Methodological preamble: this position paper is not meant as an in-depth study. It is a qualitative approach aiming to identify correlations between the systematic use of masks and the profile of virus propagation. Approximations and reference to orders of magnitude are mentioned as necessary. This paper is therefore bound to evolve in accordance with the grounded theories approach (i.e. development of a qualitative model by extension of related data sets).
Call for discussion: following the Popper-Lakatos program, any objection could be integrated in the conjecture either as a correction, relegation or integration. Submission can be made at this address: contact -at- mask-info.com.
This document is only available in English.
The purpose of this document is to highlight the critical elements contributing to reduce the outbreak of the virus, focusing on two levers:
- The systematic use of protective masks, even homemade (thereafter we refer to protective masks and similar facial protection as “masks”)
- The immediate mass production of high quality masks
This summarised document does not intend to replace an in-depth study. Its objective is to demonstrate critical factors and correlations in both a qualitative/fact-based and reasonably quantified manner. References given at the end of the document have established the basis for this analysis.
Unless stated otherwise, data on coronavirus come from the John Hopkins University Covid19 database, update of 6/04/2020. We made the implicit assumption that published numbers are comparable despite possible methodological discrepancies between countries. Country population data come from the World Bank database 2018
This analysis was conducted with a two-pronged approach:
- An empirical approach: estimating the growth rate of the epidemics in different countries with different practices regarding the use of masks, based on publicly available data.
- A bottom-up calculation of a theoretical growth (and derived Ro) based on the level of use of masks in different countries. We measured or had measured the actual share of mask use in different locations (street, shops, subway) and factored in the efficiency of different types of masks as published in the scientific literature according to laboratory tests.
To our knowledge, it is the only analysis comparing these 2 elements, establishing a tentative yet convincing evidence of correlation between the use of masks and the reduction of the Ro ratio.
We made 4 assumptions:
- The most sophisticated masks (FFP2) are reserved for medical practitioners, nurses and employees in contact with infected patients. These masks aim at protecting those individuals. Our study covers 2 other types of masks: basic 3-ply masks (usually found in pharmacies, drugstores or online) and homemade fabric masks.
- We assume a simplistic epidemiologic model following an S-curve (see appendix A). Following such a model, in the first stages the cumulated number of cases and deaths follow an exponential curve, which corresponds to empirical observations. The basic reproduction number (Ro) has recently become a popular yardstick in assessing the stage of the epidemic. A high Ro (2 or 3) means an explosive propagation whereas there is no epidemic with a Ro below 1. The Ro value below which an epidemic could be considered under control is a matter of discussion – with Ro=1.2, the propagation is relativelly slow with the peak of new cases reached after about a year (the minimum likely duration to find a vaccine). Nonetheless, even at Ro=1.2 we estimate the order of magnitude of the population not having access to needed intensive care to circa 0.5 to 1% (in comparatively well-equipped European countries), possibly resulting is as many excess casualties. Our Ro estimates are derived from observed growth rates (see appendix C) and our simple model described in appendix A (for further analysis of Ro and its impact on the dynamics of the epidemics, see here.
- We made assumptions on the filtration power of various type of masks based on available literature . We then crudely modelled rates of transmission based on an assumption of the use of masks among the population (see appendix B).
- We make no other assumptions on other preventive measures (hygiene practices or social distancing).
Of the 3,295 deaths that have been officially recorded on the 28th of March, 3,174 were in the Hubei province, the capital city of which is Wuhan with only 121 in the rest of the country (source: press). In this province, 40 million people were in total confinement for 2 months, the army ensuring compliance. 42,000 health personnel, doctors and nurses were sent from all over the country. In the rest of China, a 4 weeks partial confinement was put in place. Schools and many shops were closed. In parallel China increased its production of masks by a factor 15 (from 10 to 150 million per day) in a month mobilising its entire manufacturing infrastructure; for example, the car maker BYD, in just 4 weeks and starting from scratch ended up producing 5 million masks every day. Eventually, wearing a mask in public spaces became mandatory. In March, after this measure was put in place, the number of cases reduced dramatically and has since almost disappeared. Locally transmitted cases have disappeared. The economy is restarting, schools are gradually reopening and wearing a mask in public and at work remains an obligation. Based on available data, the epidemic appears to have been effectively stopped in China, indicating a R0 below 1.
After a crisis and a peak of cases (mainly due to a gathering in a religious sect in Daegu, caused by a “super spreader” end of February), the outbreak is now under control. The growth of cases and deaths, initially around 30-35% is now between 2-5%, implying a Ro below 1.0 From a local source, 75% of people in the streets of Seoul were wearing masks, 90% in shops, and 95% in the subway. Today, the government distributes 2 masks per week per person. South Korea has also engaged in a very aggressive testing policy especially among all the members of the sect and their acquaintances. The epidemic in South Korea is now stabilised.
The propagation in Japan remains moderate: confirmed cases grow at a rate of 8-9% and the pace of deaths, initially 15% is now down to 5%, suggesting a Ro between 1.0 and 1.2. This is in stark contrast with some Western countries. For instance as of 6 April, Japan counted 85 deaths due to COVID-19, 100 times less than France, a country of half its population. Japan was one of the first countries affected – on average Chinese tourists in Japan account for 1 million per month. The first case, supposedly brought by a tourist from Wuhan, happened on the 15th of January. From late January, the percentage of Japanese wearing masks started to increase. Observed use was about 60% in the street, 80% in shops and 90% in public transportation. During March, with a stabilised number of cases, this percentage gradually decreased. The combination of this relaxation and of the inflow of repatriated Japanese carriers, especially from Europe resulted in an increase of cases from mid-March. The government threatened additional measures and called for increased social distancing. The percentage of people wearing masks increased again and was recently measured at 80% in the streets and close to 90% in supermarkets. In April, the government will send a reusable and washable mask to all Japanese to compensate for the shortage of single-use masks. The number of available masks was 600 million in March and will surpass 700 million in April. While the data does not indicate a stable R0, the curves seem to respond to the losening and tightening of measures, of which the use the mask is prominent .
Taiwan is considered as a role model by several countries with only 373 cases and 5 deaths recorded as of 5th of April, despite close ties with the Republic of China. As of 6 April, only around 10 new cases are reported every day and no death related to COVID-19 has been reported for a week. Schools were quick to reopen with a high level of control and the number of cases remains limited. Borders were also closed early on. Army contributed to the production of masks, currently at 10 millions per day for a population of 23 million. Distribution is based on the local Social Security ID so as to prevent wrongdoings. Weekly allocation is 3 masks per adult and 5 per child. The epidemic in Taiwan is practically stopped, indicating a Ro below 1.
One of the most visited countries in the world, Thailand closed their borders early on and the use of masks is high. Only 2,220 cases and 26 deaths related to COVID-19 have been reported to 5th of April in a country as populated as France, the UK or Italy. It is early to assess the trend (the second fatality was reported only on 24 March) but it will be informative to follow the evolution in this country in the future.
The policy adopted by the Czech Republic is singular in Europe. On 18 March, the government edicted that a mask or scarf should be worn in any public space – confinement had been enforced 2 days earlier. Many Czechs ar now wearing a mask in public, which seemed to have been the case even before the government’s instructions.
Following public figures and influencers, Czech had started to manufacture protective masks at home en masse, and a grassroots movement « masks4all » turned the use of masks into a national cause.
The government followed public opinion. To demonstrate their commitment, cabinet ministers now wear masks when addressing people on TV. In parallel, testing was ramped up, 150,000 quick tests having been ordered from China. So far 4,822 cases and 78 deaths have been recorded as of 6 April. It is difficult to separate the impact of masks and confinement as the Czech government reacted early on. The first confirmed cased was recorded on 1st March, confinement put in place on 16 March, masks made mandatory on 18 march and the first death recorded on 22 March. Confirmed cases are currently growing at 11% per day and deaths at 24%, rates comparable to Germany (albeit at a third of the prevalence seen in Germany in percentage of the population). Estimated Ro including confinement measures and masks is therefore lilely to be between 1.6 and 2.7, recognising a significant lag between the adoption of measures and an impact on the death numbers. Therefore data on this country will need to be followed.
Our hypotheses are based on the performance of the various types of masks based on several studies  and explicited in Appendix B. We consider 2 types of masks:
- Surgicals masks, with an assumption efficiency of 63% both on emission and reception
- Some made masks, 50% both on emission and reception.
We consider 3 scenarios of equipment (percentage of population):
- Best case: type Taiwan, Japan or South Korea, prevalent use of surgical masks (90%)
- Short term: 15% with surgical masks, 55% with homemade masks, the remaining 30% unprotected
- Medium term: 60% with surgical masks, 20% with homemade masks, 20% unprotected
Leading to an overall efficiency for each scenario:
- Best case: 81%
- Short term: 60%
- Medium term: 73%
Observed initial growth in European countries (France, Italy, Spain, UK, Germany) is circa 30% (see appendix C) suggesting a Ro before social distancing between 2.7 and 3.4.
The best case scenario would bring the Ro to 1.1, a value consistent to the ones observed in the countries having put the pandemic fully under control. Short and medium term scenarios show a Ro of respectively 1.7 and 1.4, not sufficient in the long term. (For Ro=1.4 we estimate excess casualties in European countries to circa 1.5 to 2% of the total population)
Our theoretical calculations are in line with the empirical observation of the spread of the disease in countries where mask use is enforced and/or culturally ingrained. As has been often metioned, there are two merits in having a Ro below 1: the epidemic spreads in a quasi-linear way rather than exponentially, buying time to adjust safety measures, protecting the health system and the economy; also, even with a Ro greater than 1, the level of herd immunity HI (the share of the population that needs to be immune for the number of new cases to start decreasing) is lower the closer Ro gets to 1, following the formula HI = 1 – 1/Ro. A low Ro therefore both slows the spread of the disease and brings forward the end of the epidemic.
Confinement becomes necessary when the situation gets out of control, which quickly happens with daily growth rates of 30% as originally observed in Wuhan and Hubei province, now in Europe. Closing borders for countries where the epidemic is contained becomes necessary when all or new cases are imported as is now the case in China or Japan. In the long run, one could envision the emergence of areas of free circulation restricted to countries having managed, thanks partially to the use of masks, to eradicate the virus.
As we considered countries differing in terms of density, hygienic and sanitary practices, health prevention culture, prevalence of tests, health or transport density and infrastructure, the observed correlation between the use of protective masks and the replication rate leaves little doubt on the first-order impact of this policy. If correlation does not always imply causality, the magnitude of the discrepancy between countries using masks or not is compelling.
In the case of France, there is a short-term deficit of enough disposable or certified masks, and their production can only be gradual. A mandate to wear homemade masks seems necessary to restart the economy at the end of the confinement period. The restart would be made progressively to keep Ro close to or below 1. Strict confinement would continue for those most at risk while those going back to work would have to wear a mask. As long as an effective vaccine is not made widely available, it would be prudent to maintain the obligation to wear masks in public places so as to avoid a relapse (“overshoot”).
 Davies, A., Thompson, K., Giri, K., Kafatos, G., Walker, J., & Bennett, A. (2013). Testing the Efficacy of Homemade Masks: Would They Protect in an Influenza Pandemic? Disaster Medicine and Public Health Preparedness, 7(4), 413-418. doi:10.1017/dmp.2013.43
We used a simplistic model of epidemic propagation, assuming a daily transmission rate r and a period of infectivity of C days. Ro is the product of these two factors:
Ro = r x C
At any given period moment t, if X(t) is the cumulated proportion of confirmed cases at t, the part of the population still infections Pi is:
Pi(t) = X(t) - X(t-C)
As people having contracted the disease prior than (t-C) are not infectious anymore. Each carrier of the virus would transmit the disease to Ko individuals if nobody in the population was infected. At t, there is only a proportion (1-X(t)) that can still catch the virus.
Therefore, the cumulated proportion of population infected at t+1 will be
X(t+1) = X(t) + r x Pi(t) x (1-X(t))
X(t+1) = X(t) + r x (X(t) - X(t-C)) x (1-X(t))
Simulating this function allows to retrieve the Ro from the observed growth rate g on a stable segment (20-30 days).
Alternatively, r can be approximated with the following formula:
r ~ log(1 + g) + 0.05
Which gives us an estimate of Ro, with g the daily growth rate and C the period of infectivity:
Ro ~ C x (log(1 + g) + 0.05)
This approximation is valid for Ro ≥ 1, i.e. with our hypothesis for C (10 days) for g ≥ 5%. For an intuition on the influence of the Ro on the dynamics of the epidemic and the number of excess casualties see our paper here
Several estimates of the efficiency of masks for reception (protecting the wearer) and to some extent emission (protecting others and preventing surface contamination) are available . Based on these studies:
- For reception, one can assume a level of protection circa 50% for homemade masks, 63-80% for surgical masks (and incidentally circa 95% for protective masks FFP2 certified), for particles of relevant size (23 nm as tested compared to 60-10 nm for the virus). In this model we took the (conservative) lower value of 63% for surgical masks.
- For emission, data are few and more difficult to interpret – on a limited sample, practically full protection was observed for surgical masks in the case of conronavirus in . As a mask is most certainly more efficient outwards than inwards, in this document we took the conservative hypothesis of aligning emission protection to the value retained for reception protection i.e. 50% for homemade masks and 63% for surgical masks.
Assuming that the risk of contracting the disease is proportional to exposure and that even partial protection has a positive impact, we applied the filtering effect as a dampening factor to the rate of propagation.
Specifically, as emission and reception protection add up, the overall efficiency of the systematic use of masks stems from the double barrier: filtering inwards and outwards.
We then combine mask performance and proportion of use. If a mask with Ee efficiency (emission) and Er efficiency (reception) is used by a percentage P of the population, the rest of the population remaining unprotected, contamination between the two groups would be modeled as follows:
Unprotected -> Unprotected UU = (1-P) x (1-P) x Ro
Unprotected -> Masked UM = (1-P) x P x (1-Er) x Ro
Masked -> Unprotected MU = P x (1-P) x (1-Ee) x Ro
Masked -> Masked MM = P x P x (1-Ee) x (1-Er) x Ro
The resulting R will be UU + UM + MU + MM Similar calculations are performed if there are more than 2 groups of the population.
As a basis for our Ro estimations we calculated initial and current daily growth rate using segmented linear regression, the results are presented below for the coutries metioned in the document.