Overview

First, we developed a simulation model to generate longitudinal viral load data. The simulation model is based on a viral dynamics model, which is a mathematical model that describes the time course change in viral load within an infected individual. The model was fitted to longitudinal viral load data from patients infected by the SARS-CoV-2 Delta variant in Singapore. In the model fitting process, we tested if age and vaccination status influenced viral dynamics. Second, we implemented different isolation guidelines on viral load data and simulated them by using the parameterized model. Synthetic longitudinal viral load data was generated using the model; the leaking risk and excess isolation burden of the fixed-period and variable-period guidelines were estimated from the generated data together with the expected number of secondary infections under isolation programs (i.e., effective reproduction number). Third, we compared those two guidelines considering a certain level of risk (e.g., leaking risk of 10% and effective reproduction number of 1) and explored which length of isolation yielded the smallest excess isolation burden.

COVID-19 clinical data and longitudinal viral load

Electronic medical records of adult patients aged ≥18 years admitted to the National Center for Infectious Diseases, Singapore, from 1 April to 14 June 2021 were reviewed⁹. In this study, we focused on symptomatic patients who were infected by the Delta variant and had three or more viral load measurements. The analyzed sample of patients includes a substantial proportion of both vaccinated and unvaccinated patients. SARS-CoV-2 viral load was measured from nasopharyngeal swabs collected as part of routine clinical care and tested using a variety of commercial PCR assays, with a 1–3-day interval over 76 days since symptom onset at maximum. To obtain viral load from cycle threshold (C_t) values, the conversion formula was used¹⁰:

The detection limit was C_t = 50, corresponding to 10^−1.89 copies/mL. In addition to viral load, age and vaccination status were collected from each patient. The information about patients’ gender was not available. Note that we could not use similar data from the Omicron variant as all patients in that dataset were vaccinated. We aimed to quantify the effect of vaccination on viral dynamics.

The IRB review was exempted at Nanyang Technological University (IRB-2022-1041) for the data analysis in this study, as the data were de-identified before being shared with us. The data were provided by the corresponding author of the original multicenter cohort study⁹.

SARS-CoV-2 viral dynamics model

Viral dynamics models have been used to quantify the change in viral load of infectious diseases from infection to recovery. Specifically, to describe the viral load dynamics of SARS-CoV-2, we used the target-cell limited model^{6,7,11,12,13,14}:

The model includes two variables: the ratio of uninfected target cells at time \(t\) to that at time 0, \(f\left(t\right)\) (\(f\left(0\right)=1\) by definition), and the amount of virus (copies/mL) at time \(t\), \(V(t)\). The three model parameters, \(\beta\), \(\gamma\), and \(\delta\) represent the rate of cell infection, the maximum rate of virus replication, and the rate of infected cell loss, respectively. The time scale is the day after symptom onset. Only age (as a continuous linear term) and vaccination information were available in the dataset, thus they were accounted as potential covariates and the final set of covariates for each parameter was selected based on the model that gave the lowest Bayesian information criteria (BIC). Model parameters were estimated using a non-linear mixed effect model to account for individual variability in viral load dynamics. Random effects were considered for all parameters.

Assessing the leaking risk and excess isolation burden under different isolation guidelines

To account for individual variability, the model was run using parameter values sampled from the estimated joint posterior distributions for each simulated patient. The age distribution of the simulated patients was the same as the population structure in Singapore at the end of June 2023¹⁵, and vaccination coverage was assumed to be 50%. For each simulated patient, we implemented the fixed-period guideline and the variable-period guideline considering different lengths of isolation. The length of isolation was fixed across all patients under the fixed-period guideline, while it was dependent on age and vaccination status under the variable-period guideline. To identify the best length of isolation under a certain guideline and compare between the two guidelines, the leaking risk and excess isolation burden of isolation were estimated and compared.

First, the leaking risk was estimated as:

where \(N\) is the number of patients (= 1000), \(i\) is the patient’s ID, \({s}_{i}\) is the timing of ending isolation for patient \(i\), \({V}_{i}\left({s}_{i}\right)\) is the viral load of patient \(i\) at time \({s}_{i}\), and \(I\) is the identity function. Associated with the leaking risk, we also considered the expected secondary transmission produced by a patient (i.e., the effective reproduction number) under isolation programs, \({R}_{e}\), which is defined as an average of the expected secondary transmission produced by symptomatic patients, \({R}_{e,S},\) and that by asymptomatic patients, \({R}_{e,A}\), respectively:

where \(p\) is the asymptomatic ratio. Assuming the same transmission potential for symptomatic and asymptomatic patients given that the viral load dynamics are similar regardless of symptom presence⁷, and that isolation is performed only for symptomatic cases, \({R}_{e}\) is estimated as:

where \(\theta\) is the contact rate per day and \({P}_{i}(s)\) is per contact probability of infection of patient \(i\) at time \(s\). \({K}_{i}\) and \({L}_{i}\) are both time after infection, but \({L}_{i}\) excludes the time of isolation (assuming that isolation is implemented only for symptomatic cases). \({P}_{i}(s)\) is dependent on the viral load of patient \(i\) at time \(s\): \({P}_{i}\left(s\right)=\frac{{{V}_{i}(s)}^{\alpha }}{{{V}_{i}(s)}^{\alpha }+{\lambda }^{\alpha }}\), where \(\lambda\) is the viral load at which \({P}_{i}\left(s\right)\) reaches 50%, and \(\alpha\) is the slope parameter¹⁶ (note: \({P}_{i}\left(s\right)\) and \({V}_{i}(s)\) are positively associated). Following previous literature using the wildtype SARS-CoV-2¹⁶, we set \(\lambda ={10}^{7}\) and \(\alpha =0.8\). These parameters (\(\lambda\) and \(\alpha\)) were estimated using viral load data, individual reproduction numbers, and serial intervals. Note that the effective reproduction number without isolation is defined as \({R}_{e,0}=\frac{{\sum }_{i}{\int }_{{K}_{i}}\theta {P}_{i}(s){ds}}{N}\). \(\theta\) was computed assuming \({R}_{e,0}=3\). \(p\) was taken to be 20%¹⁷.

Second, the average per-patient excess isolation burden (excess isolation burden) was estimated as:

where \({u}_{i}\) is the time when \({V}_{i}\) first drops below the infectiousness threshold, which was set as C_t = 25, corresponding to 10^6.11 copies/mL, based on our earlier study¹⁸. Note that the excess isolation burden is negative when more relaxed guidelines are implemented.

In general, strict guidelines yield lower risk but higher excess isolation burden, thus balance between the two should be considered. Here, assuming a 10% leaking risk and 1 as an effective reproduction number at the end of the isolation period, we explored the best length of isolation that minimizes the excess isolation burden. As the 10% of leaking risk is arbitrary (i.e., the threshold is determined by various factors such as characteristics of the disease [transmission potential and severity] and socioeconomic conditions of the society), we performed the same analysis using 5% and 20% of leaking risk. Furthermore, in our sensitivity analysis, we explored different infectiousness thresholds of C_t = 20 (10^7.71 copies/mL) and C_t = 30 (10^4.61 copies/mL) because there are different estimates for the infectiousness threshold in the literature¹⁹, and using different thresholds allows us to explore different scenarios on this duration. Isolation was assumed to start immediately after symptom onset.

We employed a variable-period approach, tailoring isolation lengths based on age (below or above 60) and vaccination status (vaccinated or unvaccinated). The 60-year age threshold was selected in alignment with Singapore’s age-stratified COVID-19 public health interventions, such as the initial prioritization of COVID-19 vaccines for individuals aged 60 and older²⁰.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.