Monday, November 2, 2020

Face Masks Mandates are not to Protect You - The Mathematical Proof

Let me begin by saying that I strongly support the use of face coverings -- which meet minimum efficacy standards, are properly worn, and are disposed of or disinfected properly -- as a means to mitigate the potential infection of an individual from the spread of a viral contagion for people who feel that they need such assistance. I equally oppose the use of face coverings -- which do not meet minimum efficacy standards, are improperly worn, and are disposed of or disinfected improperly -- to give the appearance of mitigating the spread of a viral contagion but which actually facilitate it by inducing individuals to not take proper precautions.

It is my proposition that the face covering mandate imposed by Indiana Governor Holcomb and similar mandates do not provide for the protection of the individuals using them as expected by those individuals. In support I offer a mathematical proof.

To begin the analysis of the face covering requirements it is essential to know the stated purpose of these acute personal health care decision mandates. In general these orders are for the purported “prevention of SARS CoV-2 transmission”, “to reduce CoViD-19 cases” or for “the health and safety of the members of society.”

The next step is to then identify the stipulations within the mandates that fulfill those objectives.

For this analysis I am using Executive Order 20-37 issued by Indiana Governor Eric Holcombe on 24 July 2020. This order states that the purpose of the face covering requirement is “to protect the health and lives of Hoosiers” [apparently there is no concern for visitors to the state but I won’t address that here]. The filtration standard provided for in EO 20-37 to fulfill its objective is found in the definition of face coverings; “a cloth which covers the nose and mouth and is secured to the head with ties, straps, or loops over the ears or is simply wrapped around the lower face.” This means that stretching a t-shirt up over the nose qualifies.

For comparison I considered standards previously established by nearly every government in the world for personal protection face covering filtration systems intended to protect the wearer against biological agents -- bacterium and virions.

I also considered ratings based upon standards prescribed by The American National Standards Institute [ANSI], National Institute for Occupational Safety and Health, European Union: European Standardization Institute, or similar independent evaluators given to air filtration devices or systems for the removal of particle-based contaminants.

Ultimately my analysis and equations are a compilation derived from selecting criteria established by the various standards organizations for the mechanical removal of particle-based biological or industrial contaminants.

In this mathematical proof I created a hypothetical face covering, Standard [A], which I compare to Governor Holcombe’s, Standard [B].

In this analysis I begin by establishing a conservative contaminant [particulate] rate of expulsion by a diseased individual. I follow by applying this to the two standards. I conclude by providing the raw numbers followed by my assessment as to efficacy.

To determine the amount of SARS CoV-2 virions expressed by an infected person I used the typical respiration of a healthy adult male during times of moderate activity such as casually shopping or mingling. I found data stating tidal volume to be 400ml with 12 periods of respiration per minute which gives a total volume of 4800ml per minute [v/pm].

From an Italian study I got estimates of vapor droplets [particulate] by various sizes during a range of respiratory activities. The smallest vapor size quantified was 0.80μm. I selected this size because it is the most common particulate size and that size which disposable surgical masks are designed not to filter. This study found that 0.751 vapor droplets were expressed during unmodulated vocalization while 0.084 were expressed during normal breathing. These numbers represent Ni, part. cm−3 I have chosen N to be 0.15 as a compilation on the range of activities measured based on observations of group human social interactions. Multiplying the v/pm by 0.15 gives a 0.80μm droplet expulsion of 5760Np/m.

Thus, in the following I use a rate of 5760 micro aerosol particles -- those similar to cigarette smoke -- for the analysis. This is a conservative estimate of total virion expression as particles in larger ranges are not included. I later adjust for the full range of particulates up to 5.5 µm. EO 20-37 face covering standards are given after the criterion. Calculations assume an infected individual expressing 5760 aerosol particles per minute while breathing at a normal rate.

1] Target pollutant size and filtration efficiency
This standard is used to measure the efficiency of removing pollutants of a particular size range given in microns. For applications such as smoke removal, surgery, or hospital settings particulate matter in the range of 0.3 to 1.0 µm should be removed at >95%. Some of the best-rated filtration units have an efficiency rating of 99.995% which means only 5 of 100,000 particles pass through. A study done in Wuhan where COVID-19 had its initial outbreak found that the majority of aerosolized viral particles were 0.25 to 0.5 μm. Although no standard is given for this criteria in EO 20-37 a standard has been given based on observational data of what officials have determined qualifies as a face covering.
STANDARD A - filters particles ≥ 0.3 µm
STANDARD B - ≥ 2000 µm

2] Mask material minimum airflow capacity
This standard establishes the minimum amount of air that the filtrate should be able to process. It is given in liters per minute per square centimeter. This rate should at least accommodate the airflow of a moderately active healthy adult male -- 4.8 l/min. 1 l/cm2/min will easily allow for 100% of airflow to pass through the face covering medium.
STANDARD A - requires 100%
STANDARD B - allows any level ≥0%

3] Respirator efficiency value
National Institute for Occupational Safety and Health (NIOSH)-approved respirator masks have three non-powered particulate filter efficiency classes: 95, 99, and 100, for 95%, 99%, and 99.97% filtration of particulates down to 0.3 μm, respectively. This rating applies to the material of the mask not the mask as a filtration unit. N95 respirator material is expected to have a viral penetration rate of 5% but testing has shown greater than that. Some studies have shown penetration ranges of 8 to 82%. However, 95% should serve as a reasonable public milieu minimum although studies conducted in Italy have shown that numerous hospital workers wearing N95 masks have died from exposure to the SARS CoV-2 virus.
STANDARD A - 95% allows 288 droplets
STANDARD B - 0% allows 5760 droplets

4] Minimum Efficiency Reporting Value [MERV] at specific air velocity
This standard establishes the minimum efficiency of the filtration unit given at various airflow speeds as meters per second [m/s]. The lowest speed tested is 0.60 m/s which is commensurate with casual human exhalation. This standard is useful in determining whether the face covering can maintain gasket compression to the face under certain air pressures. Some face coverings may “blow out” during high pressure exhalation such as coughing or sneezing which allows air to bypass the covering. Sneezes -- these produce the greatest concentration of SARS CoV-2 virions -- can produce airflow rates of over 80 m/s in the nasal passages. I have selected 2.0 m/s as a minimum threshold speed in which the face covering should be able to maintain its integrity.
STANDARD A - ≥ 98% @ 2.0 m/s
STANDARD B - ≥ 0% @ ≥ 0.0 m/s

5] Minimum Arrestance and Pollutant Holding Capacity
This standard, usually given as a total weight, is used to measure the minimum amount of particulate that the filter can hold while still maintaining its filtration efficiency. However, this standard is applied to a specific filtration device to tell the user its capacity. Rather than try to explain how to convert a static standard volume to a particular mask I provide, instead, a time standard in which the face covering should be able to perform before becoming saturated and, thus, ineffective.
To better understand this criterion think about a filter in an HVAC system. Oftentimes the solution to feelings of not being warm or cool enough is to replace the filter. The new, unsaturated filter allows much more air to flow through and immediately the environment is warmer or cooler as desired. The air is also cleaner as less air has been forced through the far reaching gaps in the system in which air would not normally penetrate. The same applies to face coverings. Generally, typical face coverings reach a saturation point within a few hours. Observed usage by mask wearers has shown that a mask may be donned and used only momentarily or throughout an entire workday. The CDC recommends that N95 respirators not be used for more than 8 hours. Based upon these observations and recommendations I have determined that a mask should be effective for at least 4 hours, unless it is being used only momentarily before being discarded such as surgical masks.
STANDARD A - ≥ 240 mins
STANDARD B - ≥ 1 min

6] Minimum Bypass / Leakage rate of non sealed housing units
This standard is used to determine the maximum amount of air that may bypass the filtration material through gaps between it and the filter’s housing unit. For face coverings this is any gap between the face and gasketed surface of the covering. There is no particular rate for this standard but it figures into the overall MERV calculation. If the target removal rate is 95% and the filtration material removes 100% of the target pollutants then the leakage -- air passing between the face and covering -- rate could be as high as 5%. If you are using a non-commercial mask or one that does not give the MERV rating then you should test the mask yourself to ensure that it allows no more than 5% leakage.
To check for leakage, first time yourself exhaling under normal pressure and for a normal duration. Then, completely cover the filtration surface with a non permeable material and donn the face covering. While maintaining normal pressure, time the duration of tidal volume during exalation. Then divide the time while wearing the mask by the time without. If it took 3 seconds to exhale normally but 30 seconds with airflow through the filtration surface obstructed then the figure would be 0.10 or a leakage rate of 10%.

Masks should never be washed. Washing can damage the structure of the mask and detergents can degrade the impregnated filtration substrate -- the active filtration matter on which virions attach themselves. If a user wants to wear the same face covering a second or subsequent time then ultraviolet germicidal irradiation can be used for disinfecting. Disposable PPE should be donned by anyone performing the disinfection process.

Results

Standard B has no requirement for removal of any particles size at any rate. Nor is there a material handling capacity or leakage limit. Efficacy has been set at one minute for calculation purposes although the standard provides no minimum time. At a rate of expression of 5760 aerosol droplets per minute this standard would allow the passing into the atmosphere of 1,382,400 droplets in just the 0.3 µm - 0.8 µm range. In addition, all particles up to 7000 times greater in size than Standard A, which are conservatively estimated to be 25% more, are allowed to pass through. These 345,600 larger droplets represent an additional volume of 125%, based on average size, for a total weighted value of 3,110,400 droplets over a four hour period. This standard allows 100% of particles to pass the filtration system.

Standard A requires removal of particles ≥ 0.3 µm at a rate of 95% with the material being able to handle 100% of airflow but allowing for up to 2% leakage around the gasket. Efficacy should be maintained for 240 minutes. At a rate of expression of 5760 aerosol droplets per minute this standard would allow the passing into the atmosphere of 96764 droplets over a four hour period. This represents 3.1% of particulate.

Standard A would allow passage of up to 3.1% of droplets in a four hour period.
Standard B would allow passage of an equivalent of up to 3,110,400 droplets in a four hour period which is >32x Standard A. For a further comparison an N100 mask would have allowed 69 particles to pass. Thus, Holcombe’s standard would allow over 20,000 times more contaminant to pass through the filtration system than the best.

When examining the efficacy of face coverings to reduce the spread of a bacterial or viral agent it is essential that the testing procedure uses an “as employed” procedure. That means that a test that measures filtration by placing the material in a sealed system is useless just as those which use a static human model. Effective testing of face coverings uses real world simulations which include a covering being “rehandled” after application. That is, it accounts for the structural damage [micro tearing] to the covering from being stressed by repeated donning and doffing. As-employed testing also accounts for loose fits, intermittent use, and fomite transmission from handling the covering.

Although there is no standard for handling face coverings, users should be instructed on standard operating procedures when using a mask more than once to minimize contaminant transference between face side and environment side portions of the mask so as to not contaminate the opposing side.

Additionally, while there is no standard in EO 20-37 for usage design, it is important to note that mask selection should be based upon intended use. That is, does the wearer want to prevent exposure to himself or exposure to the environment. An appropriate covering should be selected from these two types.

Conclusion

Standard A provides a minimum filtration limit that would serve to protect a wearer from exposure to mildly detrimental contagions. It would still allow hundreds of times more contaminants to pass than would be acceptable for exposure to deadly bacterial or viral agents.

Standard B provides no effective guidance for the use of face coverings to protect the wearer from infection or the environment from an infected wearer. Holcombe’s standard fails to meet the minimum requirements to meet the stated objective and is, thus, invalid. If Standard B were applied to car safety seats for infants and children it would allow something like this; A booster type seat used in restaurants with a bathrobe tie used to secure the child to the seat and vinyl lawn chair webbing used to secure the seat to the automobile by stapling each end to the existing lap belts. Would you feel comfortable with your child using such a seat constructed by Holcombe or would you consider it nothing more than a symbolic gesture?

Clearly the standard established by Governor Holcomb is in no way designed to prevent exposure to the SARS CoV-2 virion. The lack of a standard of action for these devices renders them to be classified as a placebo. While there may be a slight positive placebo effect in some people -- it reminds one to take other precautions which may actually mitigate contagion -- there is a greater likelihood that users will assume that the face coverings provide sufficient protection and thus will forego effective mitigation protocols. This confidence seems to follow a linear progression consistent with ignorance as to viral etiology and epidemiology, and psychological motivation. That is, the less one knows about the origins and spread of contagions and the neurological processes involved in decision making and judgment the more likely one is to assume the false claim Holcombe makes and wear a placebo mask.

By requiring the vast members of society to donn a placebo medical device, which cannot meet the declared purpose of mitigating the spread of a contagion, the true purpose becomes clear. It is not to serve a physiological outcome but a psychological one instead. The logical evidentiary conclusion is that the purpose of EO 20-37 is a psychological study comparable to those pioneered by Asch and Milgram related to conformity and compliance. As such every person at each instance should be provided with an appropriate Informed Consent form before being required to wear a face covering. I may explore that legal requirement later but this can be confirmed if you exercise any right in a public forum such as voting. No one can legally require you to undergo an acute medical procedure -- wear a face mask -- unless you are supplied with Informed Consent and your consent is voluntary.

If you choose to donn a face covering you should wear one that, at least, meets Standard A described herein and test it for efficacy. Unless your chosen face covering is an isometric mask it should be discarded after each use and replaced. If this is not practical for you then no mask should be worn and effective mitigation protocols should be adopted instead.

When mask mandates were issued and effective mitigation protocols were abandoned a dramatic rise in the number of cases ensued. So, there is your mathematical proof. Do with it what you may.

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