Analyzed data and model fittingWe identified 7 publications including at least one case with lesion samples meeting the inclusion criteria, and a total of 90 mpox cases (see section “Methods”). All cases were symptomatic, and most of them were reported in Europe. To standardize the collected data, we converted the reported cycle threshold values to viral load (copies/ml) using the conversion formula proposed in a previous study31 (Supplementary Table 1). We then fitted a viral clearance model to the longitudinal viral load data from lesion samples (Supplementary Fig. 1a and Supplementary Fig. 2). Estimated parameters suggested a median viral load of 7.7 log10 copies/ml (95% CI: 7.3–8.2) at symptom onset and a median viral clearance rate of 0.36 day−1 (95% CI: 0.24–0.44), respectively. Using these parameters, duration of infectiousness was estimated: we first assumed a threshold value for infectiousness as 6.0 log10 copies/ml based on data on viral replication in cell culture23,32,33, and the duration of infectiousness was estimated to be 10.9 days (95% CI: 7.3–21.6) following the onset of symptoms. Additionally, a prolonged duration of viral shedding was estimated: the viral load dropped below the limit of detection of a PCR test (2.9 log10 copies/ml) 30.9 days (95% CI: 23.4–50.6) after symptom onset (Supplementary Fig. 1b). This finding is consistent with previous studies suggesting the persistent presence of mpox viruses in clinical specimens23,34.Stratification for mpox casesThe 90 analyzed mpox cases were stratified into two groups Group 1 and Group 2 (Fig. 1a–c), using the K-means clustering algorithm based on three estimated individual-level parameters: the viral load at symptom onset, the total amount of virus excreted between symptom onset and the end of shedding, and the duration of viral shedding (see Supplementary Note 2). Group 1 had a lower viral load at symptom onset and faster viral clearance, whereas Group 2 showed a higher viral load at symptom onset and slower viral clearance. As a result, the estimated duration of infectiousness in Group 2 was longer than in Group 1 (Fig. 1c and Supplementary Fig. 1b). To compare the viral dynamics between the two groups, we conducted statistical tests: Individuals in Group 2 had significantly higher viral loads at symptom onset than individuals in Group 1 (\(p=5.7\times {10}^{-10}\) from the Mann–Whitney test). Viral clearance was significantly slower in Group 2 than in Group 1 (\(p=2.1\times {10}^{-9}\) from the Mann–Whitney test). Also, individuals in Group 2 had a larger area under the viral load curve (AUC) (\(p=4.6\times {10}^{-11}\) from the Mann–Whitney test). Thus, Groups 1 and 2 were characterized as groups with low and high transmission potential, respectively (Fig. 1d). To describe the difference in timing of viral clearance, we also reconstructed the probability of virus being detectable over time by using the model with estimated parameters for each group (Fig. 1e). In both stratified groups, the probability was greater than 90% at 3 weeks after symptom onset. However, in the total group (i.e., a group of all analyzed cases), the probability dropped to 69.9% (95% CI: 67.0–73.2) at 4 weeks after symptom onset, which is the upper bound of the isolation period recommended by the CDC and ECDC19,25. The probability in Group 1 at 4 weeks after symptom onset was 61.6% (95% CI: 58.2–64.8), whereas the corresponding probability in Group 2 was 94.6% (95% CI: 93.1–96.0).Fig. 1: Stratification of mpox virus infections.a Results of K-means clustering of mpox cases based on viral load at symptom onset, area under the viral load curve (AUC), i.e., the total amount of virus shed over time, and duration of viral shedding using estimated individual parameters. Data points indicate individuals and are colored based on the group that each individual is in. Principal component analysis (PCA) was used to visualize the clusters in two dimensions. Groups 1 and 2 comprise 71 and 19 mpox cases, respectively. b Stratified viral load data points measured in lesion samples. The cross represents data points where the viral load was below the limit of detection. c Reconstructed individual viral load trajectories in each group. The horizontal dashed line means the assumed infectiousness threshold. d Comparison between groups of: viral load at symptom onset (left panel); duration of viral shedding (middle panel); and area under viral load curve (right panel), respectively. The box-and-whisker plots show the medians (50th percentile; bold lines), interquartile ranges (25th and 75th percentiles; boxes), and 2.5th to 97.5th percentile ranges (whiskers). The sizes of Group 1 and Group 2 are 71 and 19 cases, respectively. Using the two-sided Mann–Whitney test, statistically significant differences between the two groups were found for viral load at symptom onset (\({p}\,{\mbox{value}}=5.7\times {10}^{-10}\)), duration of viral shedding (\({p}\,{\mbox{value}}=2.1\times {10}^{-9}\)), and area under viral load curve (\({p}\,{\mbox{value}}=4.6\times {10}^{-11}\)). Group 1 and Group 2 represent cases with low and high risk of transmission, respectively. e Viral clearance in each group. Probability of detectable virus after symptom onset for each group (left panel). The solid lines and shaded regions indicate means and 95% confidence intervals, respectively. The dashed lines and dotted lines stand for probabilities at 3 and 4 weeks after symptom onset, respectively. Bar plots represent the probabilities for 3 weeks (right upper panel) and 4 weeks (right lower panel) after symptom onset, respectively. The centers and error bars indicate means and 95% confidence intervals, respectively. Note that the estimated probabilities are based on 100 independent simulations.Symptom-based ruleUnder the estimated viral dynamics, we compared three types of rules for ending the isolation of individuals with mpox: a symptom-based rule, a fixed-duration rule, and a testing-based rule. To assess the effectiveness of the three rules, we considered three metrics: (1) the risk of prematurely ending isolation, (2) the average estimated infectious period after ending isolation (where this period was defined to be zero for individuals who are no longer infectious at the time of ending isolation), and (3) the average estimated duration for which individuals were isolated unnecessarily after the end of their infectious period (which could be positive or negative). Whether an individual was infectious or not was ascertained based on an assumed threshold viral load value (see section “Methods”).With these metrics, we first evaluated the current symptom-based isolation guideline (i.e., patients remain isolated until their skin lesions have cleared), accounting for variations in the timing of lesion clearance between individuals. We estimated distributions of the timing of lesion clearance using data from 43 mpox patients describing the duration of lesion presence (see section “Methods”). As a result, the mean duration from symptom onset to lesion clearance was estimated to be 25.2 days (95% CI: 21.6–29.7). The median and interquartile range (IQR) were 23.2 days and 17.6–30.7 days, respectively. The estimated values were consistent with typical current isolation periods of 2–4 weeks18,19,25,26,27,28 (Supplementary Fig. 3 and Supplementary Table. 4). In the total group, the risk of prematurely ending isolation was estimated to be 8.8% (95% CI: 6.7–10.5) and Group 1 had a lower risk of 4.9% (95% CI: 3.8–6.1). In addition, both stratified groups yielded an average estimated infectious period after ending isolation of lower than 1 day. However, in Group 2, the risk of prematurely ending isolation was 25.7% (95% CI: 23.8–28.0) with a longer estimated infectious period after ending isolation of 1.6 days (95% CI: 1.4–1.8). The mean estimated duration for which individuals in the total group were isolated unnecessarily after the end of their infectious period was 12.1 days (95% CI: 11.6–12.8), whereas Groups 1 and 2 had unnecessary isolation periods of 13.5 days (95% CI: 13.0–14.1) and 6.6 days (95% CI: 5.9–7.3), respectively (Supplementary Fig. 4).Furthermore, to ensure isolation is ended safely, we considered an additional isolation period beyond the time of lesion clearance. To lower the risk of prematurely ending isolation below 5% and the estimated infectious period after ending isolation below 1 day, the total group and Group 2 required additional isolation periods of 3 and 10 days on average, respectively. However, no additional isolation periods were necessary for Group 1. The resulting unnecessarily prolonged isolation periods in the total group, Group 1, and Group 2 were estimated to be 15.1, 13.5, and 16.6 days on average, respectively (Fig. 2a).Fig. 2: Three different isolation rules for different groups.a Symptom-based rules. The vertical dotted lines mean the current symptom-based isolation guideline. The x-axis represents the additional isolation period from the current guideline. b Fixed-duration rules. The x-axis represents the fixed period of isolation. Left panels in both a and b show the risk of prematurely ending isolation for different isolation periods. The horizontal lines correspond to 5%. Estimated infectious period after ending isolation for different isolation periods (middle panels). The horizontal lines correspond to 1 day. The estimated period for which individuals are isolated unnecessarily after the end of their infectious period for different isolation periods (right panels). The squares and circles indicate the points with the lowest unnecessarily prolonged isolation period for which the following conditions are satisfied: i) the risk of prematurely ending isolation is lower than 5% and ii) the estimated infectious period after ending isolation is shorter than 1 day. The vertical dashed lines correspond to the optimal additional isolation period and the optimal fixed duration of isolation in the total group for symptom-based rules and fixed-duration rules, respectively. The solid lines and shaded regions in each panel indicate means and 95% confidence intervals, respectively. c Testing-based rules. The risk of prematurely ending isolation (first row of panels), the estimated infectious period after ending isolation (second row of panels), the estimated isolation period following the end of infectiousness (third row of panels), and the overall isolation period (fourth row of panels) are shown for different intervals between tests and numbers of consecutive tests indicating loss of infectiousness necessary to end isolation. PCR (polymerase chian reaction) tests (limit of detection \({{\boldsymbol{=}}}\) 2.9 log10 copies/ml) were used to measure viral load. The areas surrounded by solid lines are those with 5% or lower risk of prematurely ending isolation and with 1 day or shorter estimated infectious period after ending isolation, respectively. The triangles correspond to the points with the shortest estimated isolation period following the end of infectiousness for which both conditions noted above are satisfied. Color keys and symbols apply to all panels. Note that the estimated values are based on 100 independent simulations.In our main analyses, we assumed that the presence or absence of symptoms was independent of viral dynamics. However, as a sensitivity analysis, we evaluated the current symptom-based rule for the total group under different assumed relationships between individual viral dynamics and the duration of lesion presence (see section “Methods”). The risk of ending isolation prematurely was lower when increased and/or prolonged viral shedding was assumed to be more strongly correlated with slower lesion clearance—the estimated risk under our baseline assumption (i.e., that lesion clearance is independent of viral shedding) can therefore be considered as an upper bound. This is because, if the presence of lesions is shown to be positively correlated with viral shedding, patients with fast lesion clearance could end isolation safely, and thus the estimated risk under such conditions would be lower than the baseline assumption. The unnecessarily prolonged isolation periods in this supplementary analysis were found to be comparable to those under the baseline setting and were lower than 2 weeks on average (Supplementary Fig. 5).Fixed-duration ruleUnder a fixed-duration rule of ending isolation 3 weeks after symptom onset, the risk of ending isolation prematurely in the total group was estimated to be 5.4% (95% CI: 4.1–6.7). The average estimated duration for which individuals were isolated unnecessarily after the end of their infectious period was 8.3 days (95% CI: 8.0–8.6). Group 1 had a lower risk of ending isolation prematurely of 1.9% (95% CI: 1.0–2.9), and a longer unnecessary isolation period of 9.7 days (95% CI: 9.4–9.9). However, in Group 2, a higher risk of 25.7% (95% CI: 23.2–28.0) was estimated, with a shorter unnecessary isolation period of 2.8 days (95% CI: 2.4–3.1). To guarantee a risk of prematurely ending isolation below 5% and an estimated infectious period after ending isolation shorter than 1 day, we found that the total group, Group 1, and Group 2 needed to be isolated for 22, 19, and 29 days, respectively. In this case, the estimated duration for which individuals were isolated unnecessarily after the end of their infectious period was estimated to be 9.4, 7.7, and 10.8 days for the total group, Group 1, and Group 2, respectively (Fig. 2b).Testing-based ruleFor symptom-based and fixed-duration rules, isolation of individuals with mpox ends after lesion clearance or fixed-time period following symptom onset, so the three metrics considered here are determined by the mean symptom duration or the predefined isolation period (Fig. 2a, b). By contrast, a testing-based rule is dependent on both the time interval between tests and the exact criterion used for ending isolation (see section “Methods”). Under a criterion in which isolation ends following two consecutive PCR test results indicating loss of infectiousness with daily testing (similar to a criterion widely used for COVID-19)17, the total group had a risk of prematurely ending isolation of 52.2% (95% CI: 49.7–54.6), and the estimated infectious period after ending isolation was calculated to be 2.3 days (95% CI: 2.1–2.5). Similarly, high risks of prematurely ending isolation, accompanied with an estimated infectious period after ending isolation longer than 1 day, were estimated in the stratified groups (first-row and second-row panels in Fig. 2c).By varying the criteria (i.e., the required number of consecutive test results indicating loss of infectiousness and the time interval between tests), different testing-based isolation rules can be tested in terms of their effects on the three metrics. The risk of prematurely ending isolation and the estimated infectious period after ending isolation decreased with a longer interval between tests and with a larger number of consecutive test results indicating loss of infectiousness (first-row and second-row panels in Fig. 2c), whereas the estimated duration for which individuals were isolated unnecessarily after the end of their infectious period increased (third-row panels in Fig. 2c). Under the conditions that the risk of prematurely ending isolation is lower than 5% and the estimated infectious period after ending isolation is shorter than 1 day, the minimum value of the unnecessary isolation period in the total group was 7.4 days (95% CI: 7.1–7.7) with three consecutive test results indicating loss of infectiousness and an interval of 5 days between tests (purple triangles in Fig. 2c). Correspondingly, an isolation period of 20.1 days (95% CI: 19.7–20.5) was required on average. On the other hand, under the same conditions, stricter rules were needed for Group 2: four consecutive test results indicating loss of infectiousness and an interval of 2 days between tests were needed to minimize the estimated duration for which individuals were isolated unnecessarily after the end of their infectious period to 8.4 days (95% CI: 8.0–8.7), with a mean isolation period of 26.6 days (95% CI: 26.0–27.0) (red triangles in Fig. 2c).To further evaluate the uncertainty in the test-based rule, we considered a different type of measurement error model (i.e., a proportional error model), where the error variance increases in proportional to the predicted mean viral load, and examined the corresponding difference in the total group as a sensitivity analysis (see section “Methods”). While the measurement error was constant in the main analysis (i.e., constant error model), the proportional error model described higher error variance near the assumed infectiousness threshold. As a result, a stricter optimal isolation rule was needed to lower the risk and the estimated infectious period after ending isolation below 5% and 1 day, respectively: four consecutive test results indicating loss of infectiousness and an interval of 3 days between tests. However, the minimized unnecessary period and corresponding optimal isolation period under the proportional error model were comparable to the constant error model (Supplementary Fig. 6).Additionally, whereas we focused on PCR testing in our main analyses, we conducted further analyses considering rapid antigen tests (RATs) to evaluate the effectiveness of using different test types when applying the testing-based rule. Under the testing-based rules using RATs, test results correspond to negative results (i.e., measured viral loads below a limit of detection) (see section “Methods”). When RATs with either high or low sensitivity were utilized in the testing-based rule, the optimal isolation periods on average were comparable with those under PCR testing. However, the optimal testing rules for ending isolation differed depending on RAT sensitivity: 2 consecutive negative results with 3-day intervals between tests were optimal for the high sensitivity RAT and 5 consecutive negative results with 3-day intervals between tests were optimal for the low sensitivity RAT. In both scenarios, a higher number of total tests was required to meet the specified conditions (i.e., the risk of prematurely ending isolation \(\le\)5% and the estimated infectious period after ending isolation \(\le\)1 day) (Supplementary Fig. 7) than for PCR testing, since even high sensitivity RATs are typically much less sensitive than PCR tests (see Supplementary Note 5 and Supplementary Fig. 8). Additionally, RATs only provide qualitative test results (i.e. positive or negative), making it impossible to determine whether an individual who tests positive has a viral load that has fallen below the assumed infectiousness threshold.Comparison between three different isolation rules for ending isolationTo highlight the difference between the three isolation rules for each group, we compared the three types of rule by computing the optimal rules in which the estimated isolation period following the end of infectiousness is minimized while ensuring that the risk of prematurely ending isolation is less than 5% and the estimated infectious period after ending isolation is less than 1 day (squares, circles, and triangles in Fig. 2). In the total group, the optimized symptom-based (i.e., current guideline \(+\)3 days), fixed-duration, and testing-based rules gave isolation periods of 28.3, 22, and 20.1 days, resulting in minimized unnecessary isolation periods of 15.1, 9.4, and 7.4 days on average, respectively (Fig. 3). In particular, compared to the current (non-optimized) symptom-based rule, the other two optimized rules involved shorter isolation periods and reduced unnecessarily prolonged isolation periods. In Group 2, the testing-based rule led to an unnecessary isolation period that was 8.2 and 2.4 days shorter than the symptom-based and fixed-duration rules, respectively. The testing-based rule in Group 1 yielded an unnecessary isolation period of 7.1 days shorter than the symptom-based rule, whereas it was comparable to the fixed-duration rule. However, compared with the other two rules in the total group, the testing-based rule in Group 1 could reduce the unnecessary isolation period to 17.7 days, with the optimal isolation period of 6.4 days.Fig. 3: Comparison between three different isolation rules for different groups.The filled squares, circles, and triangles represent symptom-based, fixed-duration, and testing-based rules, respectively. Each symbol represents the mean length of isolation using the rule that minimizes unnecessarily prolonged isolation under the conditions that the risk of prematurely ending isolation is less than 5% and the estimated infectious period after ending isolation is less than 1 day. Note that for testing-based rules, the interval between tests and the number of consecutive tests indicating loss of infectiousness necessary to end isolation were chosen to minimize the unnecessarily prolonged isolation period. The vertical lines indicate the optimized isolation periods of three isolation rules for the total group. The unfilled square with outline indicates the current (non-optimized) symptom-based rule for the total group.In addition, to assess the effectiveness of the testing-based rule, we examined the difference between the testing-based rule and the other two rules in the total group. The considered conditions for this assessment were; three consecutive test results indicating loss of infectiousness and a 5-day interval between tests for the testing-based rule (Fig. 2c), the current isolation guideline (i.e., the estimated duration of lesion presence) for the symptom-based rule, and the 22-day isolation period for the fixed-duration rule (Fig. 2a, b). Compared with symptom-based and fixed-duration rules, 63.2% (95% CI: 60.8–66.0) and 63.5% (95% CI: 60.6–65.4) of the total group could reduce their isolation periods using the testing-based rule, respectively (Supplementary Fig. 9a). The mean isolation period was shortened by 10.8 and 5.5 days compared to symptom-based and fixed-duration rules, respectively, and the average unnecessarily prolonged isolation period was also effectively reduced (Supplementary Fig. 9b, c). In these cases, the total number of tests required for ending isolation in the testing-based rule was estimated to be from 3 to 7 times (Supplementary Fig. 9d).As a sensitivity analysis, we varied the assumed infectiousness threshold and investigated the corresponding difference in the estimated period for which individuals were isolated unnecessarily after the end of their infectious period between the three rules (Supplementary Fig. 10). When the assumed infectiousness threshold is higher, the corresponding estimated infectious period becomes shorter, leading to a shorter required isolation period and shorter period of unnecessary isolation given the same acceptable risk. Our analysis showed that a higher assumed infectiousness threshold resulted in smaller differences between the fixed-duration and testing-based rules for each stratified group, which was consistent with our previous findings for COVID-199. On the other hand, simulations for the symptom-based rule in the total group suggested that the current guideline would lead to safer ending isolation but longer unnecessary isolation periods if the assumed infectiousness threshold value was increased.We used an assumed infectiousness threshold of the viral load (6.0 log10 copies/ml) as a cut-off value for assessing isolation rules in the main analysis; however, other metrics for the risk of prematurely ending isolation could also be considered. To demonstrate this, we estimated the average area under the viral load curve (AUC) following the end of isolation for the total group under the different isolation rules, and compared the estimated values with the AUC without isolation (see Supplementary Note 6). Without any isolation, the average AUC was estimated to be 108.5 copies/ml·days (95% CI: 108.4–108.6). On the other hand, the estimates of average AUC after ending isolation were 106.3 copies/ml·days (95% CI: 106.1–106.5), 106.0 copies/ml·days (95% CI: 105.8–106.1), and 105.8 copies/ml·days (95% CI: 105.7–105.9) under the current isolation guideline (i.e., the estimated duration of symptoms) for the symptom-based rule, the 22-day isolation period for the fixed-duration rule, and three consecutive test results indicating loss of infectiousness and a 5-day interval between tests for the testing-based rule, respectively. Compared to the case of no isolation, the average AUC was reduced by more than 95% under all three isolation rules, with the optimized testing-based rule giving the greatest reduction in the AUC (Supplementary Fig. 11). This indicates that the risk of prematurely ending isolation can be limited through those isolation rules.Additionally, to highlight the necessity of the optimal isolation strategy (i.e., three consecutive test results indicating loss of infectiousness and a 5-day interval between tests) for the testing-based rules, we compared its average AUC to one under the other testing strategy. Since the mpox viral load continuously decreases over time since symptom onset, only one test result may be considered sufficient to guarantee the loss of infectiousness. However, this strategy may miss the ongoing infectiousness due to the measurement error (Supplementary Fig. 12a), whereas the optimal isolation strategy may end isolation more safely (Supplementary Fig. 12b). The average AUC under the strategy with one test result indicating loss of infectiousness and a 5-day interval between tests was estimated to be 107.8 copies/ml·days (95% CI: 107.7\(-\)107.9), much higher than one under the optimal testing strategy (Supplementary Fig. 12c).As a sensitivity analysis, we considered an alternative two-phase exponential decay model35, estimated the viral dynamics, and assessed the effectiveness of different isolation rules. In this additional analysis, to ensure that the parameters were identifiable, we used data from 30 cases (out of 90 cases with lesion samples) for which the viral load in lesion samples was recorded at four or more time points (see Supplementary Note 7). Compared to the baseline model (one-phase exponential decay model), the two-phase model indicated a higher viral load at symptom onset with a faster clearance in the first phase but with a slower clearance in the second phase (Supplementary Fig. 13a, Supplementary Fig. 14, and Supplementary Table 5), resulting in a longer estimated duration of infectiousness (p = 2.1 × 10−4 from the Mann-Whitney test) (Supplementary Fig. 13b). However, there was no significant difference in the duration of viral shedding between the baseline model and the two-phase exponential decay model (Supplementary Fig. 13c). For symptom-based and fixed-duration isolation rules under the two-phase exponential decay model, longer isolation periods on average were needed for ending isolation than using the baseline model. On the other hand, under the testing-based rules, the required isolation period was comparable with the baseline model (Supplementary Fig. 13d). Consequently, in the two-phase exponential decay model, the testing-based rules again substantially reduced the unnecessary duration of isolation, with shorter required isolation periods than under the symptom-based and fixed-duration rules.Comparison between lesion and other samples for infectiousness after ending isolationTo demonstrate that lesion samples are suitable for designing isolation rules, we compared the viral dynamics that we inferred using lesion samples to analogous results obtained using other samples. Specifically, we used longitudinal viral load data measured in upper respiratory tract, blood, and semen samples from the same mpox cases to estimate mpox virus dynamics in those samples (Supplementary Table 1, Supplementary Table 2, Supplementary Fig. 15a, and Supplementary Fig. 16). Following symptom onset, other samples exhibited lower viral loads compared with lesion samples. For example, at the optimal ending isolation period of 22 days under fixed-duration rules, the viral load in lesion samples was substantially higher than in other samples (Supplementary Fig. 15b). Moreover, we compared the predicted infectiousness in lesion samples and other samples by estimating the proportion of individuals who remained infectious on day 22 after symptom onset. Around 3% of individuals were estimated to be infectious when lesion samples were used, whereas the viral load never exceeded the assumed infectiousness threshold for the other samples (Supplementary Fig. 15c). This suggests that infectious individuals with mpox may be missed if we implement a testing-based rule with samples other than lesion samples.
