key: cord-0806518-b1wg77qo
authors: Su, H.; Cheng, Y.; Poeschl, U.
title: Synergetic measures needed to control infection waves and contain SARS-CoV-2 transmission
date: 2021-11-25
journal: nan
DOI: 10.1101/2021.11.24.21266824
sha: 71b49882339eccceccc6630bade7302a2e555e1a
doc_id: 806518
cord_uid: b1wg77qo

The public and scientific discourse on how to mitigate the COVID-19 pandemic is often focused on the impact of individual protective measures, in particular on immunization by vaccination. In view of changing virus variants and conditions, however, it seems not clear if vaccination or any other single protective measure alone may suffice to contain the transmission of SARS-CoV-2. Here, we investigate the effectiveness and synergies of vaccination and different non-pharmaceutical interventions such as universal masking (surgical, N95/FFP2), distancing & ventilation, contact reduction, and testing & isolation as a function of compliance in the population. We find that it would be difficult to contain SARS-CoV-2 transmission by any individual measure as currently available under realistic conditions. Instead, we show how multiple synergetic measures can be and have to be combined to decrease and keep the effective reproduction number (Re) below unity, even for virus variants with increased basic reproduction number (R0). We suggest that the presented approach and results can be used to design and communicate efficient strategies for mitigating the COVID-19 pandemic, depending on R0 as well as the efficacy and compliance achieved with each protective measure. At vaccination rates around 70%, the combination and synergies of universal masking, distancing & ventilation, and testing & isolation with moderate compliances around 30% appear well suited to keep Re below 1 and prevent or suppress infection waves. Higher compliance or additional measures like contact reductions (confinement/lockdown) are required to effectively and swiftly break intense waves of infection. For schools, we find that the transmission of SARS-CoV-2 can be contained by 2-3 tests per week combined with distancing & ventilation and masking.

The COVID-19 pandemic has severe health, economic, and societal effects [1] . Immunization by vaccination is one of the most important and prominent measures to control and mitigate the transmission of SARS-CoV-2, which has the benefit of not just reducing the transmission but also reducing the average severity of disease [2] . Recent developments, however, suggest that the progress and effectiveness of vaccination may not suffice for suppressing or breaking waves of infection and swiftly mitigating the spread of COVID-19 [3] . Besides vaccination, common further measures to control and contain the transmission of SARS-CoV-2 are universal masking, distancing & ventilation, contact reduction, and testing & isolation [4] [5] [6] [7] [8] [9] . Here, we investigate and quantify the effectiveness and synergies of these measures in reducing the effective reproduction number, Re. In the main text and figures we focus on a basic reproduction of R0 = 5 that approximates the transmissibility of the delta variant of SARS-CoV-2 [10] . In the supplement, we also refer to higher and lower values (R0 = 3 or 8).

A detailed account of the scientific approach and methods applied in our study is given in the supplementary text (sect. S1). Based on recent observations, we assume that the probability of SARS-CoV-2 transmission is on average reduced by approx. 70% for vaccinated persons [11] [12] [13] [14] . Universal masking reduces both the exhalation and the inhalation of respiratory viruses like SARS-CoV-2 (source control and wearer protection) and can thus reduce the probability of transmission by approx.

80% in case of surgical masks and approx. 99% in case of N95/FFP2 masks (sect. S1; . Physical distancing by at least 1-2 meters and proper ventilation of indoor environments can decrease the risk of droplet (>100 µm) and aerosol transmission (<100 µm) in indoor environments by approx. 90% (supplementary text, sect. S1), whereby distancing primarily reduces droplet transmission and ventilation primarily reduces aerosol transmission [4] [5] [6] [7] 15] . Reducing the number of contacts leads to a directly proportional decrease of Re [16] , and the effects of testing & isolation of infected persons on Re can be described as detailed in the supplement (sect. S1) [17] .

For each of the investigated protective measures, Figure 1 shows how Re decreases with increasing compliance in the population. Vaccination alone (black line) can reduce the reproduction number from R0 = 5 to Re = 2.5 at 70% compliance, which corresponds approximately to the current rate of vaccination in Germany (https://impfdashboard.de/). Even at 100% compliance, however, vaccination alone would not reduce Re below 1 as required to contain the transmission. Without other protective measures, Re would remain as high as 1.5, leading to continued exponential growth. In other words, the currently available vaccines are highly protective against the disease and severe outcomes of COVID-19 [11] [12] [13] [14] , but they are not sufficient to contain and end the transmission of SARS-CoV-2 without synergetic measures. For R0 = 5 or higher basic reproduction rates, even a vaccine that reduces the probability of infection and transmission by 95% [2] would require vaccination rates higher than 85% to decrease Re below 1 (Fig. S1 ). In theory, distancing & ventilation alone (yellow line) could decrease Re to 0.5 at 100% compliance, but at more realistic compliance rates around 50% as discussed below, Re would also remain above 1. Similarly, universal masking (red line) with 100% compliance could bring Re close to 1 in case of surgical masks (Fig. 1A) and well below 1 in case of N95/FFP2 masks (Fig. 1B ), but at more realistic compliance rates around 50%, Re would again remain above 1.

When all these measures are combined (solid blue line), compliance rates around 50% are sufficient to bring Re close to 1 in case of surgical masks (Fig. 1A) and well below 1 in case of N95/FFP2 masks is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 25, 2021. ; https://doi.org/10.1101/2021.11.24.21266824 doi: medRxiv preprint combined with distancing & ventilation ("physical measures", dashed blue line), Re would fall below 1 at 50% compliance with N95/FFP2 masking (Fig. 1B) . Note, however, that 50% compliance with masking are not easy to achieve as discussed below and in . We are not suggesting to promote these physical measures without vaccination, which would also be missing the benefit of reducing both the transmission of the virus and the severity of the disease by immunization [2, [11] [12] [13] [14] .

Nevertheless, the "physical measures" curve shows, that the synergetic effects of combining and properly applying these simple measures are strong enough to reduce the reproduction number substantially, e.g., for breaking or suppressing waves of infection.

The actual rates of vaccination vary widely due to different supplies, age limits, and willingness. For example, the percentages of fully vaccinated people are around 28% in India, 58% in the U.S.A., 68%

in Germany, 88% in Portugal, and 42% worldwide at this time (November 2021) [18] . In our study, we are not explicitly accounting for persons immunized by recovery from the disease. Depending on the level of immunization, they can be implicitly included in the vaccination rate (compliance). Given an approximate efficacy of 70% and an approximate upper limit of 90% for compliance, vaccination can only reduce Re from 5 to approx. 1.9.

For universal masking, 100% compliance would be difficult to achieve because masking is not always possible and practical, for example at home, during eating or drinking in restaurants and bars, in schools and kindergartens, etc. [6] . The potential importance of such situations is demonstrated by a recent modeling study attributing around 10% to 40% of daily infections to restaurants and cafés/bars [19] . Moreover, a lack of willingness to follow recommendations or mandates for mask use may also lead to low compliance with mask wearing. For example, inpatient respiratory protection studies show that adherence rates vary from 10% to 84% for health care personnel [20] [21] [22] . Similar effects can be expected when wearing masks with low efficiency or poor fit and high penetration or leakage rates [6, 23] . Combining these effects, we may estimate ~50% as an effective upper limit for the compliance with universal masking. For physical distancing, we may expect a similar effective upper limit of compliance because distancing may be difficult under the same or similar conditions that are unfavorable for masking. With regard to ventilation, earlier investigations indicate that the ventilation of indoor environments is often much lower than recommended, and the values recommended for common indoor environments are also lower than the ventilation rates used for effective infection control in health care units [7, 24] . We found no data specifically suited for estimating populationaverage ventilation effects [7] , but based on the available literature we assume that the effective upper limit of compliance with distancing & ventilation is similar to the value estimated for distancing (approx. 50%).

Thus, it would be difficult to contain SARS-CoV-2 transmission and end the pandemic by any individual measure as currently available under realistic conditions. On the other hand, Fig. 1 shows is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 25, 2021. ; https://doi.org/10.1101/2021.11.24.21266824 doi: medRxiv preprint that the synergetic effects of combining the investigated protective measures at realistic levels of compliance can decrease Re from R0 = 5 to well below 1. In case of new virus variants, the efficacy of vaccines may be reduced, but the effectiveness of simple physical measures should not change much.

In case of higher reproduction numbers (e.g., R0 = 8, Fig. S5 ), higher compliances or additional measures would be required as discussed below. In the following, we explore the synergies of combining vaccination with universal masking, distancing & ventilation, contact reduction, and testing & isolation. would require compliances higher than 70%, which appear unrealistically high as discussed above.

With universal masking at a level of 30% (red line), decreasing Re below 1 would require distancing & ventilation compliances around 50% in case of surgical masks (Fig. 3A ) and around 30% for N95/FFP2 masks (Fig. 3B ). As discussed above, compliance levels around 30% are not unrealistic.

Thus, high compliance with universal masking in combination with distancing & ventilation may suffice to prevent or suppress waves of infection in populations with moderate vaccination rates (e.g., in Germany).

In Figure 4 , we include the effect of contact reduction. It shows how Re decreases as a function of contact reduction for different compliances with universal masking at a fixed vaccination rate of 70%.

With universal masking at 30% compliance (Figs. 4A and 4B, red line), decreasing Re below 1 would . CC-BY-NC-ND 4.0 International license It is made available under a perpetuity.

is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint Testing & isolation of infected persons is a protective measure particularly common and relevant for mitigating the transmission of SARS-CoV-2 in schools [17] (https://www.cdc.gov/coronavirus/2019ncov/community/schools-childcare/k-12-contact-tracing/about-isolation.html ). Figure S7 shows the results obtained for various further combinations of protective measures at different levels of compliance. In practice, the frequency of testing has to be adjusted according to the rates of false negative results [28] (sect S1), and the effects of incomplete isolation have to be considered, which may reduce the effectiveness of this measure.

Nevertheless, testing & isolation may be highly effective not only in educational but also in workplace and private environments, especially with increasing vaccination rates (see Fig. S7 ).

We suggest to further extend and validate the above results by target-oriented collection and analysis of observational data. The modeling tools developed and applied in this study will be made freely available on the internet. In this context, it will be important and challenging to clarify and resolve the actual contributions of viruses in respiratory particles of different sizes, e.g., the contribution of aerosol versus droplet transmission. This will be worthwhile for both the traditional medical cut-off at 5 µm, distinguishing between fine and coarse droplets, as well as for the physical cut-off at 100 µm, distinguishing between suspended and ballistic droplets and particles, respectively [5, [29] [30] [31] [32] is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 25, 2021. ; https://doi.org/10.1101/2021.11.24.21266824 doi: medRxiv preprint N95/FFP2 masks are highly effective against aerosol transmissions, and are even more effective against droplet transmissions because of the higher filtering efficiency of masks against large droplets [36, 37] .

We suggest that the presented scientific approach, results, and tools can be used to design efficient strategies to contain the transmission of SARS-CoV-2 in different environments and to mitigate the COVID-19 pandemic worldwide. Our quantitative results are consistent with earlier studies and recommendations [3, 38, 39] , and the modeling tools can be used to explore and refine the synergetic effects of combining multiple protective measures. For example, universal masking should be promoted and the efficacy and suitability of different masks against aerosol and droplet transmission under different conditions should be further clarified and communicatedin particular, why any decent mask is better than none, why tightly fitting FFP2 masks are particularly effective, and why masks are also useful in outdoor gatherings [6, 23] . Efficient ventilation of classrooms and other indoor environments could be fostered, optimized and assessed by readily available techniques like exhaust fans, air ducts for displacement ventilation, and CO2 sensors etc. [7, 15, 40] . Testing & isolation should be extended in schools and other educational and workplace environments [17] , and the frequency of testing may be adjusted according to the non-linear relation to Re as well as the rates of false negative results [28] , and the effects of incomplete isolation. The strong dependence of Re on compliance highlights the importance of situations where masking, distancing & ventilation or isolation are not possible, impractical, or ineffectivein particular during eating/drinking in restaurants/bars, schools/kindergartens, trains/planes, and at home. In such situations, it may, for example, help to wear masks alternatingly. Obviously, infectious fluids can also be transferred via surface contacts, and standard hygiene procedures against fomite transmission should also be followed (https://www.cdc.gov/coronavirus/2019-ncov/more/science-and-research/surfacetransmission.html).

The simple and robust methods and the easy-to-understand plots of Re vs. compliance provided in this study may help to communicate these strategies and to demonstrate the importance of cooperation to the wider public. Moreover, they may help to convince both the public and decision makers that each of the currently available measures by itself is insufficient to contain the transmissions of SARS-CoV- is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 25, 2021. ; https://doi.org/10.1101/2021.11.24.21266824 doi: medRxiv preprint fast we can do it to save more lives and reduce the probability of further dangerous mutations of SARS-CoV-2.

This study was supported by the Max Planck Society (MPG). We acknowledge and emphasize the importance of Open Access to the studies and materials referenced and used in our investigations. Our research profits from Open Access policies for COVID-19-related publications, and our experience confirms that Open Access indeed accelerates scientific progress and should be extended as widely as possible. Author contribution: H.S. and Y.C. designed and led the study. Y.C., H.S. and U.P. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted November 25, 2021. 

Supplementary Text S1 Figs. S1 to S7

By definition [1], the basic reproduction number R0 can be linked to P0, the basic population average infection probability by

where d represents the average duration of infectiousness, and c represent average daily numbers of human contacts.

Vaccination, non-pharmaceutical interventions such as universal masking (surgical, N95/FFP2), distancing & ventilation, contact reduction, and testing & isolation can reduce Re by reducing the infection probability (P), duration of infectiousness or daily contacts.

The effectiveness of individual measure, Ei, can be defined as

where Re,i represents the effective reproduction number after implementing the measure i.

The effectiveness of multiple independent measures, Etot, can be calculated by

In the following, we introduced how the effects of protective measures on Re were calculated in this study.

Evac, the effectiveness of vaccination on Re depends on the vaccination rate and the corresponding effectiveness of vaccines, Evac = vaccine effectiveness * vaccination rate (S4)

Among different effectiveness parameters (e.g., against infections, or severe, critical or fatal disease), we considered the effectiveness against infections as most relevant for Re and transmission. Based on recent observations, we assume that the probability of SARS-CoV-2 transmission is on average reduced by approx. 70% for vaccinated persons [11] [12] [13] [14] . Here, we are not explicitly accounting for persons immunized by recovery from the disease. Depending on the level of immunization, they can be implicitly included in the vaccination rate.

Emask, the effectiveness of universal masking on Re is calculated for both aerosol transmission (via respiratory particle with diameters < 100 µm) and droplet transmission ( respectively, we can then use them by the third and the fourth term on the right-hand side of Eq. S5. Here, we assume a contribution 30% droplet transmission is through eyes.

Because the relative contribution of aerosol transmission (respiratory particles <100 um) versus droplet transmission (respiratory particles >100 um) is not known yet. We used the minimum effectiveness as a conservative estimate for the overall effectiveness of masking.

Physical distancing can inhibit the transport of very large droplets, but has little/much smaller impact on reducing exposure to equilibrated aerosols in indoor environment. By assuming a standard distancing without recommendation is ~ 0.25 meter, our calculation shows that the mass of large respiratory droplets may drop by ~88% at a distance of 1 meter and by 95% at a distance of 2 meter (Fig. S2) . Thus, we assumed ~90% effectiveness Edis of proper physical distancing for droplet transmission. This value of E (90%) for physical distancing is also close to Edis ~ 80% as reported by the review of Chu et al [3] , which, however, relied heavily on data from the SARS-CoV-1 and MERS [4] .

In contrast to physical distancing, standard ventilation mainly influences the aerosol transmission in indoor environment and hardly influences the transmission of large droplets > 100 µm. According to , changing from a passive ventilation to a high standard ventilation rate of 12 h -1 may reduce the virus concentration by 90%, roughly corresponding to Even ~ 90% for aerosol transmission.

Note that these values are calculated for the averaged indoor concentrations and the practical Even can be lower around a source that is away from the ventilation air flow [5] .

In this study, we limited our discussion to the combined effects of physical distancing and ventilation whenever mentioned, Edis&ven = ~90%. The reasons are (1) these two measures are very effective only on part of the transmission mode, either aerosol transmission or droplet transmission; and (2) [6] [7] [8] [9] [10] . Here, we assumed that d is ~ 10 days without any intervention [11] . When applied n tests per week, the intervened d = 7/n assuming 100% precision of tests and immediate application isolation to avoid further transmission. Then Etes&iso = (1 -0.7/n) for accurate testing and complete isolation. In practice, the frequency of testing has to be adjusted according to the rates of false negative results [28] (sect S1), and the effects of incomplete isolation have to be considered, which may reduce the effectiveness of this measure. 

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