategies of quarantine and testing against the widely implemented 164 WHO recommendation to quarantine for 14 days (without testing) 5. In this comparison, a 13-day 165 quarantine with testing on entry, a seven-day quarantine with testing on exit, and a seven-day 166 quarantine with testing on both entry and exit each provide equivalent or lower probabilities of 167 PQT (Fig. 1A, Fig. S3). 168 169 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 9 Figure 1: The probability of post-quarantine transmission and optimal day to conduct test when an infected individual enters quarantine uniformly within the incubation or asymptomatic period, 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. (A) Curves for the probability of post-quarantine transmission (one or more post-quarantine infections) without testing (red), with testing upon entry to quarantine (orange), on exit from quarantine (blue), and on both entry to and exit from quarantine (purple). Results include a one-day delay in sample collection . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 10 to results, such that testing on exit occurred the day before the end of quarantine. (B) The optimal day to test during quarantine with a one-day delay (black) and a negligible delay (gray) in obtaining test results. Assessment of quarantine and testing strategies implemented for offshore facilities 170 We applied our results in the context of employees of an off-shore oil company who were 171 working a cycle of 26 days on, then 16 days off, a schedule that had been modified to make 172 efficient use of a mandatory quarantine that was implemented during the pandemic. During the 173 early stages of the epidemic, when prevalence was low, a three-day quarantine had been 174 implemented by the company in a secured facility, with testing on entry. Our risk-reduction 175 models indicated substantial marginal benefit for increasing quarantine to 5–7 days with a test on 176 exit. Testing on entry was retained for operational purposes, and testing 96 h later was initiated, 177 accompanied by expansion to a seven-day quarantine for Region A and a five-day quarantine for 178 Region B. 179 180 To assess the practical implications of our recommendations, 4040 RT-PCR tests were 181 conducted in region A and region B (serviced by different laboratories) prior to travel to offshore 182 rigs. Among these, 69 results were positive (1.7%). Of the 1792 RT-PCR tests conducted as tests 183 on entry when the initial three-day quarantine was in effect, there were 22 positive results 184 (1.2%). After advisement, Region A deployed a seven-day home quarantine for all cycles 185 starting August 13, where testing was performed on entry and exit (96 h after the first test); 186 50.0% (1/2) of the positive tests occurred on exit, following a negative test on entry (Fig. 2A). 187 Starting June 25, Region B expanded to a five-day hotel quarantine with testing on both entry 188 and 96 h after the first test. For the period in which this strategy was implemented, 33.3% 189 (15/45) of the positive tests were obtained upon the exit test, following a negative entry test 190 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 11 (Fig. 2B). Further validation of the entry and exit testing protocol was provided through an 191 additional 155 RT-PCR tests performed post-quarantine (11 days after the initial test) in Region 192 B, all of which were negative. 193 194 Figure 2: Weekly SARS-CoV-2 testing and positivity rate between April 11 to August 26, 2020, within two regions where crew members were quarantined: (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 early strategy of testing on only entry (left) and the later strategy of testing on both entry and exit (right), including 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 (numerator) and the number of tests conducted (denominator) is denoted above the bar in parentheses. 195 No offshore worker registering negative tests on entry and on exit from quarantine was later 196 diagnosed with COVID-19 during their offshore work. To quantify the added benefit of the test 197 at 96 h, we calculated the probability of PQT for the cases detected by this second test. 198 Compared with a three-day quarantine and testing only on entry, extending the quarantine 199 duration and adding testing on exit (96 h after the first test) reduced the probability of PQT by 200 98% for the seven-day quarantine and 93% for a five-day quarantine. If the single case identified 201 on the exit test from region A had remained undetected within the seven-day quarantine, we 202 estimate an off-shore probability of PQT of 0.13. If the 15 cases that had been ascertained on exit 203 from region B had remained undetected after the five-day quarantine without testing on exit, we 204 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 12 estimate that the probability of at least one event of PQT would have been 0.99, and would have 205 resulted in an expected 9 offshore transmission events—each one a serious concern for initiating 206 further rapid spread and a disabling outbreak in the close quarters of an offshore rig. 207 208 Accounting for prevalence of disease in the community. 209 We evaluated the impact of disease prevalence in the community on the probability of PQT 210 (Fig. S6). For a cohort of 40 individuals undergoing a five-day quarantine with prevalence of 211 1%, we estimated the probability of PQT to be 0.06 for testing only on entry, and 0.005 for 212 testing on both entry and exit (Fig. S6B). For a seven-day quarantine and the same prevalence, 213 the probability of PQT drops from 0.02 for testing only on entry to 0.001 when augmented with 214 testing on exit (Fig. S6C). 215 216 Contrasting contact tracing and uniform entry into quarantine 217 Contact tracing is ideally initiated following identification of a positive case either by symptom 218 presentation or by surveillance screening through testing. We evaluated the impact of quarantine 219 initiated through contact tracing on reducing PQT under scenarios of no delay (Fig. 3A, Fig. S7–220 S8) or one-day delay in outreach to exposed contacts (Fig. S9–S10). Tracing of contacts was 221 assumed to be initiated by the onset of relevant COVID-19 symptoms. Rapid contact tracing 222

in the quarantine of infected contacts early in their infection course, thereby increasing 223 the recommended duration of quarantine and changing the relationship between test timing and 224 the probability of PQT, compared to uniform entry into quarantine (Fig. 3A vs Fig. 1A). 225 226 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 13 However, the combination of shorter quarantines with exit testing maintains high effectiveness 227 compared with 14-day quarantines without testing. When cases are identified through contact 228 tracing, we found that a seven-day quarantine with testing on exit and a six-day quarantine with 229 testing on entry and exit each result in an probability of PQT equivalent or lower than a 14-day 230 quarantine with no testing; testing on entry bestowed only trivial benefit (Fig. 3A, Fig. S8). For 231 quarantines of seven days or less, the optimal test timing was upon exit. For quarantines beyond 232 seven days, the optimal timing was day six (Fig. 3B). 233 234 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 14 Figure 3: The probability of post-quarantine transmission for no testing and three testing strategies applied to 1–14-day durations of quarantine, when an individual enters quarantine through contact tracing, specifying an incubation period of 8.29 days, 30.8% asymptomatic infections, and perfect self - isolation of symptomatic infections. (A) The probability of one or more post-quarantine infections without testing (red), with testing upon entry to quarantine (orange), on exit from quarantine (blue), and on both entry to and exit from quarantine (purple), assuming that testing on exit occurs on the penultimate day of quarantine. (B) The optimal day to test during quarantine for a specified quarantine . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 15 duration, with that one-day delay (black) and with a negligible delay (gray) in obtaining test results. 235 Optimal day of testing for a known time of exposure 236 When a specific date of exposure can be identified for a traced contact, the optimal test timing 237 differs from that calculated by integrating over all possible exposure times. When quarantined 238 one day post-infection and tested on entry, an additional test on day six of quarantine is optimal; 239 the optimal day of testing then decreases linearly. For an individual entering quarantine seven or 240 more days post-infection, the optimal test date is the test on entry (Fig. 4). 241 242 Figure 4: For a case whose date of exposure has been identified as occurring 1–14 days prior to quarantine, the optimal day to conduct the RT-PCR test, assuming perfect self-isolation of symptomatic infections, 30.8% asymptomatic infections, an incubation period of 8.29 days, and a quarantine lasting (A) 14 days, (B) seven days, (C) five days, and (D) three days. 243 Sensitivity analyses 244 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 16 We performed a comparative analysis specifying a latent period that is one day greater or lesser 245 than the reported 2.9 days 22. The expected number of secondary cases occurring before 246 symptom onset was similar among the different latent periods (1.21 infection for a latent period 247 2.9 days; 1.24 infections for a latent period of 1.9 days; and 1.27 infections for a latent period of 248 3.9 days). The infectivity profiles differed among the three latent periods, with a peak infectivity 249 that is higher for both the 1.9-day and 3.9-day latent periods when compared to our baseline 250 (Fig. S11). 251 252 For quarantine periods of at least seven days and individuals entering quarantine uniformly 253 across the time course of infection (Fig. S12–S15), the probability of PQT was lower for shorter 254 latent periods. For shorter quarantines, the relationship between the probability of PQT and latent 255 period is more intricate. For traced contacts entering quarantines of eight days or longer 256 (Fig. S16–S19), shorter latent periods entailed lower probability of PQT. For traced contacts 257 entering quarantines of fewer than eight days, the relationship of latent period to probability of 258 PQT is more complex. However, one-day changes in the latent period affect the optimal day to 259 conduct a single test by at most one day (Fig. S4). Specifically, we found that a 3.9-day latent 260 period decreased the optimal day of testing estimated for a 2.9-day latent period, whereas a 1.9-261 day latent period increased the best day to conduct a single test. 262 263 For our analysis of potential outbreaks consequent to offshore-rig quarantine and testing, we 264 analysed sensitivity of our result to the proportion of asymptomatic individuals on the probability 265 of PQT (Fig. S5). We found that the estimated probability of PQT using the strategy of testing 266 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 17 upon entry and at 96 h moderately increased if a higher proportion of infections were expected to 267 be asymptomatic (Fig. S5). 268 269

270 Here, we derived theory to calculate the probability of post-quarantine transmission of COVID-271 19 for a wide range of durations of quarantine, supplemented by testing on entry to quarantine, 272 on exit from quarantine, or both. For quarantines with durations of up to seven days, we found 273 that testing on exit provided the greatest marginal benefit in terms of reducing the probability of 274 PQT. Testing on entry provided modest benefits in combination with quarantine or with testing 275 on exit. For a quarantine with a duration longer than seven days, the optimal testing time is on 276 day five or six. Optimal testing times were fairly consistent between travel quarantines and 277 quarantines of traced contacts, differing at most by a day. The benefits of testing later in 278 quarantine were demonstrated by test results of oil crewmembers heading offshore that 279 identified 16 cases testing negative on entry and positive on exit that could easily have resulted 280 in costly and logistically difficult-to-handle offshore outbreaks. When the time of exposure is 281 known, the optimal day for a test for quarantines of a week or more starts at day six of the 282 quarantine, decreasing linearly to day-of-entry for individuals who have been infected for seven 283 or more days. It may seem counter-intuitive that the optimal test for so many identified timings 284 of exposure is on entry, yet testing on entry has so much less impact than testing on exit when 285 the date of exposure is unknown. Indeed, for individuals that are tested after the incubation 286 period (e.g. later than symptom onset), the diagnostic sensitivity of the RT-PCR test has started 287 to decline. However, for individuals late in disease, there is also far less infectivity left in their 288 disease course. The high remaining infectivity of individuals early in disease course markedly 289 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 18 outweighs the low infectivity of individuals late in disease course in influencing the optimal day 290 of testing to prevent post-quarantine transmission. 291 292 An outbreak can be triggered or sustained within an environment that is monitored only for 293 symptoms of COVID-19. Quarantining individuals before returning to work or school has been a 294 common strategy among many businesses, the military and universities to prevent potential 295 outbreaks 23,24. An offshore or military setting is one of numerous close-quarters environments in 296 modern society where an outbreak can seriously impact operational integrity, leading to 297 compromised safety and adverse economic consequences. Hence, minimizing outbreak risk 298 while maintaining staffing is critical. Testing may allow for the quarantine duration to be 299 reduced without increasing the risk of PQT. For example, many universities have implemented 300 plans for quarantining and frequent testing of students and employees, where resources allow 301 25,26. For businesses and close-quarters environments, the impact of false negatives is a 302 substantially greater issue for operational integrity than false positives. Consistent with the 303

from our analytic model (Fig. 1A and Fig. 3A), simulations from a recent agent-based 304 model suggest that testing on exit—or entry and exit—of a seven-day quarantine can avert 305 similar transmission as a 14-day quarantine with no transmission 12. Our results show that 306 testing upon entry to quarantine carries such a risk of false negatives, as infected individuals who 307 enter quarantine very early in the incubation period of disease may not be detected due to low 308 viral loads. 309 310 Our estimates for the probability of PQT for the various strategies were estimated assuming a 311 basic reproductive number of 2.5 throughout the disease course, and unchanged post-quarantine. 312 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 19 In the offshore environment, individuals are living in very confined quarters which could lead to 313 higher post-quarantine transmission and a larger number of secondary infections. In some 314 community settings, the number of secondary infections can be reduced through mask-wearing, 315 social distancing, and other non-pharmaceutical interventions. These changes in the number of 316 secondary infections post-quarantine can markedly influence the probability of PQT. However, 317 they would not affect the relative benefit of testing on exit compared to entry. Therefore, our 318 qualitative finding of the optimality of testing later in quarantine than on entry are robust to 319 settings with extensive post-quarantine transmission. 320 321 As prevalence in the general community increases (Fig. S6, blue and purple), there are benefits 322 to conducting additional tests during quarantine: as substantial numbers of infected individuals 323 enter quarantine, larger numbers of individuals may proceed through testing with rare false-324 negative test results, increasing PQT. Addressing false negatives that inevitably occur at high 325 prevalence can be aided by performing additional tests during quarantine; the impact of any 326 specific set of tests can be quantified within our model framework. In future research, the theory 327 can be applied to evaluate the impact of incorporating recent innovations such as saliva RT-PCR 328 tests and rapid antigen tests. These alternate approaches could exhibit altered optima. We have 329 not quantified more extensive testing strategies here due to the limited availability of testing, 330 potentially high and largely unknown correlations among false-negative test results for 331 individual cases, and the observed moderate marginal benefit of additional testing performed in 332 early stages of disease with lower detection rates (Fig. S28). 333 334 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 20 Optimal timing of limited testing during quarantine improves the ability to control PQT. Testing 335 several days into quarantine increases the likelihood of an infected case testing positive 336 (Fig. S4). The increasing diagnostic sensitivity of the RT-PCR test is attributable to the rapidly 337 increasing viral load following the less detectable latent stage of infection. If the infected 338 individual remains asymptomatic, testing near the end of a standard 14-day quarantine can also 339 lead to low diagnostic sensitivity due to a declining viral load as they overcome the infection 27. 340 Australia has implemented a mandatory 14-day quarantine for individuals arriving into the 341 country, with testing during the first two days of arrival and between day 10 and 12 of 342 quarantine 16. Though the differences are moderate, our analysis indicates that the lowest 343 probability of PQT is achieved by testing on day six of the standard 14-day quarantine (Fig. 1B, 344 Fig 3B). 345 346 Testing was found to result in a smaller reduction of the expected PQT when cases enter 347 quarantine through contact tracing compared to when they enter as a consequence of travel 348 regulation. Contact tracing will usually identify more infected cases per quarantined individual 349 than will travel quarantine, due to the specific exposure risk. For example, if prevalence is 1% 350 and 10 individuals are selected at random for quarantine, then on average 0.1 people would be 351 infected. Alternatively, if an index case is isolated upon symptom onset, there would be on 352 average 1.21 individuals infected (for an R0 = 2.5) prior to symptom onset and potentially 353 identified through contact tracing. With a significant chance of traced contacts being infected, 354 reducing PQT becomes increasingly important. However, traced contacts are likely to enter 355 quarantine earlier in disease (Fig. S31). Such an earlier entry necessitates a consequently longer 356 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 21 quarantine (generally). Earlier entry makes it more likely that testing early in quarantine will 357 occur during the latent period, when diagnostic sensitivity of the RT-PCR test is highly limited. 358 359 Our study is informative for businesses, military operations, and universities, providing 360 quantitative estimation of the residual risk of PQT. The calculated infection risks were used to 361 inform the quarantine and RT-PCR testing strategy deployed by an oil and gas company prior to 362 workers travelling offshore. Of the positive tests obtained under this strategy, 34% were obtained 363 on an exit test following a negative entry test. The exit test prevented 16 infected crew members 364 from exiting quarantine and entering confined quarters offshore while potentially infectious. The 365

of the time of testing for a given quarantine duration are also useful for public-health 366 decision making when quarantine is required for international, interstate, and social travel. 367 368 Our examination of the effects of durations of quarantine and timings of testing is critical to 369 future efforts to balance the risk of PQT with the economic costs, negative impact on mental 370 health, and restrictions on social liberty associated with prolonged quarantines. Timely testing 371 enables a shorter quarantine with equivalent benefits to the much longer 14-day quarantine in 372 prevention of post-quarantine transmission. Our study indicates that the strategy of testing upon 373 entry into quarantine—currently implemented by many institutions and administrative bodies—374 conveys the least benefit, if infection time is unknown. Testing at exit can provide substantially 375 higher dividends in reducing PQT; or at an optimal timing near 1 week for quarantines of a 376 week or longer. Our result was substantiated both by our integrative analysis of infectivity and 377 diagnostic sensitivity, and by test results demonstrating the utility of tests 96 h into the 378 quarantine of crew members of an offshore oil facility. In determining policies for the duration of 379 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 22 travel quarantine and quarantine of traced contacts, full consideration of how timely diagnostic 380 testing aids prevention of post-quarantine transmission is essential to effective and transparent 381 balancing of lives and livelihoods in times of a global pandemic. 382 383 384 385

386 Data of SARS CoV-2 tests during quarantine 387 Between April 11, 2020 and August 26, 2020, there were 4,040 SARS CoV-2 RT-PCR tests 388 conducted among employees of an oil and gas company coming from two regions (stratified by 389 lab location). A third region that was monitored is not included in our data set, as there was low 390 population prevalence entering quarantine and there were no positive tests. During the early 391 stages of the epidemic, both regions used a three-day quarantine with testing on entry. On 392 August 13, employees from region A quarantined at home for seven days, with testing occurring 393 on both entry and exit. While employees were at home, they were asked to practice social 394 distancing in public. Starting on June 25, employees from region B were quarantined in a hotel 395 for five days prior to their departure offshore and tested on both entry and exit. The requirements 396 of an employee to go off-shore were (1) passing the components of a screening form used to 397 filter out symptomatic cases and those potentially exposed, (2) temperature screenings, and (3) 398 completion of the quarantine with no positive RT-PCR test. Upon a positive test, the employee 399 initiated a 14-day isolation period and followed through the company's case management 400 process. After the isolation period, individuals were able to return back to work contingent upon 401 two negative RT-PCR tests. The use of this data was approved by the Human Participants 402 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 23 Review Sub-Committee, York University’s Ethics Review Board (Certificate Number: 2020-403 323). 404 405 Epidemiological parameters 406 The average incubation period is 8.29 days 18. The latent period (i.e. infected but low probability 407 of infecting contacts) is 2.9 days 22. We consider latent periods of 1.9 days and 3.9 days in a 408 scenario analysis 22 (Fig. S11–S19). 409 410 For our baseline analysis, we considered a delay of one day between sample collection and result 411 of RT-PCT test. Thus, the sample is taken one day before the end of quarantine when testing on 412 exit. We also conducted the analysis when there was no delay in testing results to examine the 413 impact on the probability of PQT (Fig. S20–S23). 414 415 In the baseline analysis, we assumed R0 = 2.5 and 30.8% of infections are asymptomatic 8,20. We 416 further analyzed the scenario in which 22.6% of infections are asymptomatic (Fig S24–S27) 28. 417 Both of these proportions are consistent with estimates from a systematic meta-analysis 21. 418 Asymptomatic infections were assumed to be equally as infectious as symptomatic infections. 419 This assumption is based on measurements of viral loads in asymptomatic infections being 420 comparable to those observed in symptomatic cases 29,30. 421 422 Infectivity profile 423 The infectivity profile has been determined to increase rapidly prior to symptom onset, peak near 424 onset of symptoms, and decrease subsequently 31. We specified our infectivity profiles based on 425 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 24 the full dataset and R code provided by He et al 17, specifying the latent period. The infectivity 426 during the latent period was expressed as exponentially lower (Supplementary Information: 427 Methods, Infectivity function). Imposing the strict threshold where 20 days after symptom 428 onset infectivity is zero 32–34 made no significant difference to our estimate of PQT for 429 quarantines of up to 14 days . 430 431 Temporal diagnostic sensitivity of a SARS CoV-2 RT-PCR assay 432 We utilized the post-symptom onset temporal diagnostic sensitivity for RT-PCR tests of infected 433 individuals 19, fitting a logistic regression function to the diagnostic sensitivity data from zero to 434 25 days post-symptom onset through minimization of least squares. To infer the diagnostic 435 sensitivity prior to symptom onset, we first used this function to perform a slight extrapolation of 436 the diagnostic sensitivity back to the peak, which occurred slightly prior to symptom onset. 437 Second, to determine the diagnostic sensitivity for the remaining portion of the incubation 438 period, we specified the interpolation function determined by the infectivity and the diagnostic 439 sensitivity from post-symptom onset, and used that interpolation function on the pre-symptom 440 onset infectivity to determine pre-symptom onset diagnostic sensitivity (Supplementary 441 Information: Methods, Diagnostic sensitivity function). This process provides the diagnostic 442 sensitivity over the entire course of infection (Fig. S28)13. We assumed that the specificity of the 443 RT-PCR assay was 100% 35. 444 445 Probability of post-quarantine transmission 446 To calculate the probability of PQT—defined to be the probability of at least one post-quarantine 447 infection—we assumed that the expected post-quarantine transmission is described by a negative 448 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 25 binomial distribution with a dispersion parameter of 0.25 36. This value for the dispersion 449 parameter is consistent with numerous published estimates 37–39. For sensitivity analyses, we also 450 computed the probability of PQT given Poisson-distributed post-quarantine transmission 451 (Fig. S29–S30). In our additional analysis accounting for the underlying prevalence within the 452 community, the probability of PQT was defined as the likelihood that at least one infected 453 individual in a cohort became a source of PQT. Similarly, to calculate the probability of PQT 454 given a negative test on entry for N infected individuals, we estimated the probability that at least 455 one of the cases contributed to PQT. 456 457 Data availability 458 The number of positive tests and tests conducted at the two regions quarantining the crew 459 members heading offshore are presented in Fig. 2, with other data used in the analysis referenced 460 in Table S1 and in the Methods. 461 462 Code availability 463 The computational code for the analysis was implemented in MATLAB, and it is available at 464 github.com/WellsRC/Optimizing-COVID19-Quarantine-and-Testing-Strategies. 465 466 Author contributions 467 JPT conceived and designed the study with contributions from other authors, developed the 468 theory and provided initial analyses. CRW derived additional theory, wrote computational code 469 and ran simulations. All authors contributed to interpretation of results, revision 470 of the manuscript and approved the final version of the manuscript. 471 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 26 472

473 We thank Justin Abshire for expert data collection. J.P.T. gratefully acknowledges funding from 474 the National Science Foundation grant CCF 1918656, the Elihu endowment, Notsew Orm Sands 475 Foundation, and BHP. G.K., B.S., and R.H.M acknowledge funding from BHP. S.M.M. 476 acknowledges support from the Canadian Institutes of Health Research (grant OV4-170643; 477 Canadian 2019 Novel Coronavirus Rapid Research), the Natural Sciences and Engineering 478 Research Council of Canada, and BHP. A.P.G. gratefully acknowledges funding from NIH UO1-479 GM087719, the Burnett and Stender families’ endowment, the Notsew Orm Sands Foundation, 480 and BHP. 481

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CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint Supplementary Information: Optimal COVID-19 quarantine and testing strategies Chad R. Wells 1*, Jeffrey P. Townsend 2,3,4,5*†, Abhishek Pandey 1, Seyed M. Moghadas 6, Gary Krieger 7, Burton Singer 8, Robert H. McDonald 9, Meagan C. Fitzpatrick 1,10, Alison P. Galvani 1,3 1 Center for Infectious Disease Modeling and Analysis (CIDMA), Yale School of Public Health, New Haven, CT 06520, USA 2Department of Biostatistics, Yale School of Public Health, New Haven, Connecticut 06510, USA 3Department of Ecology and Evolutionary Biology, Yale University, New Haven, Connecticut 06525, USA 4Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06511, USA 5Program in Microbiology, Yale University, New Haven, Connecticut 06511, USA 6 Agent-Based Modelling Laboratory, York University, Toronto, Ontario, M3J 1P3 Canada 7 NewFields E&E Boulder, CO USA 80301 and Skaggs School of Pharmacy and Pharmaceutical Science, University of Colorado Anschutz Medical Campus 8 Emerging Pathogens Institute, University of Florida, P.O. Box 100009, Gainesville, FL 32610, USA 9 Group Health, Safety and Environment; BHP; Melbourne, Victoria, Australia, 3000 10 Center for Vaccine Development and Global Health, University of Maryland School of Medicine, Baltimore, MD, 21201, USA . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 1 Theory Transmission over Time Transmission of a pathogen from an infected individual is typically time-dependent, based on pathogen shedding and behavioral changes, and can be represented over time by a function 𝑟(𝑡), for which time t = 0 represents initial infection. To represent infectiousness, a function 𝑟(𝑡) can be scaled such that ∫ 𝑟(𝑡)𝘥𝑡 = 𝑅0 ∞ 𝑡 = 0 , (1) where 𝑅0is the basic reproduction number: the expected number of infections consequent to a single infected individual under a scenario of no intervention. Specifying a discrete end to the infection at time 𝑡𝑒 such that 𝑟(𝑡 ) = 0 for 𝑡 > 𝑡𝑒, ∫ 𝑟(𝑡)𝘥𝑡 = 𝑅0 𝑡𝑒 𝑡 = 0 . Infectiousness during discrete timespans 𝑡2 − 𝑡1 (e.g. days) can be calculated as 𝑅𝑡2−𝑡1 = ∫ 𝑟(𝑡)𝘥𝑡 𝑡2 𝑡 = 𝑡1 . Self-isolation at Symptom Onset A significant means of intervention to prevent infection is self-isolation of infected individuals upon symptom onset. The expected effect on onward transmission of an intervention such as self-isolation of a case that becomes symptomatic at time 𝑡𝑠 can be calculated as 𝑅𝑖 = ∫ 𝑟(𝑡)𝘥𝑡 𝑡𝑠 𝑡 = 0 , (2) provided that all individuals self-isolate upon presentation with symptoms. If ∫ 𝑟(𝑡)𝘥𝑡 > 1 𝑡𝑠 𝑡 = 0 , then even perfect self-isolation upon symptom onset will be insufficient to extinguish disease transmission. We express the transmission over time for a symptomatic individual who isolates upon symptom onset as . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 2 If the outcome of infections leads to a proportion of infected individuals 𝑝𝑎that can infect others but that never manifest symptoms (i.e. that are asymptomatic carriers), then transmission may be partitioned into the contributions of symptomatic and asymptomatic cases as 𝑅0 = 𝑅0,𝑠𝑝𝑠 + 𝑅0,𝑎𝑝𝑎, in which the probability of a symptomatic case 𝑝𝑠 = (1 − 𝑝𝑎). 𝑅0,𝑠 and 𝑅0,𝑎 can be equated to distinct infectiousness functions 𝑟𝑠(𝑡) and 𝑟𝑎(𝑡), in the absence of self-isolation. For simplicity of presentation in ensuing theory, it will be assumed that 𝑅0,𝑠 = 𝑅0,𝑎 and the same infectivity profile in the absence of self-isolation (i.e. 𝑟𝑠(𝑡) = 𝑟𝑠(𝑡) = 𝑟(𝑡)) 1,2. Alternate overall transmission and alternate forms of infectivity over time for asymptomatic cases may easily be partitioned and tracked in the theory that follows should there be evidence to substantiate their difference. The presence of asymptomatic carriers increases the degree of transmission consequent to a self-isolation intervention from that shown by Eq. 2 to 𝑅 = 𝑝𝑠 ∫ 𝑟𝑆(𝑡)𝘥𝑡 𝑡𝑠 𝑡 = 0 + 𝑝𝑎𝑅0 . Quarantine Quarantine with a Known Time of Infection. A longstanding approach to limit disease spread is the quarantine of individuals who have no prior indication of potential for disease but intend to migrate from a population in which there is current transmission to a population with lower or zero disease prevalence. Because quarantined individuals experience a significant restriction of personal freedom, it is important to minimize the duration of quarantine 𝑞, but also maximize its effectiveness in limiting post-quarantine transmission. Quarantine of q days from . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 3 time 𝑡𝑞to time 𝑡𝑞 + 𝑞 limits total expected post-quarantine transmission to 𝑅𝑞 = 𝑅0 − ∫ 𝑟(𝑡)𝘥𝑡 𝑡𝑞 + 𝑞 𝑡𝑞 . For policy decision-making regarding quarantine duration, the expected post-quarantine transmission is typically most important, and can be calculated as 𝑅𝑞⟼ = ∫ 𝑟(𝑡)𝘥𝑡 ∞ 𝑡 = 𝑡𝑞+𝑞 . If individuals self-isolate, there is a trivial case in which 𝑡𝑠 ≤ 𝑡𝑞 + 𝑞 and 𝑅𝑞⟼ = 0; otherwise, 𝑡𝑠 > 𝑡𝑞 + 𝑞 and 𝑅𝑞⟼ = ∫ 𝑟𝑆(𝑡)𝘥𝑡 ∞ 𝑡 = 𝑡𝑞+𝑞 . Including asymptomatic carriers, 𝑅𝑞⟼ = 𝑝𝑠 ∫ 𝑟𝑆(𝑡)𝘥𝑡 ∞ 𝑡 = 𝑡𝑞+𝑞 + 𝑝𝑎 ∫ 𝑟(𝑡)𝘥𝑡 ∞ 𝑡 = 𝑡𝑞+𝑞 . Unfortunately, these expressions are unlikely to be useful in this form for quantifying the benefits of quarantine in reducing transmission. In the case of quarantine of migrants from one population to another, the time of infection—and correspondingly the time of quarantine 𝑡𝑞—are rarely known. Quarantine with an Unknown Time of Infection. In a rapidly spreading epidemic, individuals who might be entering quarantine will tend to be early in disease time course. In a rapidly declining epidemic, individuals who might be entering quarantine will tend to be later in disease time course. In a steady-state epidemic with case counts 𝑐(𝑡), 𝑑𝑐 𝑑𝑡 ≈ 0 over the period from t0 to ts such that individuals entering quarantine are evenly distributed across the disease time course. Provided all individuals experience symptoms at time 𝑡𝑠 that qualify them for isolation instead of quarantine, then the expected post-quarantine infectivity is . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 4 𝑟𝑞(𝑡) = 1 𝑡𝑠 ∫ 𝑟𝑆(𝑡 + 𝑢) 𝑡𝑠 𝑢= 0 𝘥𝑢, and expected post-quarantine transmission from an infected individual is 𝑅𝑞⟼(𝑞) = 1 𝑡𝑠 ∫ ∫ 𝑟𝑆(𝑡)𝘥𝑡 ∞ 𝑡=𝑢+𝑞 𝘥𝑢 𝑡𝑠 𝑢= 0 , a function of days of quarantine q. For asymptomatic carriers entering within disease time course te, 𝑅𝑞⟼(𝑞) = 1 𝑡𝑒 ∫ ∫ 𝑟(𝑡)𝘥𝑡 ∞ 𝑡=𝑢+𝑞 𝘥𝑢 𝑡𝑒 𝑢= 0 . Incorporating both symptomatic and asymptomatic infections, 𝑅𝑞⟼(𝑞) = 𝑝𝑠 𝑡𝑠 ∫ ∫ 𝑟𝑆(𝑡)𝘥𝑡 ∞ 𝑡=𝑢+𝑞 𝘥𝑢 𝑡𝑠 𝑢= 0 + 𝑝𝑎 𝑡𝑒 ∫ ∫ 𝑟(𝑡)𝘥𝑡 𝘥𝑢 ∞ 𝑡=𝑢+𝑞 𝑡𝑒 𝑢= 0 . A similar approach that incorporates symptomatic and asymptomatic cases by their proportions within the population may be performed throughout the rest of the scenarios below, and will not be specifically pointed out for each scenario. Testing Testing with a Known Time of Infection. Diagnostic test sensitivity 𝑠(𝑡) is also time- dependent. Assaying for components of the pathogen (e.g. DNA, RNA, or protein), diagnostic sensitivity typically is zero to low very early in disease before the pathogen load burgeons, then declines in the later stages of disease when immune responses develop and infection is suppressed (Fig. S28). In a disease for which tests can diagnose infections during the incubation phase, testing can enhance the efficacy of quarantine by identifying individuals to be isolated instead of quarantined, thereby preventing future transmission from cases that persist as infectious through an earlier exit from quarantine than would be called for in case isolation. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 5 Testing with an Unknown Time of Infection. The temporal diagnostic sensitivity of a test for infected cases with an unknown time of infection can be calculated by integrating over the unknown time of infection, such that 𝑠𝑢(𝑡) = 1 𝑡𝑒 ∫ 𝑠(𝑡 + 𝑢)𝘥𝑢 𝑡𝑒 𝑢= 0 . Quarantine and Testing Quarantine with an Unknown Time of Infection with Testing on Entry. Assuming the duration of the quarantine, q, is longer than the delay between administering the test and acting to isolate upon a positive result, the expected post-quarantine infectivity over time of a symptomatic individual whose time of infection is unknown and who is tested for disease on entry to quarantine is 𝑟𝑞⟼(𝑡) = 1 𝑡𝑠 ∫ (1 − 𝑠(𝑢))⋅ 𝑟𝑆(𝑡 + 𝑢)𝘥𝑢 𝑡𝑠 𝑢=0 , in terms of time from infection. In terms of q days of quarantine, the expected post-quarantine transmission is 𝑅𝑞⟼(𝑞) = 1 𝑡𝑠 ∫ ∫ (1 − 𝑠(𝑢))⋅ 𝑟𝑆(𝑡 + 𝑢)𝘥𝑡 ∞ 𝑡=𝑞 𝘥𝑢 𝑡𝑠 𝑢= 0 . For asymptomatic carriers, 𝑅𝑞⟼(𝑞) = 1 𝑡𝑒 ∫ ∫ (1 − 𝑠(𝑢))⋅ 𝑟(𝑡 + 𝑢)𝘥𝑡 𝘥𝑢 ∞ 𝑡=𝑞 . 𝑡𝑒 𝑢= 0 Quarantine with an Unknown Time of Infection with Testing on Entry and Exit. Expected post-quarantine transmission from an individual whose time of infection is unknown and who is tested for disease upon entry and at the last opportunity prior to the end of quarantine is 𝑅𝑞⟼(𝑞) = 1 𝑡𝑠 ∫ ∫ (1 − 𝑠(𝑢))⋅ (1 − 𝑠(𝑢 + 𝑞 − 𝑑𝑡))⋅ 𝑟𝑆(𝑡 + 𝑢)𝘥𝑡 ∞ 𝑡=𝑞 𝘥𝑢 𝑡𝑠 𝑢= 0 , . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 6 where dt is the delay between administering the test and isolation if positive. For asymptomatic carriers, 𝑅𝑞⟼(𝑞) = 1 𝑡𝑒 ∫ ∫ (1 − 𝑠(𝑢))⋅ (1 − 𝑠(𝑢 + 𝑞 − 𝑑𝑡))⋅ 𝑟(𝑡 + 𝑢)𝘥𝑡 𝘥𝑢 ∞ 𝑡=𝑞 𝑡𝑒 𝑢= 0 . Quarantine with Testing at Any Time(s). Expected post-quarantine transmission of an infected individual whose time of infection is unknown and who is tested for disease at any time 0 ≤ 𝑡𝑡 ≤ 𝑞 − 𝑑𝑡 is 𝑅𝑞⟼(𝑞) = 1 𝑡𝑠 ∫ ∫ (1 − 𝑠(𝑡𝑡 + 𝑢))⋅ 𝑟𝑆(𝑡 + 𝑢)𝘥𝑡 𝘥𝑢 ∞ 𝑡=𝑞 𝑡𝑠 𝑢= 0 . For asymptomatic carriers, 𝑅𝑞⟼(𝑞) = 1 𝑡𝑒 ∫ ∫ (1 − 𝑠(𝑡𝑡 + 𝑢))⋅ 𝑟(𝑡 + 𝑢)𝘥𝑡 𝘥𝑢 ∞ 𝑡=𝑞 𝑡𝑒 𝑢= 0 . Additional terms (1 − 𝑠(𝑢 + 𝑡𝑘)), where k indexes testing times, may be included as terms within the product inside the double integral to quantify the expected post-quarantine transmission of any schedule of testing to be applied during quarantine. Quarantine with a Negative Test on Entry. The probability density for obtaining a false negative upon entry for a symptomatic individual is and the probability density for an asymptomatic individual is The expected post-quarantine infectivity over time of a symptomatic individual who tested negative for disease on entry to quarantine is 𝑟𝑞⟼(𝑡) = ∫ 𝑓𝑆(𝑢)⋅ 𝑟𝑆(𝑡 + 𝑢)𝘥𝑢 𝑡𝑠 𝑢=0 , . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 7 in terms of time from infection. In terms of q days of quarantine, the expected post-quarantine transmission is 𝑅𝑞⟼(𝑞) = ∫ ∫ 𝑓𝑆(𝑢)⋅ 𝑟𝑆(𝑡 + 𝑢)𝘥𝑡 𝘥𝑢 ∞ 𝑡=𝑞 𝑡𝑠 𝑢= 0 . For asymptomatic carriers, the expected post-quarantine infectivity is 𝑟𝑞⟼(𝑡) = ∫ 𝑓𝐴(𝑢)⋅ 𝑟(𝑡 + 𝑢)𝘥𝑢 𝑡𝑒 𝑢=0 , and the expected post-quarantine transmission is 𝑅𝑞⟼(𝑞) = ∫ ∫ 𝑓𝐴(𝑢)⋅ 𝑟(𝑡 + 𝑢)𝘥𝑡 𝘥𝑢 ∞ 𝑡=𝑞 𝑡𝑒 𝑢= 0 . Contact Tracing Tracing of individuals who have had contact with an index case identifies persons whose quarantine would reduce the risk of disease transmission from recently exposed individuals. When an individual is identified as a contact of an index case, the expected time of infection is not the same as that of an individual selected at random from an infected population. Restricting our attention to transmissions occurring between an index case and their contacts, there are four nominal transmission relationships to be considered, of which three are considered relevant to an attentive program of contact tracing and quarantine (Table S2): the asymptomatic or pre- symptomatic contact may have infected the index case, or may have been infected by the index case. Here we excluded from calculation the case in which a pre-symptomatic individual infects the index case, because that scenario is formally impossible with a fixed 𝑡𝑠 and rigorous self- isolation and self-identification upon symptoms, and unlikely even with variable 𝑡𝑠 and imperfect adherence to self-isolation and self-identification. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 8 Table S2. Modelled infectivity functions for the contact during tracing. Contact Infected by the index case Infected the index case Symptomatic case 𝑟𝐼→𝑆(𝑡) — Asymptomatic carrier 𝑟𝐼→𝐴(𝑡) 𝑟𝐴→𝐼(𝑡) A To-be-Symptomatic Contact Infected by the Index Case but not yet Symptomatic. By assumption, infection of the contact must have occurred prior to the onset of symptoms in the index case. The likelihood that an infection from the index case occurred at a time during the disease time course of the index case should proportionally follow 𝑟(𝑡) (Eq. 1). Thus, the probability density for infection—on the timescale t of the infection of the index case that was identified at symptom onset—is The probability density for the time since infection of the to-be-symptomatic contact—on the timescale t of the contact—is 𝜂(𝑡) = 𝜄(𝑡𝑠 − 𝑡). Thus, the erstwhile expected infectivity from the contact that was infected by the index case from the time of intervention by a quarantine is 𝑟𝐼→𝑆(𝑡)=∫ 𝜂(𝑣) ⋅ 𝑟𝑆(𝑣 + 𝑡 + 𝑑𝑞) 𝘥𝑣 𝑡𝑠 𝑣=0 , where dq is the delay from identifying the index case to quarantine of the contact. The expected post-quarantine transmission by the contact after a quarantine of duration q is 𝑅𝐼→𝑆𝑞⟼(𝑞) = ∫ ∫ 𝜂(𝑣) ⋅ 𝑟𝑆(𝑣 + 𝑤) 𝘥𝑣 𝘥𝑤 ∞ 𝑤=𝑞+𝑑𝑞 𝑡𝑠 𝑣=0 . . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 9 An Asymptomatic Carrier Contact Infected by the Index Case. The expected infectivity of an asymptomatic contact infected by the index case—from time t = 0 at intervention by quarantine—is 𝑟𝐼→𝐴(𝑡)=∫ 𝜂(𝑣) ⋅ 𝑟(𝑣 + 𝑡 + 𝑑𝑞) 𝘥𝑣, 𝑡𝑠 𝑣=0 where dq is the delay from identifying the index case to quarantine of the contact. The expected post-quarantine transmission from the asymptomatic contact infected by the index case starting from the time of intervention by a quarantine of duration q is 𝑅𝐼→𝐴𝑞⟼(𝑞) = ∫ ∫ 𝜂(𝑣) ⋅ 𝑟(𝑣 + 𝑤) 𝘥𝑣 𝘥𝑤 ∞ 𝑤=𝑞+𝑑𝑞 𝑡𝑠 𝑣=0 . An Asymptomatic Contact that Infected the Index Case. Because the index case was assumed to be identified due to symptom onset, an asymptomatic contact that infected the index case must have already been infected for a duration of at least 𝑡𝑠 + 𝑑𝑞. Consequently, the probability density of infection from that contact is Setting 𝛫 = ∫ 𝑟(𝑣) 𝑑𝑣 ∞ 𝑣=𝑡𝑠+𝑑𝑞 , the expected infectivity of the asymptomatic contact that infected the symptomatic index case—from time t = 0 at intervention by quarantine—is 𝑟𝐴→𝐼(𝑡)= 1 𝛫 ∫ 𝑟(𝑣) ⋅ 𝑟(𝑡 + 𝑣)𝘥𝑣 ∞ 𝑣=𝑡𝑠+𝑑𝑞 , and the expected post-quarantine transmission is 𝑅𝐴→𝐼𝑞⟼(𝑞)= 1 𝛫 ∫ ∫ 𝑟(𝑣)⋅ 𝑟(𝑤 + 𝑣)𝘥𝑣 𝘥𝑤 ∞ 𝑣=𝑡𝑠+𝑑𝑞 ∞ 𝑤=𝑞 . . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 10 Continuing our assumption that individuals are assiduously self-isolating upon symptom onset and recalling that 𝑅𝑖 = ∫ 𝑟𝑆(𝑡)𝘥𝑡 𝑡𝑠 𝑡 = 0 (Eq. 2), we can tabulate the expected transmission by contacts of the index that are classified into three kinds (Table S3). By assumption, a contact to become symptomatic could not have infected the index case, because otherwise in an assiduously self-isolating population, that contact would have been the index case. Table S3. Expected infections from contacts of each modeled transmission type. Contact Infected by the index case Infected the index case Symptomatic case 𝑝𝑠𝑅𝑖 — Asymptomatic carrier 𝑝𝑎𝑅𝑖 𝑝𝑎𝑅𝑜 Combining all three transmission functions of contacts of an index case discovered due to appearance of symptoms, the expected post-quarantine infectivity 𝑟𝑐(𝑡) = 𝑝𝑠𝑅𝑖 𝑅𝑖 +𝑝𝑎𝑅𝑜 𝑟𝐼→𝑆(𝑡)+ 𝑝𝑎𝑅𝑖 𝑅𝑖 +𝑝𝑎𝑅𝑜 𝑟𝐼→𝐴(𝑡)+ 𝑝𝑎𝑅𝑜 𝑅𝑖+𝑝𝑎𝑅𝑜 𝑟𝐴→𝐼(𝑡). Incorporating a quarantine of duration q for contacts, the expected post-quarantine transmission 𝑅𝑐(𝑞) = 𝑝𝑠𝑅𝑖 𝑅𝑖 +𝑝𝑎𝑅𝑜 𝑅𝐼→𝑆(𝑞)+ 𝑝𝑎𝑅𝑖 𝑅𝑖 +𝑝𝑎𝑅𝑜 𝑅𝐼→𝐴(𝑞)+ 𝑝𝑎𝑅𝑜 𝑅𝑖+𝑝𝑎𝑅𝑜 𝑅𝐴→𝐼(𝑞). Probability of post-quarantine transmission The probability of post-quarantine transmission is specified to be the probability that an infected individual exits quarantine, but can still infect one or more individuals. We calculated this probability under a negative-binomial model appropriate when superspreaders play a role in transmission, as well as a Poisson distribution appropriate when transmission is fairly evenly distributed among infected individuals. Negative-binomial distribution. We specified a negative binomial distribution . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 11 𝑓(𝑥|𝑟, 𝑝) = 𝛤(𝑟+𝑥) 𝛤(𝑟)𝛤(𝑥+1)𝑝𝑘(1 − 𝑝)𝑥, with dispersion parameter k = 0.25 3 and 𝑝 = 𝑟 𝑟 + 𝑅𝑞⟼(𝑞),such that the average of the distribution was 𝑅𝑞⟼(𝑞). Thus, the corresponding probability of post-quarantine transmission with negative binomially-distributed transmissions from a case is 𝑃(𝑞) = 1 − 𝑓(0|𝑘, 𝑝). Poisson distribution. Specifying a Poisson distribution producing an expected number of secondary infections post-quarantine transmission of 𝑅𝑞⟼(𝑞), the probability of transmission after a quarantine of duration q days 𝑃(𝑞) = 1 − 𝑒−𝑅𝑞⟼(𝑞). Population prevalence Given a cohort size N and a prevalence of 𝜌, the probability of post-quarantine transmission is 1 − (1 − 𝑃(𝑞))𝑁𝜌.

Infectivity function. We use a Gamma function to specify the infectivity over the disease time course (Fig. S1 and Fig. S11). We generated the infectivity profile during the pre- symptomatic phase for each duration of the pre-symptomatic period corresponding to each latent period, using the R code provided from He et al 4. However, as a matter of accounting for the full disease time course, a level of infectivity during the latent period prior to the discrete onset of the distribution provided by He et al must also be specified. Therefore, we specified the infectivity during this early period of infection as 𝐴(𝑒𝑚⋅(𝑡) − 1), where the constants m and A are estimated . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 12 such that the infectivity function r(t) is smooth and continuous over the entire disease time course. Since the infectivity profile after the latent stage is described by a Gamma function (which has an initial value of zero), we truncate the exponential function at time tL + Δt, where tL is the duration of the latent period; Δt was set as the difference between tL and the upper bound of tL (where the difference in the log-likelihood at tL and at tL + Δt was 1.96 5). Diagnostic sensitivity function. To characterize the diagnostic sensitivity post-symptom onset, we estimated the coefficients of a logistic regression model 𝑙𝑛 ( 𝒔(𝒕) 𝟏−𝒔(𝒕)) = ∑ 𝜷𝒋(𝒕 − 𝒕𝑺)𝒋𝑵 𝒋=𝟎 , by fitting the function s(t) to diagnostic test-sensitivity data from day zero to 25 days post- symptom onset 6 through the minimization of least squares 𝑅𝑆𝑆 = 𝑚𝑖𝑛 𝛽 ∑ (𝑙𝑛 ( 𝑠(𝑖+𝒕𝑺) 1−𝑠(𝑖+𝒕𝑺)) −𝑙𝑛 ( 𝑠̃𝑖 1−𝑠̃𝑖 )) 2 25 𝑖=0 , where 𝑠̃𝑖denotes the observed diagnostic sensitivity at day i post-symptom onset. The peak infectivity occurs prior to symptom onset from the inferred infectivity curves 4, implying that the infectivity curve is monotonically decreasing over time after symptom onset. To be consistent, the sensitivity should also be monotonically decreasing over time after symptom onset as infectivity (a proxy for the viral load) is decreasing. Therefore, a constraint that the maximum sensitivity after symptom onset occurred at time zero was included in the estimation of the coefficients of the logistic regression model. To select the number of coefficients in the logistic regression model, we used the Akaike information criterion, AIC= 2(𝑁 + 1)+ 26 𝑙𝑛 (𝑅𝑆𝑆), . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 13 where there are N + 1 coefficients being estimated for the 26 data points. The logistic regression model with the lowest AIC value was used to determine the diagnostic sensitivity. We used diagnostic test-sensitivity data from zero to 25 days post-symptom onset 6 and the infectivity profile post-symptom onset 4 to construct a mapping from infectivity to diagnostic sensitivity, then used that mapping to infer the diagnostic sensitivity during the incubation period from the infectivity pre-symptom onset. To infer the diagnostic sensitivity during the unobserved incubation period, we defined an interpolation function for the diagnostic sensitivity based on the Cartesian pairing of r(t) and s(t) from symptom onset. Since the peak of infectivity occurred prior to symptom onset, we performed a slight extrapolation of the function s(t) determined by logistic regression. This extrapolation lies within a small range between the symptom-onset diagnostic sensitivity of 0.96 and an upper limit of 1.0 for each latent period considered, so that our results are not sensitive to this extrapolation. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 14 Supplementary Tables Table S1: Parameter descriptions and values used to assess quarantine and testing strategies Description Parameter Value Reference Basic reproductive number R0 2.5 and 2.0 7 Basic reproductive number for symptomatic infection R0,s R0 2 Basic reproductive number for asymptomatic infection R0,a R0 2 Incubation period tS 8.29 days 8 Duration of disease in asymptomatic individuals te tS + 20 days 9–11 Proportion of infections that are asymptomatic pa 30.8% 22.6% 12,13 13,14 Latent period tL 2.9 1.9 and 3.9 15 . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 15 Supplementary Figures Figure S1. Average infectivity profile for a known time of infection under no self-isolation upon symptom onset (black) and perfect isolation upon symptom onset (yellow line) for ( A) R0 = 2.5 and 30.8% of infections being asymptomatic (resulting in 1.6 secondary infections, yellow fill), (B) R0 = 2 and 30.8% of infections being asymptomatic (resulting in 1.3 secondary infections, yellow fill), (C) R0 = 2.5 and 22.6% of infections being asymptomatic (resulting in 1.5 secondary infections, yellow fill) and (D) R0 = 2 and 22.6% of infections being asymptomatic (resulting in 1.2 secondary infections, yellow fill). . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 16 Figure S2: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 2.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, uniform entry within the incubation period by symptomatic cases, and uniform entry across the disease time course for asymptomatic cases, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 17 Figure S3: For durations of quarantine from 1–21 days, when a symptomatic individual enters quarantine uniformly within the incubation period and asymptomatic individuals enter uniformly across the disease time course, with an incubation period of 8.29 days, a latent period of 2.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 18 Figure S4: With 30.8% of infections asymptomatic, perfect self-isolation of symptomatic infections, and an incubation period of 8.29 days, the optimal day of testing to obtain the minimum post-quarantine transmission specifying a latent period of (A) 2.9 days with uniform entry into quarantine, (B) 2.9 days and entry into quarantine as a traced contact, (C) 1.9 days and uniform entry into quarantine, (D) 1.9 days and entry into quarantine as a traced contact, (E) 3.9 days and uniform entry into quarantine, and (F) 3.9 days and entry into quarantine as a traced contact for a one-day delay in obtaining test results (black) and a negligible delay in obtaining test results (gray). . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 19 Figure S5: With perfect self-isolation of symptomatic infections, an incubation period of 8.29 days and a latent period of 2.9 days, and proportions of from 0–1 of infections being asymptomatic, the probability of post-quarantine transmission (probability of one or more post-quarantine infections) when symptomatic individuals enter quarantine uniformly within the incubation period and asymptomatic individuals enter uniformly across the disease time course, with no testing (red) and when tested on entry and exit from quarantine (blue) for a (A) five-day quarantine and a (B) seven-day quarantine. The exit test was assumed to occur 96 h after entry into quarantine. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 20 Figure S6. Specifying an incubation period of 8.29 days and a latent period of 2.9 days, the probability of post-quarantine transmission accounting for underlying community prevalence in a cohort (crew) of 40 employees for testing on entry (orange), testing on exit (blue), and testing on both entry and exit (purple) for a (A) three-day quarantine, (B) five-day quarantine, (C) seven-day quarantine, and (D) 14- day quarantine. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 21 Figure S7: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 2.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, and entry through contact tracing, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 22 Figure S8: For durations of quarantine from 1–21 days, when an individual enters quarantine through contact tracing, with an incubation period of 8.29 days, a latent period of 2.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 23 Figure S9: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 2.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, and entry through contact tracing with a one-day tracing delay, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 24 Figure S10: For durations of quarantine from 1–21 days, when an individual enters quarantine through contact tracing with a one-day tracing delay, with an incubation period of 8.29 days, a latent period of 2.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post- quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform ju st as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 25 Figure S11: Infectivity profiles of an individual for an incubation period of 8.29 days and assuming no self-isolation upon symptom onset, corresponding to the reported duration of the latent period (2.9, black), and latent periods one day longer (3.9, dashed blue), and one day shorter (1.9, dashed green), and numbers of secondary infections that occur within the incubation period for a 2.9 -day latent period (1.21, black), for a 3.9-day latent period (1.27, blue), and for a 1.9-day latent period (1.24, green). . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 26 Figure S12: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 1.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, uniform entry within the incubation period by symptomatic cases, and uniform entry across the disease time course for asymptomati c cases, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 27 Figure S13: For durations of quarantine from 1–21 days, when a symptomatic individual enters quarantine uniformly within the incubation period and asymptomatic individuals enter uniformly across the disease time course, with an incubation period of 8.29 days, a latent period of 1.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test o n exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 28 Figure S14: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 3.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, uniform entry within the incubation period by symptomatic cases, and uniform entry across the disease time course for asymptomatic cases, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 29 Figure S15: For durations of quarantine from 1–21 days, when a symptomatic individual enters quarantine uniformly within the incubation period and asymptomatic individuals enter uniformly across the disease time course, with an incubation period of 8.29 days, a latent period of 3.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 30 Figure S16: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 1.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, and entry through contact tracing, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 31 Figure S17: For durations of quarantine from 1–21 days, when an individual enters quarantine through contact tracing, with an incubation period of 8.29 days, a latent period of 1.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 32 Figure S18: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 3.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, and entry through contact tracing, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 33 Figure S19: For durations of quarantine from 1–21 days, when an individual enters quarantine through contact tracing, with an incubation period of 8.29 days, a latent period of 3.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 34 Figure S20: Expected post-quarantine infections for durations of quarantine of 0–21 days, with an incubation period of 8.29 days, a latent period of 2.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, uniform entry within the incubation period by symptomatic cases, and uniform entry across the disease time course for asymptomatic cases, with no testing, testing on entry, testing on exit, and testing on entry and exit. Testing on exit is assumed to occur on the last day of quarantine (i.e. there is negligible delay in obtaining the test result). Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 35 Figure S21: For durations of quarantine from 0–21 days, when a symptomatic individual enters quarantine uniformly within the incubation period and asymptomatic individuals enter uniformly across the disease time course, with an incubation period of 8.29 days, a latent period of 2.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Testing on exit is assumed to occur on the last day of quarantine (i.e. there is a negligible delay in obtaining the test results). Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 36 Figure S22: Expected post-quarantine infections for durations of quarantine of 0–21 days, with an incubation period of 8.29 days, a latent period of 2.9 days, 30.8% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, and entry through contact tracing, with no testing, testing on entry, testing on exit, and testing on entry and exit. Testing on exit is assumed to occur on the last day of quarantine (i.e. there is negligible delay in obtaining the test result). Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 37 Figure S23: For durations of quarantine from 0–21 days, when an individual enters quarantine through contact tracing, with an incubation period of 8.29 days, a latent period of 2.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Testing on exit is assumed to occur on the last day of quarantine (i.e. there is a negligible delay in obtaining the test result). Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 38 Figure S24: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 2.9 days, 22.6% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, uniform entry within the incubation period by symptomatic cases, and uniform entry across the disease time course for asymptomatic cases, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 39 Figure S25: For durations of quarantine from 1–21 days, when a symptomatic individual enters quarantine uniformly within the incubation period and asymptomatic individuals enter uniformly across the disease time course, with an incubation period of 8.29 days, a latent period of 2.9 days, with 22.6% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 40 Figure S26: Expected post-quarantine infections for durations of quarantine of 1–21 days, with an incubation period of 8.29 days, a latent period of 2.9 days, 22.6% of infections being asymptomatic, perfect self-isolation of symptomatic infections when symptomatic, and entry through contact tracing, with no testing, testing on entry, testing on exit, and testing on entry and exit. Because of the time required to obtain test results, sampling for the test on exit was assumed to occur the day before the quarantine was completed. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 41 Figure S27: For durations of quarantine from 1–21 days, when an individual enters quarantine through contact tracing, with an incubation period of 8.29 days, a latent period of 2.9 days, with 22.6% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections) with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indic ate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 42 Figure S28: For an incubation period of 8.29 days, the diagnostic sensitivity of the RT -PCR test over the time course of disease (A) determined using a logistic regression model (black line) fit to the empirical data of SARS CoV-2 test results from Miller et al 6(red dots) through minimization of least squares and AIC model selection, and (B) specifying latent periods of 2.9 days (black), 1.9 days (green), and 3.9 days (blue). . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 43 Figure S29: For durations of quarantine from 1–21 days, when a symptomatic individual enters quarantine uniformly within the incubation period and asymptomatic individuals enter uniformly across the disease time course, with an incubation period of 8.29 days, a latent period of 2.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections), assuming infections are Poisson distributed, with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a background color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 44 Figure S30: For durations of quarantine from 1–21 days, when an individual enters quarantine through contact tracing, with an incubation period of 8.29 days, a latent period of 2.9 days, with 30.8% of infections being asymptomatic, and perfect self-isolation of symptomatic infections, (A) the probability of post-quarantine transmission (probability of one or more post-quarantine infections), assuming infections are Poisson distributed, with no testing, when tested upon entry to quarantine, when tested on exit from quarantine, and when tested on entry and exit from quarantine, and (B) the durations of quarantine with testing on entry, testing on exit, and testing on entry and exit that perform just as well or better than a quarantine with no testing. Because of the time required to obtain test results, sampling for the test on exit is assumed to occur the day before the quarantine is complete. Cells that share a

color in common indicate equivalent durations of quarantine associated with each of the testing strategies. . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 45 Figure S31: Probability density functions for when during the disease time course cases enter quarantine, including (A) the day of disease time course in which a contact infected by an index case enters quarantine (black) compared to the uniform entry into quarantine of a case to exhibit symptoms (blue) and an asymptomatic case (red), and (B) the day of disease time course in which the asymptomatic contact that infected the index case enters quarantine (black) compared to the uniform entry into quarantine of an asymptomatic case (red). . CC-BY-NC-ND 4.0 International licenseIt 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)preprint The copyright holder for thisthis version posted November 30, 2020. ; https://doi.org/10.1101/2020.10.27.20211631doi: medRxiv preprint 46

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