Research Article

Microbiology and Infectious Disease

Revisiting the guidelines for ending isolation for COVID-19 patients

interdisciplinary Biology Laboratory (iBLab), Division of Biological Science, Graduate School of Science, Nagoya University, Japan
Department of Mathematics, Pusan National University, Republic of Korea
Department of Epidemiology and Biostatistics, Indiana University School of Public Health-Bloomington, United States
International Research Center for Neurointelligence, The University of Tokyo, Japan
Department of Virology II, National Institute of Infectious Diseases, Japan
Research Center for Drug and Vaccine Development, National Institute of Infectious Diseases, Japan
Department of Applied Biological Science, Tokyo University of Science, Japan
Department of Infectious Diseases, Nagasaki University Graduate School of Biomedical Sciences, Japan
Division of Respirology, Rheumatology, Infectious Diseases, and Neurology, Department of Internal Medicine, Faculty of Medicine, University of Miyazaki, Japan
Institute of Mathematics for Industry, Kyushu University, Japan
Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University, Japan
NEXT-Ganken Program, Japanese Foundation for Cancer Research (JFCR), Japan
Science Groove Inc, Japan
Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, United States

Jul 27, 2021

https://doi.org/10.7554/eLife.69340

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Accepted for publication after peer review and revision.

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Version of Record published: July 27, 2021 (This version)
Accepted: July 2, 2021
Received: April 12, 2021

1. Part of Collection
COVID-19: A Collection of Articles

Edited by Diane M Harper et al.
Further reading

Abstract
Introduction
Results
Discussion
Materials and methods
Appendix 1
Data availability
References
Decision letter
Author response
Article and author information
Metrics

Abstract

Since the start of the COVID-19 pandemic, two mainstream guidelines for defining when to end the isolation of SARS-CoV-2-infected individuals have been in use: the one-size-fits-all approach (i.e. patients are isolated for a fixed number of days) and the personalized approach (i.e. based on repeated testing of isolated patients). We use a mathematical framework to model within-host viral dynamics and test different criteria for ending isolation. By considering a fixed time of 10 days since symptom onset as the criterion for ending isolation, we estimated that the risk of releasing an individual who is still infectious is low (0–6.6%). However, this policy entails lengthy unnecessary isolations (4.8–8.3 days). In contrast, by using a personalized strategy, similar low risks can be reached with shorter prolonged isolations. The obtained findings provide a scientific rationale for policies on ending the isolation of SARS-CoV-2-infected individuals.

Introduction

Since the first case of a novel coronavirus (SARS-CoV-2) was identified in China in December of 2019, its associated disease, COVID-19, spread quickly around the world, with the number of cases reaching 80 million by the end of 2020. During this time, nonpharmaceutical interventions (NPIs) were used on a massive scale to suppress or mitigate SARS-CoV-2 transmission (Cowling et al., 2020). As of January 2021, several countries had started vaccination campaigns aimed at controlling SARS-CoV-2 spread (Centers for Disease Control and Prevention, 2021). Still, until such vaccination programs reach a sizable fraction of the population, NPIs will likely continue to play a crucial role for epidemic control (Yang et al., 2021a).

A simple but effective NPI is the isolation of SARS-CoV-2-infected individuals. This can be done either in the infected person’s place of residence (as is the case for most Western countries [European Centre for Disease Prevention and Control, 2020b]) or in dedicated facilities (as is the case in China [Burki, 2020]). In both cases, a criterion for determining when to end the isolation phase is needed. Although a longer isolation period may decrease the chance of transmission, it also entails both a higher burden on the mental and physical health of the patient (Mian et al., 2021) and cause higher economic loss (Ash et al., 2021). Scientifically sound guidelines for determining when to end isolation are thus warranted.

So far, two main approaches have been adopted by countries around the globe. The first approach is to isolate patients for a fixed time period (i.e. a one-size-fits-all approach). For example, the Centers for Disease Control and Prevention (CDC) created guidelines for health care practitioners concerning the discontinuation of transmission-based precautions for COVID-19 patients in health care settings that are based on the time since symptom onset or disappearance (i.e. symptom-based strategy) (Centers for Disease Control and Prevention, 2020a). In the CDC guidelines, those with mild to moderate illness can end isolation (or precautions) when the following three conditions are met: ‘At least 10 days have passed since symptoms first appeared,’ ‘At least 24 hr have passed since last fever without the use of fever-reducing medications,’ and ‘Symptoms (e.g. cough, shortness of breath) have improved.’ However, such a one-size-fits-all approach does not account for the individual variability in viral load (Iwanami et al., 2020), which is associated with both severity (Zheng et al., 2020) and persistence of symptoms (Long et al., 2020), and may thus not fully prevent further transmission.

The second approach is based on the assessment of the viral load of each isolated patient (i.e. personalized approach), and isolation ends when the viral load drops below a certain threshold value, which is associated with a low risk of further spreading the pathogen (He et al., 2020). The viral load can be measured by reverse transcription polymerase chain reaction (PCR), which can be used not only for diagnosing infection but also in determining when to end the isolation period. As an example, the CDC recommends using PCR testing in particular circumstances, such as for patients with severe immunodeficiency. The guidelines include both the resolution of symptoms and PCR test results, that is, ‘Results are negative from at least two consecutive respiratory specimens collected ≥24 hr apart’ (Centers for Disease Control and Prevention, 2020a).

The purpose of this study was to assess whether the personalized approach based on PCR test results minimizes the length of the isolation period while limiting the risk of prematurely releasing infectious individuals as compared with the one-size-fits-all approach. Moreover, we define best practices for the use of a PCR-based personalized approach. To do so, we developed a mathematical model of SARS-CoV-2 viral load dynamics (Ejima et al., 2020; Iwanami et al., 2020) that accounts for individual heterogeneity and is calibrated on longitudinal viral load data.

Results

Descriptive statistics

We identified four papers meeting the inclusion criteria (Kim et al., 2020a; Wölfel et al., 2020; Young et al., 2020; Zou et al., 2020). Among the patients reported in these four studies, 30 patients (approximately 60% of the participants in the original studies) met our inclusion criteria (Table 1). Three studies were from Asia and one was from Europe. The lowest and highest detection limit among those studies were 15.3 copies/mL and 68 copies/mL, respectively. These are relatively lower than the commonly used threshold values (the median was 100 copies/mL [Fung et al., 2020; Giri et al., 2021; van Kasteren et al., 2020]). The data were collected by February of 2020, which was during the early phase of the COVID-19 pandemic. Participants were hospitalized patients of ages ranging from 28 to 78 years; the sex ratio was mostly even.

Table 1

Summary of the viral load data used for modeling.

Source	Country	# of included (excluded) patients	Sampling site	Reporting unit	Detection limit (copies/mL)	Symptom onset of patients	Age^‡	Sex (M:F)
Young et al.	Singapore	12 (6)	nasopharynx	cycle threshold^*	68.0	1/21 - 1/30	37.5 (31–56)	6:6
Zou et al.	China	8 (8)	nose	cycle threshold^*	15.3	1/11 - 1/26	52.5 (28–78)	3:5
Kim et al.	Korea	2 (7)	nasopharynx and oropharynx	cycle threshold^*	68.0	NA	NA	NA
Wölfel et al.	Germany	8 (1)	pharynx	viral load (copies/swab)^†	33.3	1/23 - 2/4	NA	NA

*Viral load was calculated from cycle threshold values using the conversion formula: $\log_{10} (Viral \ load \ [copies/mL]) = - 0.32 \times Ct \ values \ [cycles] + 14.11$ (Peiris et al., 2003).

† One swab = 3 mL (Wölfel et al., 2020).
‡ Median (range).

Model fitting

Three models were fitted to the data: the baseline model, the ‘eclipse phase’ model, and the ‘innate immune response’ model. The estimated model parameters, the estimated (mean) curves and the individual fitted curves are reported in Supplementary file 1, Figure 1, respectively. Although all the three models lead to similar results (Figure 1), the baseline model shows a longer tail than the two other models, due to the lower estimated death rate of infected cells (Supplementary file 1). Further, the three models showed similar values of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) (Supplementary file 2). Unless otherwise stated, the results presented in thereafter refer to the baseline model.

Figure 1 with 1 supplement see all

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Estimated viral load curves from the three analyzed models.

The solid lines are the estimated viral load curves of the three models for the best fit parameters (Blue: baseline model, Green: ‘ecliplse phase’ model, Yellow: ‘innate immune response’ model). The shaded regions correspond to 95% predictive intervals. The 95% predictive interval was created using bootstrap approach.

Figure 1—source data 1 Estimated viral load curves from the three analyzed models. The numbers in parentheses are the 95% empirical CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig1-data1-v1.docx
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One-size-fits-all approach

By considering a fixed time of 10 days since symptom onset as the criterion for ending isolation, the probability of releasing patients who are still infectious was estimated to be 0.9% (95%CI: 0.6 to 1.2), with a lengthy prolonged isolation of 6.8 days (95% empirical CI: 1 to 8) when considering 10⁵ copies/mL as the infectiousness threshold value (Figure 2AB). The estimated probability of prematurely ending isolation becomes 6.6% (95%CI: 5.8 to 7.4) and 0% with a prolonged isolation of 4.8 days (95% empirical CI: −2 to 8) and 8.3 days (95% empirical CI: 6 to 10) if we consider 10^4.5 and 10^5.5 copies/mL as infectiousness threshold values, respectively (Figure 2A). To guarantee a probability lower than 5%, we estimated that patients need to be isolated for 7 days, 11 days, and 5 days for infectiousness threshold values of 10^5.0, 10^4.5, and 10^5.5 copies/mL, respectively (Figure 2A). In this case, again, the length of the prolonged isolation was estimated to be substantial (Figure 2B): 3.8 days (95% empirical CI: −2 to 5), 5.8 days (95% empirical CI: −2 to 8), and 3.3 days (95% empirical CI: 0 to 4) for infectiousness threshold values of 10^5.0, 10^4.5, and 10^5.5 copies/mL, respectively. In sum, to guarantee low probabilities to prematurely end the isolation and thus release patients who are still infectious, the associate cost is to have unnecessary long isolations for the majority of patients.

Figure 2

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One-size-fits-all approach.

(A) Probability of prematurely ending the isolation of infectious patients for different lengths of the isolation period and for different infectiousness threshold values. (B) Mean length of unnecessarily prolonged isolation for different lengths of the isolation period and for different infectiousness threshold values. Color keys and symbols apply to both panels. Note that the symbols correspond to the shortest isolation periods when the condition is met.

Figure 2—source data 1 Probability of prematurely ending isolation and mean length of unnecessarily prolonged isolation under the one-size-fits-all approach. The numbers in parentheses are the 95% empirical CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig2-data1-v1.docx
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Personalized approach using PCR test results

By considering two consecutive negative test results repeated at an interval of 1 day as the criterion for ending isolation, the probability of prematurely ending isolation was estimated to be 8.1% (95%CI: 7.2 to 9.0) with a negligible length of prolonged isolation of 1.2 days (95% empirical CI: −1 to 3) when considering 10^5.0 copies/mL as the infectiousness threshold value (Figure 3A). By acting on the testing strategy, we can control both the probability of prematurely ending isolation and the length of prolonged isolation. The probability of ending isolation of infectious patients decreased with a longer interval between testing and more consecutive negative results (the upper panel in Figure 3A). However, the length of prolonged isolation increased at the same time (the lower panel in Figure 3A). If a 5% or lower risk of prematurely ending isolation is considered, three consecutive negative test results with the tests performed every day minimizes the length of unnecessary isolation (2.3 days [95% empirical CI: 0 to 5]) (Figure 3A). We repeated the same analyses using different infectiousness threshold values (10^4.5 and 10^5.5 copies/mL). Both the probability of prematurely ending isolation and the length of prolonged isolation were not much influenced by infectiousness threshold values, because the viral load is directly measured in the personalized approach (Figure 3B,C).

Figure 3

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Personalized approach.

(A) Probability of prematurely ending isolation (upper panels) and mean length of unnecessarily prolonged isolation (lower panels) for different values of the interval between PCR tests and the number of consecutive negative results necessary to end isolation; the infectiousness threshold value is set to 10^5.0 copies/mL. The areas surrounded by purple and pink dotted lines are those with 1% or 5% or lower of risk of prematurely ending isolation of infectious patients, respectively, and the triangles and circles correspond to the conditions which realize the shortest prolonged isolation within each area. (B) Same as A, but for an infectiousness threshold value of 10^4.5 copies/mL. (C) Same as A, but for an infectiousness threshold value of 10^5.5 copies/mL. Color keys and symbols apply to all panels.

Figure 3—source data 1 Probability of prematurely ending isolation of infectious patients with different guidelines (with 10^5.0 copies/mL as an infectiousness threshold value). The cell with numbers in bold corresponds to the baseline. The numbers in parentheses are the 95% CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig3-data1-v1.docx
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Figure 3—source data 2 Length of unnecessarily prolonged isolation with different guidelines (with 10^5.0 copies/mL as an infectiousness threshold value). The cell with numbers in bold corresponds to the baseline. The numbers in parentheses are the empirical 95% CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig3-data2-v1.docx
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Figure 3—source data 3 Probability of prematurely ending isolation of infectious patients with different guidelines (with 10^4.5 copies/mL as an infectiousness threshold value). The cell with numbers in bold corresponds to the baseline. The numbers in parentheses are the 95% CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig3-data3-v1.docx
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Figure 3—source data 4 Length of unnecessarily prolonged isolation with different guidelines (with 10^4.5 copies/mL as an infectiousness threshold value). The cell with numbers in bold corresponds to the baseline. The numbers in parentheses are the empirical 95% CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig3-data4-v1.docx
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Figure 3—source data 5 Probability of prematurely ending isolation of infectious patients with different guidelines (with 10^5.5 copies/mL as an infectiousness threshold value). The cell with numbers in bold corresponds to the baseline. The numbers in parentheses are the 95% CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig3-data5-v1.docx
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Figure 3—source data 6 Length of unnecessarily prolonged isolation with different guidelines (with 10^5.5 copies/mL as an infectiousness threshold value). The cell with numbers in bold corresponds to the baseline. The numbers in parentheses are the empirical 95% CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig3-data6-v1.docx
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Comparison between the one-size-fits-all and the personalized approach

To highlight the differences between the one-size-fits-all and the personalized approaches, we systematically compared the two approaches by looking at the length of the prolonged isolation for a 5% or lower (Figure 4A) or 1% or lower (Figure 4B) risk of prematurely ending isolation. For the personalized approach, the best combination of the number of consecutive negative test results and the interval of tests was selected for each infectiousness threshold value. The personalized approach was not influenced by the infectiousness threshold values and yielded to shorter prolonged isolation compared with the one-size-fits-all approach. However, because the prolonged isolation for the one-size-fits-all approach was influenced by infectiousness threshold values, the difference between the one-size-fits-all and personalized approaches in prolonged isolation became smaller with higher infectiousness threshold values.

Figure 4

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Comparison between the one-size-fits-all and the personalized approach.

(A) Mean length of prolonged isolation for different infectiousness threshold values and for the two approaches when considering a 5% or lower risk of prematurely ending isolation. Note that for the personalized approach, the interval between PCR tests and the number of consecutive negative results necessary to end isolation were selected to minimize the duration of prolonged isolation. (B) Same as A, but considering a 1% or lower risk of prematurely ending isolation. Color keys apply to both panels.

Figure 4—source data 1 Mean length of unnecessarily prolonged isolation (days) with different guidelines and infectiousness threshold values controlling the risk of prematurely ending isolation ≤ 5% and ≤ 1%. The numbers in parentheses are the empirical 95% CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig4-data1-v1.docx
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Influence of model selection

Figure 5 shows the length of the prolonged isolation for a 5% or lower or 1% or lower risk of prematurely ending the isolation for all the analyzed models. Regardless of the considered models, the personalized approach allows shorted length of unnecessarily isolation. Nonetheless, it is important to remark that the length of prolonged isolation is slightly different among the analyzed models. For example, under the one-size-fits-all approach, it was longer for the ‘innate immune response’ model as compared with the other two; this is due to larger variability in viral load especially at the late phase of the infection (Figure 1). Under the personalized approach, the length of prolonged isolation was longer in the baseline model as compared to the two alternative models (Figure 1). In summary, by comparing the three models, we can conclude that the one-size-fits-all approach is sensitive to the variability of the viral load curve, whereas the personalized approach is sensitive to the decay speed of the viral load.

Figure 5

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Comparison between alternative models.

(A) Mean length of prolonged isolation for different infectiousness threshold values and for the two approaches when considering a 5% or lower risk of prematurely ending isolation and for the three analyzed models. Note that for the personalized approach, the interval between PCR tests and the number of consecutive negative results necessary to end isolation were selected to minimize the duration of prolonged isolation. (B) Same as A, but considering a 1% or lower risk of prematurely ending isolation. Color keys apply to both panels.

Figure 5—source data 1 Mean length of unnecessarily prolonged isolation (days) with different guidelines and infectiousness threshold values controlling the risk of prematurely ending isolation ≤ 5% and ≤ 1% for the three analyzed models. The numbers in parentheses are the empirical 95% CI.: https://cdn.elifesciences.org/articles/69340/elife-69340-fig5-data1-v1.docx
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Discussion

Guidelines for ending the isolation of COVID-19 patients that balance the risk of prematurely ending isolation with the burden of prolonged isolation are a crucial topic of discussion. Here, we propose a highly flexible modeling framework to quantify both viral dynamics and measurement errors. Using this approach, we tested alternative policies regulating the isolation of SARS-CoV-2-infected individuals by accounting for individual variability in the immune response. We estimated the probability of prematurely ending isolation and the length of unnecessarily prolonged isolation with two approaches: the one-size-fits-all approach and the personalized approach using PCR test results.

By considering a risk of 5% or lower of prematurely ending the isolation of a SARS-CoV-2-infected individual, our central estimate for the one-size-fits-all approach requires an isolation period of 7 days after symptom onset, with a prolonged isolation phase lasting about 4 days, depending on the threshold for infectiousness considered. On the other hand, the personalized approach entails a prolonged isolation phase of approximately 2 days, independently of the considered infectiousness threshold values. The better performance of the personalized approach is not surprising. In this approach, viral load is observed directly and is compared against the threshold by using PCR test results. By contrast, the one-size-fits-all approach considers only the time since symptom onset and does not refer to viral load, which has substantial interindividual variation. Further, the personalized approach can be optimized by choosing the best testing schedule (i.e. interval of testing and the number of consecutive negative test results). However, it should be noted that the personalized approach is more costly, due to the need for performing multiple PCR tests, thus entailing logistic challenges because patients need to be tested by health care professionals. The logistics of testing isolated patients is particularly challenging in Western countries, where patients not requiring hospital care are isolated in their place of residence (European Centre for Disease Prevention and Control, 2020b), in contrast with countries like China, where they are isolated in dedicated facilities (Burki, 2020). The development of PCR tests using saliva samples may help to overcome some of these challenges, promising to decrease the work burden and lower the risk of infection for health care workers (Azzi et al., 2020; Tu et al., 2020; Wyllie et al., 2020). Indeed, the viral load measured from saliva is comparable to or slightly higher than that from nasopharyngeal samples, which guarantees a similar level of sensitivity (Tu et al., 2020; Wyllie et al., 2020).

In this study, we used PCR tests to define the end of an isolation period in the personalized approach. PCR tests provides quantitative viral load estimates, which can be directly compared against the infectiousness threshold. Meanwhile, reverse transcription loop-mediated isothermal amplification (RT-LAMP) tests and rapid antigen tests for SARS-CoV-2 have been developed and recommended for repeated screenings, given that they are less expensive and with a shorter turnaround time than PCR tests (less than an hour vs. a day or two) (Butler et al., 2021; Dao Thi et al., 2020; Larremore et al., 2021; Yang et al., 2021b). Although these tests have lower sensitivity (the detection limit is about 10^5.0 copies/mL; Butler et al., 2021; Dao Thi et al., 2020; Miyakawa et al., 2021; Yang et al., 2021b) than PCR tests, they can help mitigating SARS-CoV-2 transmission when used for population screenings (Larremore et al., 2021) and contact tracing (Quilty et al., 2021); in fact, the viral load threshold of infectiousness is considered to be higher than the detection limits of RT-LAMP tests and rapid antigen tests. Epidemiological studies are needed to assess whether isolation strategies based on RT-LAMP or rapid tests have a similar mitigation effect to those based on PCR testing.

Two guidelines for ending isolation were considered in this study. In most countries, the one-size fits-all approach is employed; however, the duration is slightly different among countries. The WHO recommends isolation for 10 days after symptom onset or a positive test for asymptomatic individuals (World Health Organization, 2020). The ECDC recommends isolation of 10 or 20 days for mild/moderate or severe cases, respectively, whereas for asymptomatic individuals, 10 days isolation after a positive test is recommended (European Centre for Disease Prevention and Control, 2020a). However, these durations actually vary from 7 to 14 days depending on each member state of the European Union (European Comission, 2020).

We submit that our approach can be used as a scientific backup or to adjust isolation guidelines currently in use in different countries. Nonetheless, the following limitations should be kept in mind. First, the number of samples analyzed were relatively small (30 patients), they did not cover all age groups, and pertained to symptomatic hospitalized patients only. This did not allow us to test whether the duration of the isolation is influenced by the severity of the disease. In particular, the duration may be shorter than that predicted in this study, as the analyzed samples were composed by hospitalized patients. Guidelines considering fixed durations of the isolation depending on disease severity may be easier to implement and limit the length of unnecessary prolonged isolations. Still concerning the analyzed sample, it is important to stress that patients were infected in the early stages of the pandemic and thus likely infected by the historical SARS-CoV-2 lineages. To what extent our findings can be generalized to other categories of individuals (e.g. asymptomatic infections) and SARS-CoV-2 variants remains to be seen. The confidence intervals reported in this paper need to be cautiously interpreted as the extent and quality of relevant viral load data is unfortunately quite limited. Further, should the input data be non-representative, this could have caused a bias in our estimates of the duration of the isolation period. It is, however, important to stress that exactly in light of this scarcity of longitudinal data, model-based simulations are a powerful tool for properly integrating temporal trends in the collected data and for assessing individual variabilities. Second, we did not explicitly model the longitudinal clinical course of symptoms in SARS-CoV-2-infected individuals because of the lack of data associating the clinical course with viral load. Further research in this direction is warranted (He et al., 2020), especially as several countries (including the US) consider the presence or absence of symptoms among the criteria for ending isolation. Third, a deeper knowledge of the association between the viral load and the transmission risk would be a key to narrow the uncertainty surrounding the minimum viral load level that still allows SARS-CoV-2 transmission. Specifically, 10^4.5, 10^5.0, and 10^5.5 copies/mL were used and were based on epidemiological observations of transmission events from contact tracing data (Hu et al., 2020; Sun et al., 2021). Other studies used a different perspective to approach the same research question and investigated the threshold relying on experimental virological data (i.e. culturability). For example, van Kampen et al., 2021; Wölfel et al., 2020 found that the virus was culturable if the viral load is above 10^6.0 copies/mL. Such uncertainty is reflected in the high variability in the results obtained for the one-size-fits-all approach; on the other hand, the personalized approach provided stable results with respect to the infectiousness threshold values. Fourth, we considered arbitrary values for the risk of prematurely ending isolation (namely, 1% or 5%). Whether such risks are acceptable depends on several factors such as the epidemiological context (e.g. the prevalence of the infection and disease burden), the aim of the adopted policies (e.g. suppression of transmission, mitigation of disease burden), propensity to take risks. Nonetheless, it is worth remarking that, if for a certain level of risk, the difference between the personalized and one-size-fits-all approaches is small, the fixed duration approach may have the advantage in terms of simplicity, cost, and resources. We also note that in the personalized approach, we used qualitative PCR test results only (i.e. whether the viral load is above or below a given threshold). The use of quantitative PCR test results may enable us to predict the optimal day to end isolation for each patient. Finally, although some of patients were tested (and isolated) before symptom onset or a few days after symptom onset, in this study, we assumed the testing starts immediately after symptom onset. As this analysis primarily focuses on the time when the viral load crosses the infectiousness threshold, we do not expect that the timing of the first test does not influence much our findings. However, starting the tests too early since isolation (or symptom onset) might be impractical and it should be determined based on operational and cost constraints. Future research could be dedicated to examining whether the starting day of testing could be defined on the basis of disease severity.

The guidelines regulating the length of isolation of COVID-19 patients require further updating following new epidemiologic and clinical knowledge, patient characteristics, and the capability of health sectors, such as test availability. Indeed, in several countries, these guidelines have been updated several times throughout the course of the pandemic (Centers for Disease Control and Prevention, 2020a; European Centre for Disease Prevention and Control, 2020a; Public Health England, 2020) and the emergence of new variants can spark new adjustments in the future as well. Our proposed modeling framework is very flexible and could be easily adapted to simulate the immune response and effect of antiviral therapies as well as to the study of other infectious diseases. In particular, it might prove quite relevant should new SARS-CoV-2 variants show different temporal infectiousness profiles than the historical lineage (Davies et al., 2021).

In conclusion, until the vaccination effort successfully suppresses the widespread circulation of SARS-CoV-2, nonpharmaceutical interventions, and patient isolation in particular, will continue to be a primary tool for mitigating SARS-CoV-2 spread. Understanding when isolated patients may be released will thus remain a key component in the fight against COVID-19.

Materials and methods

Viral load data

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We searched PubMed and Google Scholar for papers reporting longitudinal viral load data of COVID-19 patients. We set five inclusion criteria: (1) multiple observations of the viral load were reported per patient (if cycle thresholds were reported instead of viral load, they were transformed to viral load by using the following conversion formula [Zou et al., 2020]: $\log_{10} (Viral load [copies/mL]) = - 0.32 \times Ct values [cycles] + 14.11$ ); (2) viral load was measured from upper respiratory specimens (i.e. nose, pharynx) for consistency; (3) viral load along with the time since symptom onset was reported; (4) the patients were not under antiviral treatment (antiviral therapy can directly influence the viral dynamics); and (5) patients were symptomatic (because we used the time since symptom onset as the time scale). We used the de-identified secondary data from published studies, and thus ethics approval for this study was not necessary.

Modeling SARS-CoV-2 viral dynamics

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We developed a mathematical model of SARS-CoV-2 viral dynamics (Ikeda et al., 2016; Kim et al., 2020b; Perelson, 2002). The model is composed of two components: (1) the ratio between the number of uninfected target cells at time $t$ and the number of uninfected target cells at time 0 ( $t = 0$ corresponds to the time of symptom onset), $f (t)$ ; and (2) the amount of virus per unit in sample specimen (copies/mL) at time $t$ , $V (t)$ . $V (t)$ exponentially increases since infection, reaches a peak, and starts declining because of the depletion of target cells, which is consistent with the observed viral dynamics. Model parameters were calibrated by fitting the longitudinal data with a mixed-effect model. Details on the model and the fitting procedure are reported in Appendix 1. To account for individual variability in the viral dynamics, we simulated $V (t)$ for 1000 patients by sampling from the posterior distributions of the model parameters. To simulate the viral load measured by a PCR test, $\hat{V} (t)$ , we added a measurement error to $V (t)$ (see Appendix 1 for details). The model used here (baseline model) is one of the simplest models for viruses causing acute respiratory infection. Given that the biological infection process has not been fully understood yet, we believe using a simple model represents an appropriate baseline choice. Specifically in the literature of SAS-CoV-2 studies, several different models have been used including the baseline model (Gonçalves et al., 2020; Goyal et al., 2020; Goyal et al., 2021; Kim et al., 2020b). Nonetheless, to investigate to what extent the model choice affects our findings, we considered two alternative models: the ‘eclipse phase’ model (Baccam et al., 2006; Gonçalves et al., 2020) and the ‘innate immune response’ model (Baccam et al., 2006). The detailed description of the analyzed models is reported in Appendix 1.

Assessment and comparison of the one-size-fits-all and the personalized approach

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In the one-size-fits-all approach, we assumed isolation to end after a fixed time since symptom onset, whereas in the personalized approach using PCR tests, isolation ends after obtaining a given number of consecutive negative test results (with a given time interval between the tests). As the baseline scenario for the one-size-fits-all approach (here referred to as the ‘symptom-based strategy’), we considered a fixed time of 10 days. As the baseline scenario for the personalized approach (here referred to as the ‘test-based strategy’), we considered two consecutive negative test results repeated at a daily interval (in agreement with the CDC guidelines [Centers for Disease Control and Prevention, 2020a]). Here, we assumed the testing starts immediately after symptom onset.

Epidemiological studies based on contact tracing data suggest that infectiousness nearly disappears 8 days after symptom onset (Hu et al., 2020; Sun et al., 2021). According, to Kim et al., 2020b, the 97.5 percentile of the viral load 8 days after symptom onset is 10^5.0 copies/mL (Kim et al., 2021). We thus use 10^5.0 copies/mL as threshold to define whether a patient is still infectious (i.e. able to transmit the infection). All the obtained results are reported also by considering viral load threshold values of 10^4.5 copies/mL and 10^5.5 copies/mL as sensitivity analyses.

To evaluate the different strategies, we computed two metrics based on the simulated viral loads: the probability of prematurely ending isolation and the length of unnecessarily prolonged isolation. The probability of prematurely ending isolation is the chance that infected patients are released from isolation while they are still infectious. The length of prolonged isolation is defined as the difference between the time at which a patient is no longer infectious and the time when her or his isolation ends. Note that when the prolonged isolation is negative, it means that the isolation period has ended when the patient is still infectious.

As sensitivity analyses, we considered the length of isolation in the range of 2 to 20 days for the one-size-fits-all approach. For the personalized approach, the frequency of testing (i.e. the interval between consecutive tests) was considered to vary between 1 and 5 days and the number of consecutive negative test results to vary between 1 and 5. Details about the performed analyses are reported in Appendix 1 and a schematic of the methodology is shown in Figure 6.

Figure 6

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Appendix 1

Data

In the study from Singapore (n=12), (Young et al., 2020) specimens (blood, stool, urine samples, and nasopharyngeal swabs) were collected over time for the first 2 weeks since study enrollment (all patients were hospitalized) and viral load was quantified by PCR. Viral load as measured in the nasopharyngeal swabs was used in the analysis for consistency with the other datasets. In the study from Zhuhai, China (n=8), (Zou et al., 2020), both nasal and throat swabs were collected, and the viral load was quantified by PCR. We used the viral load measured in the nasal swabs because the cycle threshold values were generally lower than the values for the throat swabs. In the second study from Germany (n=8), (Wölfel et al., 2020) viral load was measured from sputum, pharyngeal swabs, and stool collected every day. We used the data from the pharyngeal swabs for the analysis. In the study from Korea (n=2), (Kim et al., 2020b) upper (nasopharyngeal and oropharyngeal) and lower (sputum) respiratory specimens were collected daily or every other day after the diagnosis of infection. The viral load data measured in upper respiratory specimens were used for the analysis.

Eight cases reported from China and one case reported from Germany were excluded because their viral load was above the detection limit only two times or fewer. Five cases who received lopinavir-ritonavir treatment and one case with less than two data points from Singapore were excluded. Seven cases from Korea were excluded because they were under lopinavir-ritonavir treatment.

A mathematical model for SARS-CoV-2 virus dynamics

Baseline model

SARS-CoV-2 viral dynamics without antiviral treatment is described by a mathematical model previously proposed and applied in Ikeda et al., 2016; Kim et al., 2020b; Perelson, 2002:

\frac{d T (t)}{d t} = - β T (t) V (t),

\frac{d I (t)}{d t} = β T (t) V (t) - δ I (t),

\frac{d V (t)}{d t} = p I (t) - c V (t),

where the three variables $T (t)$ , $I (t)$ , and $V (t)$ are the number of uninfected target cells, the number of infected target cells, and the amount of virus per unit of sample specimens (copies/mL) at time $t$ , respectively. Note that time after symptom onset is used as the timescale; thus, $t = 0$ is the time of symptom onset (the date on which symptoms of COVID-19 [fever, cough, and shortness of breath] first began [Centers for Disease Control and Prevention, 2020b]). The parameters $β$ , $δ$ , $p$ , and $c$ denote the rate constant for virus infection, the death rate of infected cells, the virus production rate, and the virus clearance rate, respectively. Because the virus clearance rate, $c$ , is typically much larger than the death rate of the infected cells, $δ$ , in vivo, (Ikeda et al., 2016; Martyushev et al., 2016; Nowak and May, 2000) a quasi-steady state (QSS) for the amount of virus can be assumed: $d V (t) / d t = 0$ . Then $I (t) = c V (t) / p$ is derived by solving Equation 3. Substituting this into Equation 2, we obtain

\frac{d V (t)}{d t} = \frac{p β}{c} T (t) V (t) - δ V (t) .

Further, we define the ratio between the number of uninfected target cells at time $t$ and the number of uninfected target cells at time 0: $f (t) = T (t) / T (0)$ . The original three-dimensional system (Equation 1-3) is reduced to the following two-dimensional system:

\frac{d f (t)}{d t} = - β f (t) V (t),

\frac{d V (t)}{d t} = γ f (t) V (t) - δ V (t),

where $γ = p β T (0) / c$ corresponds to the maximum viral replication rate. Note that $f (t)$ is a monotonically decreasing function.

‘Eclipse phase’ model

A model considering an eclipse phase of infection, which slows viral growth, has been used to describe the virus dynamics of SARS-CoV-2 and other viruses (Baccam et al., 2006; Gonçalves et al., 2020). This model is driven by the following system of differential equations:

\begin{aligned} \frac{d f_{T} (t)}{d t} & = - β f_{T} (t) V (t), \\ \frac{d f_{I} (t)}{d t} & = β f_{T} (t) V (t) - k f_{I} (t), \\ \frac{d V (t)}{d t} & = γ f_{I} (t) - δ V (t), \end{aligned}

where $f_{T} (t)$ is the ratio of uninfected cells at time $t$ to those at time 0, $f_{I} (t)$ is the ratio of infected cells in the eclipse phase and to the uninfected cells at time 0, and $V (t)$ is the concentration of virus (copies/mL). $1 / k$ is the mean length of the eclipse phase. To decrease the number of parameters to be estimated, parameters $f_{I} (0)$ and $k$ were fixed at 0.1 and 3.0, respectively, as previously estimated for SARS-CoV-2 (Gonçalves et al., 2020).

‘Innate immune response’ model

A model considering an innate immune response (e.g., interferons [IFNs]) was used in previous influenza studies (Baccam et al., 2006). The model is regulated by the following system of differential equations:

\begin{aligned} \frac{d f (t)}{d t} & = - \frac{1}{1 + η F (t)} β f (t) V (t), \\ \frac{d V (t)}{d t} & = \frac{1}{1 + η F (t)} γ f (t) V (t) - δ V (t), \\ \frac{d F (t)}{d t} & = s V (t) - α F (t), \end{aligned}

where $f (t)$ is the ratio of uninfected cells at time $t$ to those at time 0, $V (t)$ is the concentration of virus (copies/mL), and $F (t)$ is the concentration of IFNs produced from infected cells. $1 / η$ means the concentration of INFs that produces a half-maximum rate constant for viral replication. $s$ and $α$ are the rate constant which is proportional to secretion of INFs from infected cells and the rate of removal of IFNs, respectively. Parameters $η$ , $s$ , and $α$ were assumed to decrease the number of free parameters and guarantee convergence.

Parameter estimation with the nonlinear mixed-effect model

A nonlinear mixed-effect model was used to fit the model to the longitudinal viral load data. A mixed model was used (Best et al., 2017; Gonçalves et al., 2020) because it can capture the heterogeneity in viral dynamics. Both a fixed effect (same among individuals) and a random effect (different between individuals) in each parameter are considered. Specifically, the parameter for patient $k$ , $ϑ_{k} (= ϑ \times e^{π_{k}})$ is a product of $ϑ$ (a fixed effect) and $e^{π_{k}}$ (a random effect), where $π_{k}$ follows the normal distribution: $N (0, Ω)$ . Fixed effects and random effects were estimated using the stochastic approximation Expectation/Maximization (SAEM) algorithm and empirical Bayes method, respectively. To account for the left-censoring problem (i.e., when the viral load is under the detection limit, or tests negative), the likelihood function was developed using a left-truncated Gaussian distribution assuming such data are in the censoring interval (0 to the detection limit) (Samson et al., 2006). Finally, we fit the normal distribution ( $N (0, σ)$ ) to the residuals (i.e., difference between true viral load and measured viral load) to quantify the measurement error used in the subsequent simulation. Fitting was performed on MONOLIX 2019R2 (http://www.lixoft.com) (Traynard et al., 2020).

Simulation of viral dynamics

We randomly resampled the parameter set (i.e., $β$ , $γ$ , $δ$ , and $V (0)$ ) from the estimated distribution and ran the model. We assumed viral load obtained by running the model over time, $V (t)$ , is true (or expected) viral load. However, the viral load quantified by the PCR test is influenced by a measurement error. Thus, we added the measurement error to the true viral load and obtained measured viral load, $\hat{V} (t)$ : $\hat{V} (t) = V (t) + ε, ε \sim N (0, σ) .$ The variance of the error, $σ^{2}$ , was estimated in the fitting process (see the previous section). We assumed the error is independent and identically distributed (i.e., the errors are not correlated among patients or among multiple measurements from the same patients).

Probability of prematurely ending isolation and the length of prolonged isolation for the personalized approach

Although the interval of tests and the consecutive negative results necessary to end isolation can vary, for the purpose of illustration in the following explanation, we assumed that the tests were performed every day and that two consecutive negative results were necessary.

By running the model with parameter sets resampled from the estimated distributions, we obtain true viral load, $V (t)$ (thick black lines in Figure 6), and measured viral load, $\hat{V} (t)$ (gray dots in Figure 6) over time since symptom onset for 1000 ‘virtual patients’. Negative results correspond to the measured viral load below an infectiousness threshold value (gray dots circled in blue in Figure 6). We denoted the timing of the second negative results as $s_{i}$ and the day when the true viral load drops below the infectiousness threshold value as ${\hat{s}}_{i}$ for patient $i$ .

Then, we computed the probability that true viral load is above the detection limit when the second consecutive negative result is obtained:

p = \sum_{i = 1}^{1000} I (V_{i} (s_{i}) > i n f e c t i o u s n e s s t h r e s h o l d v a l u e) / 1000

where $I$ is the identity function. In the upper panel in Figure 6, the true viral load is below the detection limit when the second consecutive negative result is observed. The length of unnecessarily prolonged isolation for patient $i$ was defined as the difference between the time of ending isolation, $s_{i},$ and the time that the true viral load drops below the infectiousness threshold value, ${\hat{s}}_{i}$ : $s_{i} - {\hat{s}}_{i}$ . The 95% confidence intervals (CIs) of the probability of prematurely ending isolation, $p$ , was computed assuming a binominal distribution: $p \pm 1.96 \sqrt{p (1 - p) / 1000}$ .

Data availability

The viral load data were directly extracted from published literature. The data are publicly available, however, we are not allowed to share the data. The sources of the data are summarized in Table 1. The data to replicate the figures are available as source data. The detailed computational process is available in Appendix 1.

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Decision letter

Joshua T Schiffer

Reviewing Editor; Fred Hutchinson Cancer Research Center, United States
Eduardo Franco

Senior Editor; McGill University, Canada
Joshua T Schiffer

Reviewer; Fred Hutchinson Cancer Research Center, United States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This paper uses a simulation approach to demonstrate that a personalized viral load based testing approach has the potential to limit the duration of unnecessary isolation among infected people while not increasing the risk of releasing an infectious person. This work could influence policies regarding duration of isolation is hospitals and at home.

Decision letter after peer review:

Thank you for submitting your article "Revisiting the guidelines for ending isolation for COVID-19 patients" for consideration by eLife. Your article has been reviewed by 2 peer reviewers, including Joshua T Schiffer as the Reviewing Editor and Reviewer #1, and the evaluation has been overseen by a Senior Editor.

As is customary in eLife, the reviewers have discussed their critiques with one another and with the editors. What follows below is the Reviewing Editor's edited compilation of the essential and ancillary points provided by reviewers in their critiques and in their interaction post-review. Please submit a revised version that addresses these concerns directly.

Essential Revisions:

1) Please enhance the literature review to discuss the relevance of this paper in light of new, less expensive testing strategies including rapid antigen testing. Please also discuss more specifically how different countries around the world are differing in terms of isolation policies.

2) Please test different intra-host models against the data using residuals and AIC and see if different models alter conclusions about optimal isolation guidelines in anyway.

Reviewer #1:

1) Overall, the paper is under referenced and state of the art testing approaches are not described in sufficient detail in the intro or discussion. A brief review of national practices that incorporate one strategy or the other to inform the reader of the current standard would be helpful to highlight the importance of the work.

2) There is no mention of the use of antigen tests which are less sensitive for viral RNA but more specific for infectious virus. These are far less expensive, have far less turnaround and are now widely used in many countries. Antigen tests should be contextualized given the results of this modeling. Saliva testing is also widespread in many places. Modeling of both approaches is available in the literature and should be cited.

3) Several groups have published intra-host viral dynamic models (the Guedj and Schiffer groups) with slightly different mechanistic assumptions. These models should be discussed and in particular it should be mentioned whether their slightly different structures could alter the paper's conclusions. Similarly, a couple of research groups have made estimates of viral load thresholds required for transmission and these should be referenced as well.

4) The model is fit to very little data (as very little is available) and while the posterior sampling method to generate 1000 in silico patients is reasonable, it is no substitute for real data. The authors should acknowledge that confidence intervals reported in the paper are quite speculative in the sense that the extent and quality of relevant viral load data for intra-host modeling is unfortunately quite limited. If the model is misclassified based on non-representative input data, then estimations about duration of isolation could be biased.

5) For the test-based strategy, are there any assumptions about when the first test might occur? Can this only occur after development of symptoms or after a certain number of days of infection? This section of the methods should provide more detail.

Reviewer #2:

Jeong et al., examined the important question of the guidelines for ending the isolation of COVID-19 patients. Two types of guidelines are commonly used: 1) A fixed duration (10 days or 2 weeks) of isolation following the development of symptoms, which the authors call 'one-size-fits-all'. 2) Two successive RT/PCR negative test results separated by 24 hours for ending isolation, which the authors term 'personalized'. In the former, a long duration would lead to unnecessarily long isolation periods, whereas a short duration may end up releasing individuals still able to transmit the disease. The latter avoids these pitfalls, but requires multiple tests, increasing costs and the burden on healthcare staff. To identify which of these strategies is better, the authors develop a mathematical model of within-host SARS-CoV-2 dynamics and apply it to data of viral load changes post infection from untreated patients. Using the parameters estimated, they create a pool of 1000 virtual patients and simulate dynamics in these patients and assess the consequences of the two isolation ending approaches by calculating the probability that a patient released is still able to transmit and the excess or unwarranted duration of isolation. They find that in general the personalized approach fares better on both metrics.

The question is important and timely given the raging COVID-19 pandemic. The conceptual approach developed is novel and is also likely to be applicable beyond the current pandemic. The application of the approach and the resulting inferences drawn, however, need stronger justification. My reasons are below.

1. In the personalized approach, where RT/PCR tests are used, the chance that a person who is infectious is declared non-infectious (or vice versa) is due to measurement error. This error is estimated in the study as the variance of the normal distribution fit to the residuals of the best-fits of the mathematical model to the patient data of viral load changes (see lines 464 and 473). The error is thus strongly dependent on the model. One could use a model with more parameters and obtain a 'better' fit to the data, with smaller residuals, which could then presumably change the inferences above. Indeed, many other models have been developed to describe SARS-CoV-2 dynamics and have been applied to some of the datasets the present study has used.

2. A second concern, which the authors too recognize, is that the data used is all from hospitalized patients, which may not be representative of the vast fraction of infected individuals undergoing (home or institutional, but not hospital) isolation following mild/moderate symptoms. The required durations of isolation may then be even shorter than predicted. Would guidelines that account for this heterogeneity in disease severity be easier to implement? In other words, individuals could be categorized into disease severity classes (say asymptomatic, mild, moderate, or severe) and have fixed but different durations of isolation for each class. For personalized treatments, one could still use these categories to decide when to start measurements. In the present study, when to start measurements in the personalized approach is not mentioned and it appears that measurements are assumed to be made daily from the time of isolation, which may be unnecessary and impractical.

3. Finally, the two approaches are compared at 5% and 1% probabilities of ending isolation prematurely (Figure 4). While 1% appears small, whether it is small enough from an epidemiological perspective remains to be addressed. In other words, whether 1% 'leakage' of infectious individuals from isolation is tolerable would depend on the setting, particularly, the population density and the propensity for risky behavior. If at an epidemiologically identified threshold, the difference between the two approaches is small, the fixed duration approach may have the advantage of simplicity and of doing away with additional tests.

1. One way to address comment 1 above could be to compare alternative models and identify the best model based on estimates of AIC, or other such metrics, and use it to estimate the measurement error. Alternatively, if experimental uncertainties in RT/PCR measurements are known, using them instead of the variance of the normal distribution fit to residuals could provide an independent verification of the inferences.

2. The authors should show fits of the model to the data and list the model parameter values estimated; this would help appreciate the inferences drawn better.

https://doi.org/10.7554/eLife.69340.sa1

Author response

Essential Revisions:

1) Please enhance the literature review to discuss the relevance of this paper in light of new, less expensive testing strategies including rapid antigen testing. Please also discuss more specifically how different countries around the world are differing in terms of isolation policies.

We thank the editors and reviewers for this comment and fully agree about the importance of these new technologies. RT-LAMP tests and rapid antigen tests have been developed and recommended for repeated screening, given that they are less expensive and test results are available faster than PCR tests (10-15 mins vs. a few hours) regardless of their lower sensitivity. We add the following paragraph to discuss the current use of these tests and their application in the context of isolation strategies (Page 9 Line 195-206):

“In this study, we used PCR tests to define the end of an isolation period in the personalized approach. PCR tests provide quantitative viral load estimates, which can be directly compared against the infectiousness threshold. Meanwhile, reverse transcription loop-mediated isothermal amplification (RT-LAMP) tests and rapid antigen tests for SARS-CoV-2 have been developed and recommended for repeated screenings, given that they are less expensive and with a shorter turnaround time than PCR tests (less than an hour vs. a day or two) (Butler et al., 2021; Dao Thi et al., 2020; Larremore et al., 2021; Yang et al., 2021). Although these tests have lower sensitivity (the detection limit is about 10^5.0 copies/mL; Butler et al., 2021; Dao Thi et al., 2020; Miyakawa et al., 2021; Yang et al., 2021) than PCR tests, they can help mitigating SARS-CoV-2 transmission when used for population screenings (Larremore et al., 2021) and contact tracing (Quilty et al., 2021); in fact, the viral load threshold of infectiousness is considered to be higher than the detection limits of RT-LAMP tests and rapid antigen tests. Epidemiological studies are needed to assess whether isolation strategies based on RT-LAMP or rapid tests have a similar mitigation effect to those based on PCR testing.”

Moreover, as suggested, we have added a more comprehensive review of isolation policies in different countries (Page 9 Line 207-213):

“Two guidelines for ending isolation were considered in this study. In most countries, the one-size-fits-all approach is employed; however, the duration is slightly different among countries. The WHO recommends isolation for 10 days after symptom onset or a positive test for asymptomatic individuals (World Health Organization, 2020). The ECDC recommends isolation of 10 or 20 days for mild/moderate or severe cases, respectively, while for asymptomatic individuals, 10 days isolation after a positive test is recommended (European Centre for Disease Prevention and Control, 2020). However, these durations actually vary from 7 to 14 days depending on each member state of the European Union (European Comission, 2020).”

2) Please test different intra-host models against the data using residuals and AIC and see if different models alter conclusions about optimal isolation guidelines in anyway.

The model we used in the study (baseline model) is one of the simplest models. As the editors and the reviewers suggested, the model can be extended to incorporate other factors. Following their suggestion, we have added two alternative models, both of which are still universally used for viruses causing acute respiratory infection.

1) “Eclipse phase” model

A model considering an eclipse phase of infection, which slows viral growth, has been used to describe the virus dynamics of SARS-CoV-2 and other viruses (Baccam, Beauchemin, Macken, Hayden, and Perelson, 2006; Gonçalves et al., 2020). This model is driven by the following system of differential equations:

\begin{aligned} \frac{d f_{T} (t)}{d t} & = - β f_{T} (t) V (t), \\ \frac{d f_{I} (t)}{d t} & = β f_{T} (t) V (t) - k f_{I} (t), \\ \frac{d V (t)}{d t} & = γ f_{I} (t) - δ V (t), \end{aligned}

where $f_{T} (t)$ is the ratio of uninfected cells at time $t$ to those at time 0, $f_{I} (t)$ is the ratio of infected cells in the eclipse phase to the uninfected cells at time 0, and $V (t)$ is the concentration of virus (copies/mL). $1 / k$ is the mean length of the eclipse phase. To decrease the number of parameters to be estimated, parametrs $f_{I} (0)$ and $k$ were fixed at 0.1 and 3.0, respectively, as previously estimated for SARS-CoV-2 (Gonçalves et al., 2020).

2) “Innate immune response” model

\begin{aligned} \frac{d f (t)}{d t} & = - \frac{1}{1 + η F (t)} β f (t) V (t), \\ \frac{d V (t)}{d t} & = \frac{1}{1 + η F (t)} γ f (t) V (t) - δ V (t), \\ \frac{d F (t)}{d t} & = s V (t) - α F (t), \end{aligned}

where $f (t)$ is the ratio of uninfected cells at time $t$ to those at time 0, $V (t)$ is the concentration of virus (copies/mL), and $F (t)$ is the concentration of IFNs produced from infected cells. $1 / η$ is the concentration of INFs that produces a half-maximum rate constant for viral replication. $s$ and $α$ are the rate constant which is proportional to secretion of INFs from infected cells and the rate of removal of IFNs, respectively.

In the revised version of the manuscript these two new models are presented alongside the baseline model and compared based on the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). The three models provided very consistent results, which are summarized in Supplementary File 2 and Figure 1.

Next, to further investigate the sensitivity of our findings to the selected model, we performed the same simulations presented in the original manuscript for the baseline model also for the calibrated “eclipse phase” model and “innate immune response” model. Overall, all the three models suggest that the personalized approach allows shorted length of unnecessarily isolation and provide quantitatively similar estimates. Together with a new figure (Figure 5), the following section has been added in the main text (Page 8, Line 156-165):

“Influence of model selection Figure 5 shows the length of the prolonged isolation for a 5% or lower or 1% or lower risk of prematurely ending the isolation for all the analyzed models. Regardless of the considered models, the personalized approach allows shorted length of unnecessarily isolation. Nonetheless, it is important to remark that the length of prolonged isolation is slightly different among the analyzed models. For example, under the one-size-fits-all approach, it was longer for the “innate immune response” model as compared with the other two; this is due to larger variability in viral load especially at the late phase of the infection (Figure 1). Under the personalized approach, the length of prolonged isolation was longer in the baseline model as compared to the two alternative models (Figure 1). In summary, by comparing the three models, we can conclude that the one-size-fits-all approach is sensitive to the variability of the viral load curve, whereas the personalized approach is sensitive to the decay speed of the viral load.”

We would like to thank once again the editors and reviewers for this comment as we believe that comparing alternative models remarkably strengthens our analysis and supports the robustness of our results.

Reviewer #1:

1) Overall, the paper is under referenced and state of the art testing approaches are not described in sufficient detail in the intro or discussion. A brief review of national practices that incorporate one strategy or the other to inform the reader of the current standard would be helpful to highlight the importance of the work.

We apologize for the lack of sufficient discussion and agree about the relevance of providing the reader with a better context for our analysis. We have revised the Discussion to include an overview of the isolation policies recommended by the WHO and ECDC (in addition to those recommended by the CDC) (Page 9, Lines 207-213):

2) There is no mention of the use of antigen tests which are less sensitive for viral RNA but more specific for infectious virus. These are far less expensive, have far less turnaround and are now widely used in many countries. Antigen tests should be contextualized given the results of this modeling. Saliva testing is also widespread in many places. Modeling of both approaches is available in the literature and should be cited.

We apologize for the lack of discussion about antigen tests. We agree with reviewer about their importance, which we now acknowledge in the revised version of our manuscript (Page 9, Line 195-206). For further details about antigen testing, we refer the reviewer to the response above.

Regarding saliva testing, we have added the following paragraph to acknowledge its relevance and recognize the literature on the topic (Page 9, Line 189-194):

“The development of PCR tests using saliva samples may help to overcome some of these challenges, promising to decrease the work burden and lower the risk of infection for health care workers (Azzi et al., 2020; Tu et al., 2020; Wyllie et al., 2020). Indeed, the viral load measured from saliva is comparable to or slightly higher that from nasopharyngeal samples, which guarantees a similar level of sensitivity (Tu et al., 2020; Wyllie et al., 2020).”

3) Several groups have published intra-host viral dynamic models (the Guedj and Schiffer groups) with slightly different mechanistic assumptions. These models should be discussed and in particular it should be mentioned whether their slightly different structures could alter the paper's conclusions. Similarly, a couple of research groups have made estimates of viral load thresholds required for transmission and these should be referenced as well.

As suggested, we have now included two alternative models in our analysis. The results of the two additional models are in overall agreement with those obtained with the model presented in the originally submitted manuscript, thus reinforcing our findings. We refer the reviewer to the response above for details.

Regarding the estimates of the viral load thresholds required for transmission, we have relied on epidemiological evidence of transmission as derived from contact tracing data. Nonetheless, we agree with the reviewer that there exists an important body of literature about the connection between SARS-CoV-2 transmission and viral load. We have added the following paragraph to acknowledge the relevance of these studies (Page 10, Line 233-240):

“Third, a deeper knowledge of the association between the viral load and the transmission risk would be a key to narrow the uncertainty surrounding the minimum viral load level that still allows SARS-CoV-2 transmission. Specifically, 104.5, 105.0, and 105.5 copies/mL were used and were based on epidemiological observations of transmission events from contact tracing data (He et al., 2020). Other studies used a different perspective to approach the same research question and investigated the threshold relying on experimental virological data (i.e., capturability). For example, Wölfel et al. and van Kampen et al. found that the virus was culturable if the viral load is above 106.0 copies/mL (van Kampen et al., 2021; Wölfel et al., 2020).”

4) The model is fit to very little data (as very little is available) and while the posterior sampling method to generate 1000 in silico patients is reasonable, it is no substitute for real data. The authors should acknowledge that confidence intervals reported in the paper are quite speculative in the sense that the extent and quality of relevant viral load data for intra-host modeling is unfortunately quite limited. If the model is misclassified based on non-representative input data, then estimations about duration of isolation could be biased.

We fully agree with the reviewer that our analysis suffers from the limitations mentioned by the reviewer and we apologize for not having stressed them enough in the originally submitted version of the manuscript. We have revised the discussion as follow (Page 10, Line 224-227):

“The confidence intervals reported in this paper need to be cautiously interpreted as the extent and quality of relevant viral load data is unfortunately quite limited. Further, should the input data be non-representative, this could have caused a bias in our estimates of the duration of the isolation period.”

5) For the test-based strategy, are there any assumptions about when the first test might occur? Can this only occur after development of symptoms or after a certain number of days of infection? This section of the methods should provide more detail.

We apologize for the lack of detail. We assumed that the test is conducted (and the isolation starts) immediately after symptom onset. This has been clarified in the Methods (Page 13, Line 311-312).

Moreover, we have added the following paragraph in the Discussion to acknowledge the limits of our choice (Page 11, Line 250-256):

“Finally, although some of patients are tested (and isolated) before symptom onset or a few days after symptom onset, in this study, we assumed the testing starts immediately after symptom onset. As this analysis primarily focuses on the time when the viral load crosses the infectiousness threshold, we do not expect that the timing of the first test does not influence much our findings. However, starting the tests too early since isolation (or symptom onset) might be impractical and it should be determined based on operational and cost constraints. Future research could be dedicated to examining whether the starting day of testing could be defined on the basis of disease severity.”

Reviewer #2:

Jeong et al., examined the important question of the guidelines for ending the isolation of COVID-19 patients. Two types of guidelines are commonly used: 1) A fixed duration (10 days or 2 weeks) of isolation following the development of symptoms, which the authors call 'one-size-fits-all'. 2) Two successive RT/PCR negative test results separated by 24 hours for ending isolation, which the authors term 'personalized'. In the former, a long duration would lead to unnecessarily long isolation periods, whereas a short duration may end up releasing individuals still able to transmit the disease. The latter avoids these pitfalls, but requires multiple tests, increasing costs and the burden on healthcare staff. To identify which of these strategies is better, the authors develop a mathematical model of within-host SARS-CoV-2 dynamics and apply it to data of viral load changes post infection from untreated patients. Using the parameters estimated, they create a pool of 1000 virtual patients and simulate dynamics in these patients and assess the consequences of the two isolation ending approaches by calculating the probability that a patient released is still able to transmit and the excess or unwarranted duration of isolation. They find that in general the personalized approach fares better on both metrics.

The question is important and timely given the raging COVID-19 pandemic. The conceptual approach developed is novel and is also likely to be applicable beyond the current pandemic. The application of the approach and the resulting inferences drawn, however, need stronger justification. My reasons are below.

We would like to thank the reviewer for the careful evaluation of our manuscript and her/his constructive input. We are also glad that the reviewer found our research question “important and timely” and appreciated our modeling approach.

1. In the personalized approach, where RT/PCR tests are used, the chance that a person who is infectious is declared non-infectious (or vice versa) is due to measurement error. This error is estimated in the study as the variance of the normal distribution fit to the residuals of the best-fits of the mathematical model to the patient data of viral load changes (see lines 464 and 473). The error is thus strongly dependent on the model. One could use a model with more parameters and obtain a 'better' fit to the data, with smaller residuals, which could then presumably change the inferences above. Indeed, many other models have been developed to describe SARS-CoV-2 dynamics and have been applied to some of the datasets the present study has used.

We would like to thank the reviewer for this comment that allowed us to strengthen our analysis. As suggested, we have now considered two additional models (taken from the literature). The results obtained with these two additional models are in overall agreement with those obtained in the original analysis, although some quantitative differences do exist, especially in the description of the late phase of the infection.

2. A second concern, which the authors too recognize, is that the data used is all from hospitalized patients, which may not be representative of the vast fraction of infected individuals undergoing (home or institutional, but not hospital) isolation following mild/moderate symptoms. The required durations of isolation may then be even shorter than predicted. Would guidelines that account for this heterogeneity in disease severity be easier to implement? In other words, individuals could be categorized into disease severity classes (say asymptomatic, mild, moderate, or severe) and have fixed but different durations of isolation for each class. For personalized treatments, one could still use these categories to decide when to start measurements. In the present study, when to start measurements in the personalized approach is not mentioned and it appears that measurements are assumed to be made daily from the time of isolation, which may be unnecessary and impractical.

We echo the reviewer about the possibility that guidelines accounting for disease severity may represent a viable option. Unfortunately, as discussed in the originally submitted version of our manuscript and also recognized by the reviewer, the data (un)availability prevented us to test this hypothesis. We have added the following paragraph to discuss this point, which is still open for future studies (Page 10, Line 215-221):

“First, the number of samples analyzed were relatively small (30 patients), they did not cover all age groups, and pertained to symptomatic hospitalized patients only. This did not allow us to test whether the duration of the isolation is influenced by the severity of the disease. In particular, the duration may be shorter than that predicted in this study, as the analyzed samples were composed by hospitalized patients. Guidelines considering fixed durations of the isolation depending on disease severity may be easier to implement and limit the length of unnecessary prolonged isolations.”

Regarding the personalized approach, we assumed that the test is started immediately after symptom onset and we apologize for the omission of this detail. We have now specified it in the text (Page 13, Line 311-312). We also agree with the reviewer’s suggestion that the start of the testing for isolated patients may be optimized by taking into account disease severity. We have added the following paragraph to discuss this interesting topic (Page 11, Line 250-256):

“Finally, although some of patients were tested (and isolated) before symptom onset or a few days after symptom onset, in this study, we assumed the testing starts immediately after symptom onset. As this analysis primarily focuses on the time when the viral load crosses the infectiousness threshold, we do not expect that the timing of the first test does not influence much our findings. However, starting the tests too early since isolation (or symptom onset) might be impractical and it may be determined based on operational and cost constraints. Future research could be dedicated to examining whether the starting day of testing could be defined on the basis of disease severity.”

3. Finally, the two approaches are compared at 5% and 1% probabilities of ending isolation prematurely (Figure 4). While 1% appears small, whether it is small enough from an epidemiological perspective remains to be addressed. In other words, whether 1% 'leakage' of infectious individuals from isolation is tolerable would depend on the setting, particularly, the population density and the propensity for risky behavior. If at an epidemiologically identified threshold, the difference between the two approaches is small, the fixed duration approach may have the advantage of simplicity and of doing away with additional tests.

We apologize for the lack of detail. As correctly pointed out by the reviewer, 1% and 5% probabilities to prematurely ending the isolation were fully arbitrary choices made to provide two illustrative examples. Whether these risks are considered to be acceptable depends on several factors and political choices. We have added the following paragraph to clarify this key point/study limitation and acknowledge that the one-size-fits-all approach may be the best choice if for a predetermined risk level the two approaches show similar results (Page 11, Line 242-248):

“Fourth, we considered arbitrary values for the risk of prematurely ending isolation (namely, 1 or 5%). Whether such risks are acceptable depends on several factors such as the epidemiological context (e.g., the prevalence of the infection and disease burden), the aim of the adopted policies (e.g., suppression of transmission, mitigation of disease burden), propensity to take risks. Nonetheless, it is worth remarking that, if for a certain level of risk, the difference between the personalized and one-size-fits-all approaches is small, the fixed duration approach may have the advantage in terms of simplicity, cost, and resources.”

1. One way to address comment 1 above could be to compare alternative models and identify the best model based on estimates of AIC, or other such metrics, and use it to estimate the measurement error. Alternatively, if experimental uncertainties in RT/PCR measurements are known, using them instead of the variance of the normal distribution fit to residuals could provide an independent verification of the inferences.

Thank you for this comment. As suggested by the reviewer, we have added two alternative models and compared them using both AIC and BIC, finding little difference between them.

2. The authors should show fits of the model to the data and list the model parameter values estimated; this would help appreciate the inferences drawn better.

We apologize for these omissions. In the revised version, we have added the individual fitting results and the estimated parameter values in the Supplementary Information (Figure 1—figure supplement 1 and Supplementary File 1).

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https://doi.org/10.7554/eLife.69340.sa2

Article and author information

Author details

Yong Dam Jeong
1. interdisciplinary Biology Laboratory (iBLab), Division of Biological Science, Graduate School of Science, Nagoya University, Nagoya, Japan
2. Department of Mathematics, Pusan National University, Busan, Republic of Korea
Contribution
Data curation, Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

Contributed equally with
Keisuke Ejima and Kwang Su Kim

Competing interests
No competing interests declared

"This ORCID iD identifies the author of this article:" 0000-0002-3970-7690
Keisuke Ejima

Department of Epidemiology and Biostatistics, Indiana University School of Public Health-Bloomington, Bloomington, United States

Contribution
Conceptualization, Formal analysis, Supervision, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing

Contributed equally with
Yong Dam Jeong and Kwang Su Kim

For correspondence
kejima@iu.edu

Competing interests
No competing interests declared

"This ORCID iD identifies the author of this article:" 0000-0002-1185-3987
Kwang Su Kim

interdisciplinary Biology Laboratory (iBLab), Division of Biological Science, Graduate School of Science, Nagoya University, Nagoya, Japan

Contribution
Formal analysis, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

Contributed equally with
Yong Dam Jeong and Keisuke Ejima

Competing interests
No competing interests declared
Shoya Iwanami

interdisciplinary Biology Laboratory (iBLab), Division of Biological Science, Graduate School of Science, Nagoya University, Nagoya, Japan

Contribution
Formal analysis, Investigation, Methodology, Writing - original draft, Writing - review and editing

Competing interests
No competing interests declared
Ana I Bento

Department of Epidemiology and Biostatistics, Indiana University School of Public Health-Bloomington, Bloomington, United States

Contribution
Writing - original draft, Writing - review and editing

Competing interests
No competing interests declared
Yasuhisa Fujita

interdisciplinary Biology Laboratory (iBLab), Division of Biological Science, Graduate School of Science, Nagoya University, Nagoya, Japan

Contribution
Writing - original draft, Writing - review and editing

Competing interests
No competing interests declared
Il Hyo Jung

Department of Mathematics, Pusan National University, Busan, Republic of Korea

Contribution
Writing - original draft, Writing - review and editing

Competing interests
No competing interests declared
Kazuyuki Aihara

International Research Center for Neurointelligence, The University of Tokyo, Tokyo, Japan

Contribution
Investigation, Writing - original draft, Writing - review and editing

Competing interests
No competing interests declared
Koichi Watashi
1. Department of Virology II, National Institute of Infectious Diseases, Tokyo, Japan
2. Research Center for Drug and Vaccine Development, National Institute of Infectious Diseases, Tokyo, Japan
3. Department of Applied Biological Science, Tokyo University of Science, Noda, Japan
Contribution
Writing - original draft, Writing - review and editing

Competing interests
No competing interests declared
Taiga Miyazaki
1. Department of Infectious Diseases, Nagasaki University Graduate School of Biomedical Sciences, Nagasaki, Japan
2. Division of Respirology, Rheumatology, Infectious Diseases, and Neurology, Department of Internal Medicine, Faculty of Medicine, University of Miyazaki, Miyazaki, Japan
Contribution
Conceptualization, Writing - original draft, Writing - review and editing

Competing interests
No competing interests declared
Takaji Wakita

Department of Virology II, National Institute of Infectious Diseases, Tokyo, Japan

Contribution
Conceptualization, Writing - original draft, Writing - review and editing

Competing interests
No competing interests declared
Shingo Iwami
1. interdisciplinary Biology Laboratory (iBLab), Division of Biological Science, Graduate School of Science, Nagoya University, Nagoya, Japan
2. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan
3. Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University, Kyoto, Japan
4. NEXT-Ganken Program, Japanese Foundation for Cancer Research (JFCR), Tokyo, Japan
5. Science Groove Inc, Fukuoka, Japan
Contribution
Conceptualization, Supervision, Funding acquisition, Investigation, Methodology, Writing - original draft, Project administration, Writing - review and editing

For correspondence
iwami.iblab@bio.nagoya-u.ac.jp

Competing interests
is an employee of Science Groove Inc.

"This ORCID iD identifies the author of this article:" 0000-0002-1780-350X
Marco Ajelli
1. Department of Epidemiology and Biostatistics, Indiana University School of Public Health-Bloomington, Bloomington, United States
2. Laboratory for the Modeling of Biological and Socio-technical Systems, Northeastern University, Boston, United States
Contribution
Conceptualization, Supervision, Investigation, Writing - original draft, Project administration, Writing - review and editing

Competing interests
No competing interests declared

Funding

National Research Foundation of Korea (2019R1A6A3A12031316)

Kwang Su Kim

Japan Society for the Promotion of Science (18KT0018)

Shingo Iwami

Japan Society for the Promotion of Science (18H05103)

Shingo Iwami

Japan Society for the Promotion of Science (18H01139)

Shingo Iwami

Japan Society for the Promotion of Science (19H04839)

Shingo Iwami

Japan Society for the Promotion of Science (15H05707)

Kazuyuki Aihara

Japan Society for the Promotion of Science (20H05042)

Shingo Iwami

Japan Agency for Medical Research and Development (JP20dm0307009)

Kazuyuki Aihara

Japan Agency for Medical Research and Development (19gm1310002)

Shingo Iwami

Japan Agency for Medical Research and Development (20wm0325007h0001)

Shingo Iwami

Japan Agency for Medical Research and Development (20wm0325004s0201)

Shingo Iwami

Japan Agency for Medical Research and Development (20wm0325012s0301)

Shingo Iwami

Japan Agency for Medical Research and Development (20wm0325015s0301)

Shingo Iwami

Japan Agency for Medical Research and Development (19fk0410023s0101)

Shingo Iwami

Japan Agency for Medical Research and Development (19fk0108156h0001)

Shingo Iwami

Japan Agency for Medical Research and Development (20fk0108140s0801)

Shingo Iwami

Japan Agency for Medical Research and Development (20fk0108413s0301)

Shingo Iwami

Japan Agency for Medical Research and Development (19fk0210036h0502)

Shingo Iwami

Japan Agency for Medical Research and Development (19fk0310114h0103)

Shingo Iwami

Japan Society for the Promotion of Science (16H04845)

Shingo Iwami

Japan Science and Technology Agency (JPMJMS2021)

Kazuyuki Aihara

Japan Science and Technology Agency (JPMJMS2021)

Shingo Iwami

Japan Science and Technology Agency (JST MIRAI)

Shingo Iwami

Japan Science and Technology Agency (JPMJMS2025)

Shingo Iwami

Mitsui Sumitomo Insurance Welfare Foundation

Shingo Iwami

Advanced Medical Research Foundation

Shingo Iwami

Suzuken Memorial Foundation

Shingo Iwami

Life Science Foundation of Japan

Shingo Iwami

Secom Science and Technology Foundation

Shingo Iwami

Japan Prize Foundation

Shingo Iwami

Fusion Energy Sciences

Shingo Iwami

Taiju Life Social Welfare Foundation

Koichi Watashi

Takeda Science Foundation

Koichi Watashi

National Institute of General Medical Sciences (3U24GM132013-02S2)

Keisuke Ejima
Marco Ajelli

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This study was supported in part by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education 2019R1A6A3A12031316 (to KSK); Grants-in-Aid for JSPS Scientific Research (KAKENHI) Scientific Research B 18KT0018 (to SIWAMI), 18H01139 (to SIWAMI), 16H04845 (to SIWAMI), Scientific Research S 15H05707 (to KA), Scientific Research in Innovative Areas 20H05042 (to SIWAMI), 19H04839 (to SIWAMI), 18H05103 (to SIWAMI); AMED JP20dm0307009 (to KA); AMED CREST 19gm1310002 (to SIWAMI); AMED Japan Program for Infectious Diseases Research and Infrastructure, 20wm0325007h0001, 20wm0325004s0201, 20wm0325012s0301, 20wm0325015s0301 (to SIWAMI); AMED Research Program on HIV/AIDS 19fk0410023s0101 (to SIWAMI); AMED Research Program on Emerging and Re-emerging Infectious Diseases 19fk0108156h0001, 20fk0108140s0801 and 20fk0108413s0301 (to SIWAMI); AMED Program for Basic and Clinical Research on Hepatitis 19fk0210036h0502 (to SIWAMI); AMED Program on the Innovative Development and the Application of New Drugs for Hepatitis B 19fk0310114h0103 (to SIWAMI); Moonshot R and D Grant Number JPMJMS2021 (to KA and SIWAMI) and JPMJMS2025 (to S.IWAMI); JST MIRAI (to SIWAMI); Mitsui Life Social Welfare Foundation (to SIWAMI); Shin-Nihon of Advanced Medical Research (to SIWAMI); Suzuken Memorial Foundation (to SIWAMI); Life Science Foundation of Japan (to SIWAMI); SECOM Science and Technology Foundation (to SIWAMI); The Japan Prize Foundation (to SIWAMI), and Foundation for the Fusion of Science and Technology (to SIWAMI); Taiju Life Social Welfare Foundation (to KW); Takeda Science Foundation (to KW). This research was supported through the MIDAS Coordination Center (MIDASSUGP2020-6) by a grant from the National Institute of General Medical Science (3U24GM132013-02S2) (to KE and MA). The study does not necessarily represent the views of the funding agencies listed above.

Senior Editor

Eduardo Franco, McGill University, Canada

Reviewing Editor

Joshua T Schiffer, Fred Hutchinson Cancer Research Center, United States

Reviewer

Joshua T Schiffer, Fred Hutchinson Cancer Research Center, United States

Version history

Received: April 12, 2021
Accepted: July 2, 2021
Version of Record published: July 27, 2021 (version 1)

Copyright

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.