key: cord-0255688-mp44acnb authors: Arav, Y.; Fattal, E.; Klausner, Z. title: Increased transmissibility of emerging SARS-CoV-2 variants is driven either by viral load or probability of infection rather than environmental stability date: 2021-07-22 journal: nan DOI: 10.1101/2021.07.19.21260707 sha: 3c9c5b752ded5f940009e55c528c78770f9210f7 doc_id: 255688 cord_uid: mp44acnb Understanding the factors that increase the transmissibility of the recently emerging variants of SARS-CoV-2 (such as the Alpha, Epsilon, and Delta variants) can aid in mitigating their spread. The enhanced transmissibility could be attributed to one or more factors: higher stability on surfaces or within droplet nuclei suspended in air, increased maximal viral load or higher probability of infection. The relative importance of these factors on the transmission was examined using a validated stochastic-jump-continuous hybrid model. The transmissibility was quantified in terms of the household secondary attack rate (hSAR) which is the probability of transmission from an infected individual to a susceptible one in a household. We find that an increase in either the maximal viral load or the probability of infection is consistent with the observed hSAR of the variants. Specifically, in order to reach the relative increase in the hSAR of 40%, 55%, and 87% reported for the Epsilon, Alpha, and Delta variants (respectively), the maximal viral load should increase by 56%, 78%, and 125%, respectively. Alternatively, the probability of infection should increase by 34%, 53%, and 193%, respectively. Contrary to these results, even a dramatic increase in environmental stability increases hSAR by no more than 10%. Since December 2020 the genomic surveillance effort in many countries has led to the detection of numerous variants of SARS-Cov-2 1-3 , some of which have exhibited an increased transmissibility. These variants have raised concerns in the public health authorities worldwide due to the risk that they will spread faster than vaccine production and distribution 2, 4, 5 . All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.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 July 22, 2021. ; https://doi.org/10.1101/2021.07. 19 .21260707 doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. Understanding the mechanism that enhances the transmissibility of these variants is an important step in devising methods to control their transmission 6 . Respiratory viruses such as SARS-CoV-2 propagate via four modes of transmission 7 Genetic variations that affect any of the modes of transmission might be the factor that increases the transmissibility of a SARS-CoV-2 variant compared to the wild-type, which is the previously dominating virus strain 6 . Specifically, increased stability on surfaces, would increase the number of virus copies that survive on contaminated surfaces (such as hands, fomites, or environmental surfaces) and would increase the transmission through the direct (transmission mode 1) and indirect modes (transmission modes 2 and 3) 8 , hereafter referred to as factor 1; increased stability in droplet nuclei would increase the 2/10 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 8 , hereafter referred to as factor 2; increased maximal viral load 4, 9 would increase the viral shedding (the contagiousness of the primary) and thereby increase the transmission through all the modes 4, 9 , hereafter referred to as factor 3; probability of infection by a single plaque forming unit (PFU), meaning that a smaller number of virus copies is required to initiate an infection (increase the susceptibility of the secondary) 4 , hereafter referred to as factor 4. We note that the spread of variants whose increased transmissibility is due to factor 1 or 2 could be mitigated by adhering to stricter regimes of various hygienic and behavioral measures. There are several ways to characterize the transmissibility of a new virus variant. It can be quantified as the effective reproduction number of the invading new variant and compared to that of the wild-type 10 . This comparison is often expressed in relative terms 9, 11 . Another possibility is to describe transmissibility by estimating the secondary attack rate (SAR) defined as the probability of an infected person to infect a susceptible person 12, 13 . Often, the SAR is stratified by the different environments in which people may be exposed to an infected person, e.g., public transportation, healthcare and households 14, 15 . Among these, it was found that household settings are associated with high risk of infection by the SARS-CoV-2 virus 14, 16, 17 . This can be illustrated by the fact that during the first wave of the COVID-19 pandemic in Israel, 65.8% of the cases were infected at home 18 . The household SAR (hSAR) is closely related to the reproduction number 17, 19 , several studies have characterised the The aim of this work is to identify the factor (or factors) that can lead to the higher transmissibility of an emerging SARS-CoV-2 variant. A mechanistic mathematical model that describes SARS-CoV-2 transmission in a household 25 (which was not certified by peer review) 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 July 22, 2021. ; https://doi.org/10.1101/2021.07.19.21260707 doi: medRxiv preprint droplet and droplet nuclei, Figure 1 ). An outline of the model is presented here. The detailed model equations, parameters and validation are described in Arav, et al. 25 . The model equations are formulated in a hybrid continuous and stochastic-jump framework 26 in order to take into account two distinct dynamical regimes: fast-discrete random events that represent the actions of the individuals (such as coughing, talking, touching), and slow-continuous events (such as the decay of the virus on surfaces, hands, and in the air). In this framework, the actions of the individuals are described as stochastic jump Poisson processes, and represent behavior patterns that typically occur in the living room, kitchen, bath, and bedrooms. The model describes the transfer of virus copies that result from each action, and consequently it is not necessary to follow the specific location of each individual. The environmental decay processes of the virus on the hands and on surfaces are described using continuum dynamics. Since the actions of the individuals are represented as a stochastic process, we conducted a Monte Carlo simulation in which multiple realizations were computed to obtain the appropriate ensemble statistics. Thus it is possible to explicitly calculate higher order statistics crucial for the reconstruction of the observed serial interval distribution as well as the time dependant probability of infection 25 . The model validation was performed on data prior to December 2020, so it can be considered as describing the wild-type strain, before the emergence of the highly transmissible lineages. The examination of the effect of genetic variations that increase the stability of the variant in the environment was divided into two parts: genetic variations that increase the stability on surfaces (factor 1) and in the droplet nuclei that are suspended in the air (factor 2). The effect of factor 1 was examined by decreasing the decay rate on furniture (α f urniture ), fomites (α f omite ) and on the hands of the primary and the secondary individuals (α hand ). The effect of factor 2 was examined by decreasing the decay rate of the virus in the aerosol (α air ). The benchmark values that represent the wild-type were α air , α f urniture , and α f omite of 1, 6, and 6 1/h, respectively 27 . In order to quantify the effect of either factor 1 or 2 relative to the wild-type, the relevant decay rates were divided by values, from 2 up to 8. It should be noted that α f urniture and α f omite were set to equal values, based on the fact that the difference between environmental and fomite surfaces lies in their area and the rate that each type of surface is touched, but not in the decay rate of virus copies that are deposited on them 25 . In order to examine the effect of factor 3, the maximal viral load (L max ), we conducted simulations with a relative increase of this parameter, from 10% up to 100% with respect to the wild-type. The benchmark value of L max was 2 · 10 8 copies 28 . The effect of factor 4, genetic variations that increase the probability of infection by a single PFU was examined by increasing the reciprocal of the dose-response coefficient All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 July 22, 2021. ; https://doi.org/10.1101/2021.07.19.21260707 doi: medRxiv preprint k. For the SARS-CoV-2 wild-type, the value of k was 410 PFU, which translates to 1.2 · 10 5 viral copies 29, 30 . The effect of factor 4 was examined by performing model simulation with a relative decrease in the parameter k, from 10% to 200%. The increase of virus stability exhibited similar behavior regarding both stability on surfaces, factor 1, and in droplets nuclei suspended in the air, factor 2 ( Figure 2 ). Relative decrease in the decay rates of up to 2 leads to a relative increase of the hSAR but only up to 10%. However, a further decrease of the decay rates does not lead to further increase of the hSAR. The relative increase of the hSAR of 10% is far even from the reported relative hSAR increase of 40% associated the Epsilon variant, let alone from the even more transmissible variants, Alpha and Delta [21] [22] [23] [24] . Regarding the effect of the maximal viral load (factor 3) and the probability of infection by a single PFU (factor 4), it was found that the relative increase in the relative parameters is linearly associated with the relative increase of the hSAR (Figure 3 ). In both cases, the association is a strong positive relationship (R 2 = 0.99). Specifically, the fitted linear model describing the effect of factor 3 yields a slope of 0.68 and an intercept of 0.342 (R 2 = 0.99), whereas the coefficients of the fitted regression model describing the effect of factor 4 are a slope of 0.79 and an intercept of 0.342 (R 2 = 0.99). Using these linear relationships it is possible to estimate the relative increase in each of these factors in order to reach the relative increase in the hSAR of All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 July 22, 2021. ; https://doi.org/10.1101/2021.07.19.21260707 doi: medRxiv preprint 40%, 55%, and 87% reported for the Epsilon, Alpha, and Delta variants, respectively [21] [22] [23] [24] . If the increased transmissibility of the Epsilon, Alpha and Delta is driven by increase in factor 3, the maximal viral load should increase by 56%, 78%, and 125%, respectively. Regarding factor 4, the probability of infection by a single PFU should increase by 34%, 53%, and 193%, respectively. It should be noted that the increase of the hSAR resulted by the increase of either factors 3 and 4, does not change the relative contribution of each mode to the overall transmission. This is similar to the relative contribution in the wild-type, that is, approximately 70% of the copies transfer by direct contact, 20% by indirect contact of fomites, 10% by the droplet nuclei mode, and transmission by environmental surface is negligible 25 . Analysis of the model results showed that variants with enhanced environmental stability (either on surfaces, factor 1, or in the air, factor 2) exhibit only a modest increase of up to 10% in the hSAR (Figure 2A and B, respectively) . Since the hSAR of the Alpha, Epsilon, and Delta variants is 40% − 87% higher than the wild-type [20] [21] [22] 24 , we conclude that increased environmental stability could not be the factor that drives the increased transmissibility of these variant. This conclusion is consistent with the results of Schuit, et al. 8 , that found that the stability of SARS-CoV-2 aerosols does not vary greatly among circulating lineages, including the Alpha variant, thus indicating that the increased transmissibility is not due to enhanced environmental survival. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The results regarding factor 1 can be explained due to the fact that the survival of virus on the surfaces is not the rate limiting step in the direct and indirect transfer. Indeed, Arav, et al. 25 have shown that the rate limiting step in direct and indirect contact is the frequency of contact events on fomites and the face, which has a period of approximately 30 to 40 minutes. Regarding factor 2, can be attributed to the fact that the concentration of the droplet nuclei in the air is determined by the ventilation rate of the household which is 0.3h −1 31, 32 . Alternatively to the limited effect of factors 1 and 2, we have found that the hSAR increases linearly (coefficient of 0.7 − 0.8) with the maximal viral load, factor 3, and the probability of infection by a single PFU, factor 4 ( Figure 3A and B, respectively). Moreover, we were able to estimate the relative change in each factor that may lead to the observed increase of the hSAR of the Epsilon, Alpha, and Delta variants. These results support the possibility that genetic variations that increase either the contagiousness of the primary individual (factor 3) or the susceptibility of the secondary individual (factor 4) may be responsible for the observed increase in the transmissibility of these three variants. While these two factors have comparable impact on the hSAR, it should be noted regarding the Alpha and Epsilon variants, it was reported that the viral load associated with these variants was not significantly different from the viral load of other circulating strains 21, 33 . As these reports rule out the possibility of factor 3, it leaves factor 4 as the only factor that can lead to the increased transmissibility of the Epsilon and Alpha variants. While the exact mechanism by which genetic variations increase the probability of infection by a single PFU is not currently known, Nelson, et al. 34 and Gan, et al. 35 have shown that certain variations in the spike receptor binding domain (S RBD) increase the affinity to the human angiotensin-converting enzyme 2 (hACE2) and thereby promote the entry to the cell. This enhanced affinity of the S RBD to the hACE2 is likely to explain the greater transmissibility of many variants. It seems reasonable that the manifestation of this affinity is the increased probability of infection by a single PFU. This study found that the increase in the transmissibility is not due to environmental stability. Therefore, from a public health point of view, leading even stricter hygienic and behavioral measures are not expected to achieve a pronounced mitigating effect. However, the results that factors that possibly drive the increased transmissibility were found to be thos that affect all modes of transmission, may strengthen the importance of wearing masks in indoors environments. YA conceived the study, performed the formal analysis, developed the methodology, software and visualization, wrote the original draft and critically revised the manuscript. EF conceived the study, developed the methodology, acquired the funding and the computational infrastructure, and critically revised the manuscript. ZK conceived the study, performed the formal 7/10 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 July 22, 2021. ; https://doi.org/10.1101/2021.07.19.21260707 doi: medRxiv preprint analysis, developed the methodology, wrote the original draft and critically revised the manuscript. All authors gave final approval for publication and agree to be held accountable for the work performed therein. Genetic Variants of SARS-CoV-2 -What Do They Mean? 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No reuse allowed without permission.(which was not certified by peer review) 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 July 22, 2021. ; https://doi.org/10.1101/2021.07.19.21260707 doi: medRxiv preprint All rights reserved. No reuse allowed without permission.(which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.