key: cord-1004077-0e7q4xek
authors: Marc, A.; Kerioui, M.; Blanquart, F.; Bertrand, J.; Mitja, O.; Corbacho-Monne, M.; Marks, M.; Guedj, J.
title: Quantifying the relationship between SARS-CoV-2 viral load and infectiousness.
date: 2021-05-08
journal: nan
DOI: 10.1101/2021.05.07.21256341
sha: 416ba3c73e46c2dc22cf6ebea375666d6769fb62
doc_id: 1004077
cord_uid: 0e7q4xek

The relationship between SARS-CoV-2 viral load and infectiousness is not known. Using data from a prospective cohort of index cases and high-risk contact, we reconstructed by modelling the viral load at the time of contact and the probability of infection. The effect of viral load was particularly large in household contacts, with a transmission probability that increased to as much as 37% when the viral load was greater than 10 log 10 copies per mL. The transmission probability peaked at symptom onset in most individuals, with a median probability of transmission of 15%, that hindered large individual variations (IQR: [8, 37]). The model also projects the effects of variants on disease transmission. Based on the current knowledge that viral load is increased by 2 to 4-fold on average, we estimate that infection with B1.1.7 virus could lead to an increase in the probability of transmission by 8 to 17%.

After more than 16 months of an unprecedented pandemic, some key aspects of disease transmission remain poorly understood. While respiratory droplets and aerosols have been rapidly demonstrated to be a major route of transmission of SARS-CoV-2 1 , the role of the viral load as a driver of infectiousness has been suspected but not formally established. This lack of evidence is due to the fact that documented high-risk contacts occur mostly before the index has been diagnosed, with no information on the viral load level at the time of the contact. The relationship between viral load and infectiousness determines the timing of transmission, part of the inter-individual heterogeneity in transmission, and the impact of interventions (contact / case isolation, vaccination) on transmission. In the context of variants of concern 2,3 , that are likely associated with larger viral loads, it becomes even more critical to delineate the contribution of viral shedding from other suspected factors associated with an increased transmission. Further, as antiviral and vaccine strategies are being implemented, that directly reduce the amount of viral shedding 4 , it is essential to understand how they may contribute to a reduction in SARS-CoV-2 transmission.

One of the most exhaustive clinical study to address the question of viral load and infectiousness has been obtained through individuals included in a randomised controlled trial done in March-high-risk contact and the viral load measured at the time of diagnosis 5 . This suggests that viral load is associated with transmission; however, it does not quantify the role of viral load in disease transmission, as the viral load at the exact time of the contact remains unknown and may greatly differ from that measured, several days later, at the time of diagnosis.

In order to study in detail the role of viral load on the probability of transmission, we reanalysed these data by using a within-host model of viral dynamics 6, 7 to reconstruct the viral load levels of the index cases at the time of contact, and to infer the relationship between viral load and the probability of transmission after a high-risk contact. Further, we used the model to predict the effects of changes in viral load levels on the probability of transmission, representing the effects of infection with a variant of concern or infection in an individual in which vaccine would confer a partial protection against viral replication.

A total of 257 index cases and their 574 high-risk contacts (simply called contacts in the following) were included in this analysis (Supplementary Figure 1) . A high risk contact was defined as a contact of >15 min within 2 meters of distance from a symptomatic case 8 .

The majority of index cases were female (72%) with a median age of 42 (interquartile range, IQR: [31, 52]). A total of 544 swab samples were performed at days 0, 3 and 7 days after study inclusion. Symptoms occurred at a median time of 4 days (IQR: [3, 5] ) before the first swab

The majority of contacts (65%) and of infection events (65%) occurred ±1 day from symptoms onset (Supplementary Figure 2) .

Overall, 87 household contact led to an infection (proportion of transmission of 25.1%) and 29 non-household contacts led to an infection (proportion of transmission of 13%).

We used a target cell limited model to reconstruct the viral load kinetics of the index cases over time, assuming that the infection started 5 days before the onset of symptoms 6 . Although several models relating viral load to infectiousness were evaluated (see below), they all provided nearly identical fits to the viral load data predicted in the index cases ( Figure 1 ). In the final model (Model M2), the basic within-host reproductive number, 0 , quantifying the number of cell infections that occur from a single infected cell at the beginning, was estimated to 16.2, the loss rate of productively infected cells, , to 0.83 d -1 (corresponding to a half-life of 20 hours) and viral production , to 4.1 × 10 5 cells −1 .d -1 (Table 2) .

When reconstructing the viral profiles, the model predicted that the median peak viral load coincided with symptoms onset, with a median peak value of 9.8 log10 copies per mL (IQR: [9.1, 10.4] ).

We tested several models of probability transmission (see Methods) and estimated the parameters of both viral dynamics and probability of transmission simultaneously. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint Of note our models were associated with a large between-subject variability on the effect of the viral load, (as measured by the standard deviation of the associated random effects, )

suggesting that several other factors are involved in transmission, besides viral load. To represent this variability, we sampled 1,000 individuals in the population distribution to get prediction intervals for the viral load and the probability of transmission.

Using the simulated individuals, we inferred the viral load levels and the mean probability of transmission for both household and non-household contacts, that we compared with the observed proportion of infection for different viral load level category ( Figure 2 ). The mean probability of transmission increased from the fixed nominal value of 5% for viral load levels <10 6 copies per mL, to as much as 37% and 17% for viral load ≥10 10 copies per mL for household and non-household contacts respectively. This is in agreement with the value of 37% and 29% observed in the clinical study ( Figure 2 ).

Over the time of infection, the probability of transmission peaked at the time of symptom onset, albeit with large inter-individual variabilities ( Figure 3 ). In household contacts, the median peak of the probability of transmission was 15% (IQR: [8, 37] ), but the mean value was much larger, . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint to about 28%. The peak was much lower in non-household contacts, with a median value of 8% (IQR: [6, 13] , and mean value of 13%. As a consequence of our assumption that the probability of transmission after a high-risk contact returned to baseline level when viral load dropped below the threshold of viral culture, i.e., 6 log10 copies per mL 6 , the window for infection was much shorter than the duration of viral shedding. The probability of transmission was above baseline during a median duration of 12 days (IQR: [10, 15] ).

Finally, we used our model to characterize the effects of changes in viral load levels on the probability of transmission. For that purpose, we evaluated the impact of a change in the viral production rate, p, by a fold 2-100, which corresponds to an average increase in viral load of 1-7 cycle thresholds (Ct), at each time point.

To get a sense of the impact of these changes on infectiousness, we calculated the average probability of transmission after a high-risk contact in the overall population during the whole study period. We took into account the fact that contacts are not uniformly distributed, and we assumed a similar distribution of contacts as found in the original study for both household and . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint non-household contacts (Supplementary Figure 2 ). For the baseline scenario using the estimated parameters in our population, the model accurately reproduced the observed transmission probability, at 25% and 11% for household and non-household contacts, respectively. With an increased value of viral production rate p by a factor 2, which corresponds to the viral load increase caused by B1.1.7 strain in large scale epidemiological studies 9-11 , the average probability of transmission would increase to 27% and 12% for household and nonhousehold contacts respectively. With a 4-fold increase as suggested elsewhere 2 the average probability of transmission would increase to 29% and 13%, respectively ( Figure 4 ). The estimates for the P1 and B1.1.351 variants are much less well established, with values ranging from a 2-fold 2 to a 10-fold increase 12 . Assuming an increase by 8-fold of the viral load, the average probability of transmission would increase to 31% and 14%, respectively, i.e., an increase of more than 25% from the baseline scenario ( Figure 4 and Supplementary Table S2 ).

Conversely, we studied the effects of lower levels of viral load, as expected from a partial protection conferred by vaccination. Epidemiological studies in Israel reported a 3-5-fold lower viral load in infected vaccinated individuals as compared to unvaccinated individuals 4 .

Assuming a reduction by a factor 4 of the viral production rate, p, would lead to an average . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint probability of transmission of 21 and 10% for household and non-household contacts respectively. In another study relying on systematic repeated viral testing in both symptomatic and asymptomatic individuals, the effect of vaccine was much more dramatic, with a 100-fold reduction in viral load levels 13 . This would translate into an average transmission probability of 12 and 7%, which represents a decrease of 50% and 38% from the baseline scenario for household and non-household contacts respectively (Figure 4 and Supplementary Table S2 ).

In addition, we also tested the sensitivity of our results to the assumptions made for the effects of viral load. Exploring alternative models (M3) led to a largely similar result (Supplementary Table S2 ).

This is the first detailed description of the relationship between viral load and infectiousness.

We here quantified the impact of viral load on infectiousness obtained on a highly detailed data obtained in a large epidemiological study 8 . The effect of viral load was particularly large in household contacts, with a mean transmission probability that increased to as much as 37%

when the viral load was over 10 log10 copies per mL. Unlike what has been suggested until now by theoretical models 14, 15 , the probability of transmission increased continuously with viral load and no saturation effects were visible at high viral loads (Supplementary Figure 3) . However, and consistent with reports suggesting that the probability of transmission 16 greatly vary between individuals, the effect of viral load was individual-dependent. For instance, at the peak of infectiousness, the median probability of transmission during household contact was 15%, but ranged from 5 to 100%.

The model also provided information on the effects of variants on disease transmission. We relied on results found in large-scale epidemiological data, that reported an average increase of the B1.1.7 virus by 1-2 Ct 2, 9, 10 . This can be reproduced in our model by assuming that viral . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint production increases by a factor 2. Alternatively, as only the product p×T0 can be identified, this could also be due to B1.1.7 being able to infect twice as much target cells, as suggested by the fact that the N501Y substitution improved the affinity of the viral spike protein 3 . Regardless of the origin of this increased viral load, we estimated that an increase of viral load by a factor of 2 would increase the average transmission probability in household contacts from 25 to 27% (8% increase from baseline scenario). Assuming an increase by 4-fold of the viral load (2 Ct on average) would lead to a much more dramatic effect, increasing the average transmission probability in household contacts to 29% (17% increase from baseline scenario). Of note assuming a steeper effect of the viral load on the probability of transmission would lead to larger effect of variants (Supplementary Table S2 ).

Conversely, vaccination rollout is expected to confer a large level of protection, partly due to lower virus carriage in infected individuals. The exact magnitude of this decrease is difficult to quantify, and depends on the design of the studies, that include or not asymptomatic individuals.

In fact preliminary reports have reported numbers going from a 5 to 100-fold reduction in viral load levels 13 . Whatever the exact value, it is clear that such reductions could be associated with large reductions in the probability of transmission.

Our study has some important limitations that need to be acknowledged. First, the reporting of high-risk contacts is partial and remains prone to various reporting biases. One of them is the fact that at the time where the study was conducted, there was no firm evidence of the role of pre-symptomatic transmission. This could explain why in our study a large number of high-risk household contact were reported to occur the day of symptom onset. It is also possible that several of the household contacts were not unique and occurred multiple times. Because we had no information on these contacts, we did not conduct specific analyses on repeated contacts, but it is something that future epidemiological studies will need to investigate. Another limitation is that we had no genomic data to ensure that infection observed in contact individuals . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint results from an infection by the index case. In most infected contacts, we also did not have data on the time of symptom onset, which prevented us from detecting infections unlikely related to the contact identified in our study. However, the temporality of symptoms would not be sufficient to bring a decisive information on the infection event. Indeed, the study was Given the difficulty to access to very early virological data, this will remain a major limitation to this type of analysis. This can be partly studied in animal models 18 but obviously at the cost of a very specific system with limited translation to human epidemiology.

To conclude our study quantifies the probability of infection according to viral load level after a high-risk contact. This relationship can be used to predict the effects of changes in virus paradigm, caused by the emergence of new variants and/or the rollout of vaccination. We . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 8, 2021. estimate that 2-to 4-fold increase in viral load level observed with B1.1.7 virus could lead to an increase in the probability of transmission by 8 to 17% after a high-risk contact.

The study has received financial support from the National Research Agency (ANR) through 

Data used come from a cluster-randomized trial which included individuals with PCRconfirmed COVID-19 and their close contacts, and evaluated the efficacy of hydroxychloroquine as a pre-or post-exposure prophylaxis. The trial was conducted between March, 17 and April 28, 2020 in three out of nine health-care area in Catalonia, Spain. More details on the study protocol and main results can be found in the original publication 8 .

All index cases were aged 18 years or older with no hospitalisation, nasopharyngeal PCR positive results at baseline and mild symptoms onset within 5 days of inclusion. High-risk contacts were adults with a recent history of exposure and absence of COVID-19 like symptoms within the 7 days preceding enrolment. In the original publication, 282 index cases and the resulting 753 contacts were enrolled 5 ; here we did not include 3 index individuals (and their corresponding 25 contacts) for which no viral load data was available, 8 index individuals (and . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint their corresponding 19 contacts) for which no viral load was detected at any time point. Further, in 12 index cases (and their corresponding 127 contacts), no date of contact was available.

Finally, we removed contacts occurring more than 5 days before symptoms onset, as they are unlikely to originate from the index case given the disease incubation time 6 . Thus, overall, our analysis was performed on 257 index and 574 contacts (see Supplementary Figure 1 ). In 12 index cases, the date of symptoms onset was not known and was imputed to 4 days before their first swab sampling, which corresponds to the median value observed in this population.

Type of contact was considered as household or non-household, which included Nursing home contacts, Health-care worker and other undefined contacts.

We used a target cell-limited model to reconstruct nasopharyngeal viral kinetics in index cases 6, 19, 20 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 

Some parameters were fixed to ensure identifiability. The clearance rate was fixed at 10 −1 and the eclipse phase to 4 −1 based on previous work 6, 7, 24 . The proportion of infectious virus was assumed constant over time and was fixed to 10 −4 as observed in animal model 24 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. where: = ( 1 ℎ + 0 (1 − ℎ )) × exp ( ) with 1 (resp. 0 ) the effect of viral load on the probability of transmission in household contact (resp. non-household), and a Gaussian individual random effect with variance 2 . The baseline probability of transmission was fixed to 5% (α=-2.94) for viral load lower than 6 log10 copies per mL, which corresponds to the threshold for viral culture 6, 15 .

For each model, we estimated simultaneously the vector of individual parameter , which depends on both the parameters of the viral kinetic model ( 0 , , , 0 , , ) and the parameters of the transmission model ( , ). The model providing the lowest BIC was retained. All parameters were estimated by computing the maximum-likelihood estimator using the stochastic approximation expectation-maximization (SAEM) algorithm implemented in Monolix Software 2020R1 (http://www.lixoft.eu/) [27] [28] [29] .

We provided prediction intervals for viral load and transmission probability over time, depending on the nature of contact, namely household (ℎ = 1) or not (ℎ = 0). In this purpose, we performed simulations, sampling = 1000 individual vectors of parameters from the population distribution. Then, we derived the predicted viral load ( , ) and the predicted transmission probability at all times according to the type of contact ℎ ( , ).

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint

We then calculated the median viral load, ̂( t) and the median transmission probability ĥ ( ) over the simulated individuals, as well as the first and third empirical quantiles to provide prediction intervals.

All simulations were performed using the Simulx package on R.3.6.0.

Calculating the average probability of transmission We computed the resulting increase or decrease of the probability of transmission compared to the baseline scenario.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) Table S2 : Impact of changes in viral production rate on the average transmission probability during a high-risk contact. .

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

The copyright holder for this preprint this version posted May 8, 2021. ; https://doi.org/10.1101/2021.05.07.21256341 doi: medRxiv preprint

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