Version 1
: Received: 10 April 2020 / Approved: 12 April 2020 / Online: 12 April 2020 (17:41:10 CEST)
Version 2
: Received: 12 May 2020 / Approved: 13 May 2020 / Online: 13 May 2020 (13:16:04 CEST)
Version 3
: Received: 10 July 2020 / Approved: 12 July 2020 / Online: 12 July 2020 (16:11:50 CEST)
Version 4
: Received: 30 October 2020 / Approved: 2 November 2020 / Online: 2 November 2020 (10:18:00 CET)

Howard, J.; Huang, A.; Li, Z.; Tufekci, Z.; Zdimal, V.; van der Westhuizen, H.-M.; von Delft, A.; Price, A.; Fridman, L.; Tang, L.-H.; et al. An Evidence Review of Face Masks against COVID-19. Proceedings of the National Academy of Sciences, 2021, 118. https://doi.org/10.1073/pnas.2014564118.
Howard, J.; Huang, A.; Li, Z.; Tufekci, Z.; Zdimal, V.; van der Westhuizen, H.-M.; von Delft, A.; Price, A.; Fridman, L.; Tang, L.-H.; et al. An Evidence Review of Face Masks against COVID-19. Proceedings of the National Academy of Sciences, 2021, 118. https://doi.org/10.1073/pnas.2014564118.

Howard, J.; Huang, A.; Li, Z.; Tufekci, Z.; Zdimal, V.; van der Westhuizen, H.-M.; von Delft, A.; Price, A.; Fridman, L.; Tang, L.-H.; et al. An Evidence Review of Face Masks against COVID-19. Proceedings of the National Academy of Sciences, 2021, 118. https://doi.org/10.1073/pnas.2014564118.
Howard, J.; Huang, A.; Li, Z.; Tufekci, Z.; Zdimal, V.; van der Westhuizen, H.-M.; von Delft, A.; Price, A.; Fridman, L.; Tang, L.-H.; et al. An Evidence Review of Face Masks against COVID-19. Proceedings of the National Academy of Sciences, 2021, 118. https://doi.org/10.1073/pnas.2014564118.

Abstract

The science around the use of masks by the general public to impede COVID-19 transmission is advancing rapidly. Policymakers need guidance on how masks should be used by the general population to combat the COVID-19 pandemic. In this narrative review, we develop an analytical framework to examine mask usage, considering and synthesizing the relevant literature to inform multiple areas: population impact; transmission characteristics; source control; PPE; sociological considerations; and implementation considerations. A primary route of transmission of COVID-19 is via respiratory droplets, and is known to be transmissible from presymptomatic and asymptomatic individuals. Reducing disease spread requires two things: first, limit contacts of infected individuals via physical distancing and other measures, and second, reduce the transmission probability per contact. The preponderance of evidence indicates that mask wearing reduces the transmissibility per contact by reducing transmission of infected droplets in both laboratory and clinical contexts. Public mask wearing is most effective at reducing spread of the virus when compliance is high. The decreased transmissibility could substantially reduce the death toll and economic impact while the cost of the intervention is low. Given the current shortages of medical masks we recommend the adoption of public cloth mask wearing, as an effective form of source control, in conjunction with existing hygiene, distancing, and contact tracing strategies. Because many respiratory droplets become smaller due to evaporation, we recommend increasing focus on a previously overlooked aspect of mask usage: mask-wearing by infectious people ("source control") with benefits at the population-level, rather than mask-wearing by susceptible people, such as health-care workers, with focus on individual outcomes. We recommend that public officials and governments strongly encourage the use of widespread face masks in public, including the use of appropriate regulation.

Keywords

COVID-19; SARS-CoV-2; masks; pandemic

Subject

Medicine and Pharmacology, Epidemiology and Infectious Diseases

Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received:
15 July 2020
Commenter:
FvhG
The commenter has declared there is no conflict of interests.

Comment:
Could the authors please clarify the graph shown in Figure 1? It implies that at 100% mask efficacy, an adherence rate of about 40% will reduce the R_e to 1. This seems mathematically incorrect.

Given an R_0 of 2.4, a reproduction number R_e of 1 requires a 58% decrease of the reproduction number (1 - (1/2.4)). The graph however shows that at 100% mask efficacy, a ~40% adherence rate reduces the R_e to 1. This seems incorrect. Absent any other factors, it is expected that an R_0 of 2.4 requires a 100% mask efficacy and an adherence rate of 58% in order to obtain an R_e that is equal to 1.

Received:
16 July 2020
Commenter:
Jacqueline Jones
The commenter has declared there is no conflict of interests.

Comment:
Commenting on the comment by FvhG. Using the equation used to calculate the data in Fig.1, with a mask efficacy of 100% and mask adherence of 40%, my calculations are:-

Received:
30 July 2020
Commenter:
FvhG
The commenter has declared there is no conflict of interests.

Comment:
Just to clarify in a more intuitive way:

Consider a virus that one person passes on to two other persons on average (i.e., a virus having an R_0 of 2). To stop the spread, one person must only pass on the virus to at most one other person which is half the number of people (i.e,, the R_0 must be reduced from 2 to 1), which translates to a 50% decrease of the reproduction number (being 2 times 0.5). At 100% mask efficacy this requires an adherence rate of 50%.

From this, it is trivial to understand that more contagious SARS-CoV-2 virus (assumed to have an R_0 of 2.4) must be reduced more than a factor 2 or 50%. So, at 100% mask efficacy, a reduction of the R_0 from 2.4 to 1 requires an adherence rate of 58%.

In general, a virus with an R_0 of r requires a change in R_0 by a factor of (1 - (1/r)).

Response 3 to
Comment 2

Received:
7 August 2020
Commenter:
Zhiyuan Li
The commenter has declared there is no conflict of interests.

Comment:
Hi FvhG,

Thanks for the interest in this simplified model. The "reduction factor" (1-e*pm)^2 is not to be subtracted from R0, instead, it is a factor that multiplies with R0.
Therefore, to reduce R from 2.4 to 1, we need 2.4* (1-e*pm)^2=1 , which means e*pm~0.35

Response 4 to
Comment 2

Received:
16 August 2020
Commenter:
FvhG
The commenter has declared there is no conflict of interests.

Comment:
Hi Zhiyuan Li,

Thank you for for responding. I believe that the formula you are using may be incorrect. Applying your formula (assuming e is for efficacy and "pm" is for adherence rate), we indeed get: 2.4* (1-1*pm)^2=1 or pm ~= 0.35. I believe however that this number is incorrect.

Consider a measure having an efficacy of 100% ("e"=1). Then I believe that the reduction factor equals (1-"pm") and not (1-"pm")^2. For instance, a 50% adherence rate of a measure having 100% efficacy is expected to cut R in halve and thus have a reduction factor of 0.5. However applying your formula, we get a factor of (1-1*0.5)^2 = 0.25.

The correct equation should be R0*(1-"e"*"pm") = 1. Then, for a measure having 100% efficacy we solve for 2.4*(1-1*"pm") = 1 which gives "pm" ~= 0.58.

Response 5 to
Comment 2

Received:
8 September 2020
Commenter:
Zhiyuan Li
The commenter has declared there is no conflict of interests.

Comment:
Hi FvhG,

Please see http://www.zhiyuanlab.xyz/MASK_0906.html for a detailed description of the model. The effect of population-wide mask-wearing is not linear, that's why it needs a model to quantify.
Actually, a 50% adherence rate of a measure having 100% efficacy indeed reduces R to 25% of its original value. This is called a non-linear effect. An intuitive explanation is that: for a perfect mask as you assumed fully prevent transmission, regardless if it is worn by the contagious individual or the healthy individual. Under this assumption, the only situation for two individuals to meet and transmit is that none of them having masks, the probability of which is 0.5*0.5=0.25.

Response 6 to
Comment 2

Received:
9 September 2020
Commenter:
FvhG
The commenter has declared there is no conflict of interests.

Comment:
Hi Zhiyuan,

Clear, I understand now. Thank you for the helpful link and clarification!

Comment 3

Received:
6 August 2020
Commenter:
Melvin A Quezada Haro
The commenter has declared there is no conflict of interests.

Comment:
I have only read the abstract or intro to this article but it seems to me that the conclusions of the authors are a bit over stressed. I like the comment by “ FvhG” because looking at the math and their explanation of what the variables mean makes sense and they have a stronger argument. I am an Ag student and biochem minor at Chico and looking at comments in this forum helps with understanding this debate from a scientific perspective.

Received:
2 November 2020
Commenter:
Michael Landon
The commenter has declared there is no conflict of interests.

Comment:
The RCT you cite in (14) did not find masks to significantly protect against flu. It was not until they adjusted the data set for “compliance” that an effect was found. Population-level mandates cannot assume 100% compliance or proper usage, nor do they require the use of P2 or medical-grade masks as in this study.

As an aside, evidence should be presented from past flu studies where countries where mask use is prevalent do not show decreased rates of flu.

Commenter: Jeremy Howard

Commenter's Conflict of Interests: Author

Commenter: FvhG

The commenter has declared there is no conflict of interests.

Given an R_0 of 2.4, a reproduction number R_e of 1 requires a

58%decrease of the reproduction number (1 - (1/2.4)). The graph however shows that at 100% mask efficacy, a~40%adherence rate reduces the R_e to 1. This seems incorrect. Absent any other factors, it is expected that an R_0 of 2.4 requires a 100% mask efficacy and an adherence rate of58%in order to obtain an R_e that is equal to 1.Commenter: Jacqueline Jones

The commenter has declared there is no conflict of interests.

(1 - (1x0.4)) = 0.6

0.6 squared = 0.36

= 0.36 x 2.4

= 0.864

Commenter: FvhG

The commenter has declared there is no conflict of interests.

Consider a virus that one person passes on to two other persons on average (i.e., a virus having an R_0 of 2). To stop the spread, one person must only pass on the virus to at most

oneother person which ishalfthe number of people (i.e,, the R_0 must be reduced from 2 to 1), which translates to a50%decrease of the reproduction number (being 2 times 0.5). At 100% mask efficacy this requires an adherence rate of 50%.From this, it is trivial to understand that more contagious SARS-CoV-2 virus (assumed to have an R_0 of 2.4) must be reduced

morethan a factor 2 or 50%. So, at 100% mask efficacy, a reduction of the R_0 from 2.4 to 1 requires an adherence rate of58%.In general, a virus with an R_0 of

rrequires a change in R_0 by a factor of (1 - (1/r)).Commenter: Zhiyuan Li

The commenter has declared there is no conflict of interests.

Thanks for the interest in this simplified model. The "reduction factor" (1-e*pm)^2 is not to be subtracted from R0, instead, it is a factor that multiplies with R0.

Therefore, to reduce R from 2.4 to 1, we need 2.4* (1-e*pm)^2=1 , which means e*pm~0.35

Commenter: FvhG

The commenter has declared there is no conflict of interests.

Thank you for for responding. I believe that the formula you are using may be incorrect. Applying your formula (assuming

eis for efficacy and "pm" is for adherence rate), we indeed get: 2.4* (1-1*pm)^2=1 orpm~= 0.35. I believe however that this number is incorrect.Consider a measure having an efficacy of 100% ("e"=1). Then I believe that the reduction factor equals (1-"pm") and not (1-"pm")^2. For instance, a 50% adherence rate of a measure having 100% efficacy is expected to cut R in halve and thus have a reduction factor of

0.5. However applying your formula, we get a factor of (1-1*0.5)^2 =0.25.The correct equation should be R0*(1-"e"*"pm") = 1. Then, for a measure having 100% efficacy we solve for 2.4*(1-1*"pm") = 1 which gives "pm" ~= 0.58.

Commenter: Zhiyuan Li

The commenter has declared there is no conflict of interests.

Please see http://www.zhiyuanlab.xyz/MASK_0906.html for a detailed description of the model. The effect of population-wide mask-wearing is not linear, that's why it needs a model to quantify.

Actually, a 50% adherence rate of a measure having 100% efficacy indeed reduces R to 25% of its original value. This is called a non-linear effect. An intuitive explanation is that: for a perfect mask as you assumed fully prevent transmission, regardless if it is worn by the contagious individual or the healthy individual. Under this assumption, the only situation for two individuals to meet and transmit is that none of them having masks, the probability of which is 0.5*0.5=0.25.

Commenter: FvhG

The commenter has declared there is no conflict of interests.

Clear, I understand now. Thank you for the helpful link and clarification!

Commenter: Melvin A Quezada Haro

The commenter has declared there is no conflict of interests.

Commenter: Michael Landon

The commenter has declared there is no conflict of interests.

As an aside, evidence should be presented from past flu studies where countries where mask use is prevalent do not show decreased rates of flu.