key: cord-0831612-p3ek0qdi
authors: Ashcroft, P.; Lehtinen, S.; Bonhoeffer, S.
title: Quantifying the impact of quarantine duration on COVID-19 transmission
date: 2020-09-25
journal: nan
DOI: 10.1101/2020.09.24.20201061
sha: dec1eb75a9177908f4490e0ed93e11a44f8ae071
doc_id: 831612
cord_uid: p3ek0qdi

The numbers of confirmed cases of SARS-CoV-2 infection are increasing in many places. Consequently, the number of individuals placed into quarantine is increasing too. The large number of individuals in quarantine has high societal and economical costs, as well as infringing on the freedom of the individual. This has led to a vigorous debate about the duration of quarantine, particularly in light of the potentially low specificity of quarantine (i.e. low probability of quarantined individuals indeed being infected). We present a mathematical model that leverages empirically determined distributions of incubation period, infectivity, and generation time to quantify how the duration of quarantine affects transmission. With this model we address the impact of shortening the quarantine for returning travellers and traced contacts of confirmed cases, both in terms of prevented transmission and the ratio of prevented transmission to days spent in quarantine. We also consider the impact of i) test-and-release strategies; ii) additional hygiene measures imposed upon release after a negative test; iii) the development of symptoms during quarantine; iv) the relationship between quarantine duration and adherence; and v) the specificity of quarantine. When considering the benefit versus cost utility of quarantine, we find that the diminishing impact of longer quarantine on transmission prevention may support a quarantine duration below 10 days, particularly for returning travellers. A greater gain of utility can be achieved through a test-and-release strategy, and this can be even further strengthened by imposed hygiene measures post-release. We also find that unless a test-and-release strategy is considered, the specificity of quarantine does not affect the optimal duration of quarantine. Therefore, the argument that we should shorten quarantine because of lack of specificity is misguided.

have been identified as a recent close contact of a confirmed case by contact tracing, or Using this model, we explore multiple factors that affect the duration of quar-64 antine. Specifically we address how test-and-release strategies affect the fraction of between these distributions can be found in Lehtinen Fig. 1 The timeline of quarantine. Individuals are exposed to an infector at time t E , and then quarantined at time t Q . Under the standard quarantine protocol, this individual is quarantined until time t R , and no onward transmission is assumed to occur during this time. Under the test-and-release protocol, quarantined individuals are tested at time t T and released at time t R − if they receive a negative test result. Otherwise the individual remains in quarantine until t R + .

Ultimately, the fraction of transmission prevented by the quarantine of an infected . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 

(1)

If only a fraction s of the individuals placed in quarantine are infected, then the aver-103 age reduction in transmission across all individuals in quarantine is sF. We refer to s 104 as the specificity of quarantine.

A further quarantine strategy is to prematurely release individuals who produce a 107 negative test result during the quarantine. As illustrated in Fig. 1 

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The copyright holder for this this version posted September 25, 2020. 123 We further consider the possibility of a reduced quarantine, where individuals re-124 leased after a negative test are asked to maintain strict hygiene, mask wearing, and 125 social distancing protocols until t R + . We assume transmission is reduced by a fraction 126 r due to these protocols, and hence the onward transmission prevented by quarantin-127 ing an infected individual is

where the extra term is the transmission prevented by the reduced quarantine when 129 an infected individual is prematurely released from quarantine. 131 We consider the scenarios of a traced contact and a returning traveller differently,

because the values of t E , t Q , and t R are implemented differently in each case. 5 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 25, 2020. . 142 Following a positive test result, a confirmed index case has their recent close contacts 143 traced. From contact tracing interviews, we know when these traced contacts were 144 last exposed to the index case (t E ) relative to the symptom onset of the index case 145 (t = 0). The contacts are then placed into quarantine at time t Q = ∆ Q , where ∆ Q is 146 the sum of the delay to the index case receiving a positive test result after developing 147 symptoms and the further delay to tracing the contacts. Under the standard quaran-148 tine procedure, the traced contacts are quarantined until day t R = t E + n, i.e. they 149 are quarantined until n days after there last exposure. Note that the time spent in 150 quarantine is t E + n − ∆ Q , which is shorter than n.

The expected onward transmission (from an infected contact) that is prevented 

(4), is

which depends on the specificity s. However, comparing two different strategies n 169 and n through their relative utility, i.e. U(n )/U(n), eliminates this dependence on s.

Therefore, the argument that we should shorten quarantine because of lack of speci-171 ficity is misguided. By calculating the relative utility we observe that there exists an 172 optimal strategy which maximises the benefit/cost ratio (Fig. 3B ). This would be a 173 duration of six to eight days, depending on the delay to starting quarantine ∆ Q .

Testing and releasing 175 We consider a test-and-release strategy where quarantined individuals are tested x 176 days after exposure and released if the test result is negative. As above, quarantine

Individuals with a negative test result are 179 released, otherwise they remain in quarantine until time t R + = t E + n. 

(4), is

We can now compare the test-and-release strategy of duration n and test day x with 194 standard quarantine of duration n using the relative utility U test (n , x)/U(n), which 195 now depends on the specificity s. Based on this metric of utility, we see that early 196 7 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 6)]. We use t E = 0, which from the infectivity profile is the mean infection time of contacts if the index case develops symptoms at t = 0, and ∆ Q = 3 as the delay until quarantine begins. Individuals are tested on day x after exposure (colour) and released on day x + 2 if negative (we assume it takes ∆ T = 2 days to receive a test result). We assume a specificity of s = 0.1 and that there are no false-positive test results. Dotted lines in both panels assume the released individuals have a 50% reduced transmission (r = 0.5) due to extra hygiene and social distancing measures imposed by reduced quarantine [Eq. (3)].

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The copyright holder for this this version posted September 25, 2020. . https://doi.org/10.1101/2020.09.24.20201061 doi: medRxiv preprint testing is the optimal strategy (Fig. 4B) . Testing on day five and releasing on day seven (we consider a fixed delay ∆ T = 2 days) with a quarantine duration of n = 10 198 days has a relative utility of 1.5 compared to a standard 10 day quarantine, but with 199 transmission only reducing from 90% to 82%. Another factor that can affect the efficacy of quarantine is the level of adherence to 210 a given strategy. For a quarantine duration of n days, a fraction α(n) of identified 211 contacts will adhere to the strategy, while a fraction 1 − α(n) will ignore the guideline.

Hence the fraction of transmission prevented due to quarantine is sα(n)F(n), where 213 again s is the specificity of quarantined individuals which we assume is independent 214 of n. We expect α(n) to be a decreasing function of n, i.e. longer quarantines have a 215 lower adherence. For two quarantine strategies with durations n and n to have the 216 same overall efficacy, the adherences must satisfy

In other words, the change in the fraction of transmission prevented by quarantine 218 must be compensated by an inverse change in the adherence. Shortening the dura-219 tion of quarantine from 10 days to 5 days would require more than twice as many 220 individuals to adhere to the quarantine guidelines in order to maintain the same over-221 all efficacy (Fig. 5A ). If quarantine is shortened further, then the required increase in . We fix ∆ Q = 3 as the delay until quarantine, and t S = 5, which is the mean incubation time. The curve for a = 1 corresponds to Fig. 3A . In both panels we use t E = 0, which is the mean infection time of secondary cases based on the infectivity profile.

tantly, this individual would be removed from the population regardless of quaran-232 tine, so the reduction of cases due to their isolation should not be counted towards the 233 efficacy of quarantine.

Let a be the fraction of asymptomatic cases, who will be quarantined using the 235 standard strategy from time t Q = ∆ Q until t R = t E + n. We assume that the symp-236 tomatic cases would anyway be isolated once they develop symptoms (at time t S as 237 described by the incubation period distribution, Fig. 2C ), so these individuals are 238 effectively quarantined until t R = min(t E + n, t S ). Therefore, for each traced con-239 tact who is put into quarantine, the fraction of infections that would be prevented by

The fraction of transmission prevented by quarantine is an increasing function of the 242 fraction of asymptomatic cases (Fig. 5B ). This means that we likely overestimate the 243 efficacy of quarantine as we are also counting transmission that is prevented by isola-244 tion following a positive test result. 

. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 25, 2020. . https://doi.org/10.1101/2020.09.24.20201061 doi: medRxiv preprint fection dynamics. As the relative utility [Eq. (9)] is independent of the specificity s, the prevalence of disease in the travel destination (which should correlate the frac-273 tion of travellers becoming infected at that destination) does not influence the optimal 274 quarantine duration.

Testing and releasing 276 If a returning traveller is tested at time t T = x during quarantine then they are released 277 on day t R − = x + ∆ T if the test is negative, or else kept in quarantine until day t R + = n.

The fraction of transmission prevented by quarantining an infected traveller [F test ; Eq.

(2)] accounts for false-negative test results. We show that there is little increase in 280 transmission if quarantine is shortened for returning travellers who are tested on day 281 x (Fig. 7A) . However, the timing of the test has a significant impact on prevented 282 transmission. Standard quarantine for ten days prevents 73% of transmission, testing 283 on day five and releasing on day seven prevents 72% of transmission, but testing upon 284 return at day zero only prevents 31% of transmission. (1)] B) The relative utility of different test-and-release quarantine durations compared to standard quarantine with duration n = 10 days, i.e. U test (n , x)/U(10). We consider a travel duration of y = 7 days and we assume infection can occur on any day −y ≤ t E ≤ 0 with uniform probability. Individuals are tested on day x (colour) after returning on day 0 and released on day x + 2 if negative (we assume it takes ∆ T = 2 days to receive a test result). We assume a specificity of s = 0.1 and that there are no false-positive test results. Dotted lines in both panels assume the released travellers have a 50% reduced transmission (r = 0.5) due to extra hygiene and social distancing measures imposed by reduced quarantine [Eq. (3) ].

Again the function F test shown in Fig. 7A describes only the epidemiological bene-286 fit of quarantining individuals. The average duration of quarantine will be x + ∆ T + 287 12 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

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Comparing the test-and-release strategy of duration n and test day x with standard 289 quarantine using the relative utility, i.e. U test (n , x)/U(n), we see that shortening the 290 duration of quarantine from 10 days (with x fixed) has small positive impact on the 291 utility, but early testing greatly reduces the average duration of quarantine and hence 292 leads to increased utility (Fig. 7B ). Enforcing additional hygiene and social distancing 293 guidelines following a negative test and release, we see large increases in both efficacy 294 and utility for early testing strategies, but with diminishing returns as the time at 295 which tests are conducted is increased (dotted lines in Fig. 7) . We note that the relative 296 utility of the test-and-release strategy depends on the specificity of quarantine s, and 297 this specificity may change depending on disease prevalence at the travel destination 298 and the duration of travel. E.g., the infected fraction of travellers returning from a long 299 stay in a high-risk country is likely to be higher than the infected fraction of travellers 300 returning from a short stay to a low risk country. In Fig. 7B we keep s fixed. are also counting transmission that is prevented by isolation (Fig. 8B) .

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The copyright holder for this this version posted September 25, 2020. Fig. 8 A) The change in adherence needed to maintain quarantine efficacy of the n = 10 day strategy if we change the quarantine duration to n days (x-axis), i.e. α(n )/α(10). B) The impact of symptomatic cases on the fraction of total onward transmission per quarantined traveller that is prevented by quarantine. We fix the travel duration to y = 7 days and assume t E is uniformly distributed between −y and 0. The curve a = 1 corresponds to Fig. 6 . We use the mean incubation time of five days, such that t S = t E + 5. the optimal duration of quarantine. Therefore, the argument that we should shorten 335 quarantine because of lack of specificity is misguided.

To further improve the utility of quarantine, the quarantined individuals can be 337 tested and released given a negative result. This test-and-release strategy will lead to 338 14 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

The copyright holder for this this version posted September 25, 2020.

an increase in the specificity of quarantine, and a lower average quarantine duration across infected and non-infected individuals. However, due to the considerable false-340 negative probability of the PCR test (Kucirka et al., 2020), this strategy also leads to 341 increased transmission as infectious individuals are prematurely released. Neverthe-342 less, a strategy of testing on day five and releasing negative cases on day seven carries 343 a 1.5-fold increase in utility compared to a standard 10 day quarantine for traced con-344 tacts.

An argument for shortening the duration of quarantine is that it could lead to 346 higher adherence. We quantify the increase in adherence that is required to maintain 347 quarantine efficacy if the duration of quarantine is modified. Halving the duration 348 from 10 days to 5 days would require more than twice as many individuals to enter 349 quarantine to maintain the same efficacy. If quarantine is shortened further then the 350 required increase in adherence would be too much to achieve. Hence this argument is 351 limited in its usefulness. to find the potentially exposed individuals in a short time, as well as surveillance of 367 disease prevalence to identify high-risk travel. Further improving the speed and accu-368 racy of testing will allow average quarantine durations to be shorter, which increases 369 the benefit to cost ratio of quarantine. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) preprint

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COVID-19 Infectivity Profile Correction

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