A recently published study has concluded that the airborne route is the primary mode of transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and that extreme lockdown measures, including stay-at-home and universal mask-wearing orders, have been effective at reducing the spread of the virus. However, the conclusions that the authors draw do not follow from their findings but are arrived at through fallacious reasoning and dependent on a fraudulent premise.
The study, written by Renyi Zhang and coauthors and published on June 11 in PNAS, the journal of the Proceedings of the National Academy of Sciences of the United States of America, is titled “Identifying airborne transmission as the dominant route for the spread of COVID-19”. In it, Zhang et al. claim to have proven by analyzing case data from Wuhan City in China, Italy, and New York City that airborne transmission “represents the dominant route to spread the disease.”
Taking that conclusion further, they claim that extreme lockdown measures implemented by government “are insufficient by themselves in protecting the public” but are effective when accompanied by orders of universal use of masks in the community setting. “We conclude that wearing of face masks in public corresponds to the most effective means to prevent interhuman transmission,” they state in the abstract.
However, to arrive at these conclusions, they depend on the counterfactual assumption that the cumulative number of cases in each location would have continued to grow indefinitely in a linear manner had it not been for mask-wearing orders. An examination of the data from New York City reveals that this assumption is not merely counterfactual but falsifiable.
The study is therefore a useful illustration of the phenomenon of professional propagandists masquerading in their role as scientists to serve the function of manufacturing consent for government policies, similar to how throughout the pandemic the fearmongering mainstream media have typically been doing policy advocacy rather than journalism.
- Attempting to Overturn the Scientific Consensus on SARS-CoV-2 Transmission
- How the PNAS Study Arrives at Its Conclusions
- Major Fallacy #1: Equating Correlation with Causation
- Major Fallacy #2: Drawing a Conclusion That Doesn’t Follow from the (Presumed) Premise
- Major Fallacy #3: Assuming a Premise That Is Falsifiable
The consensus view within the scientific community has until now been that SARS-CoV-2, the virus that causes coronavirus disease 2019 (COVID-19), is predominantly spread through direct contact or respiratory droplets produced by coughing, sneezing, or talking at higher volumes. Once emitted, these droplets can travel some distance but in a short time fall to the ground. This is the basis for “social distancing” guidelines recommending that individuals keep a certain distance from each other when out in public, such as the six feet of distancing recommended by the US Centers for Disease Control and Prevention (CDC).
As the World Health Organization (WHO) states,
According to the current evidence, COVID-19 virus is primarily transmitted between people via respiratory droplets and contact routes. Droplet transmission occurs when a person is in close contact (within 1 metre) with an infected person and exposure to potentially infective respiratory droplets occurs, for example, through coughing, sneezing or very close personal contact resulting in the inoculation of entry portals such as the mouth, nose or conjunctivae (eyes).
A second possible route is fomite transmission, which refers to the spread of the virus through contact with infected surfaces.
Airborne transmission, in contrast to larger respiratory droplet transmission, refers to smaller aerosolized particles that can likewise be produced by coughing, sneezing, talking, or even breathing. These smaller particles can linger in the air for an extended duration and travel farther. Whether SARS-CoV-2 is airborne transmissible and, if so, the extent to which this mode of transmission drives the spread of the virus has been the subject of controversy.
As the WHO also notes (bold emphasis added throughout),
In specific circumstances and settings in which procedures that generate aerosols are performed, airborne transmission of the COVID-19 virus may be possible. The scientific community has been discussing whether the COVID-19 virus might also spread through aerosols in the absence of aerosol generating procedures (AGPs). This is an area of active research. So far, air sampling in clinical settings where AGPs were not performed found virus RNA in some studies but not in others. However, the presence of viral RNA is not the same as replication- and infection- competent (viable) virus that could be transmissible and capable of sufficient inoculum to initiate invasive infection. Furthermore, a small number of experimental studies conducted in aerobiology laboratories have found virus RNA and viable virus, but these were experimentally induced AGPs where aerosols were generated using high-powered jet nebulizers and do not reflect normal human cough conditions.
The WHO adds that further high-quality studies including randomized trials are required to address the knowledge gaps related to the potential airborne transmission of SARS-CoV-2. As the WHO summarizes, “Current evidence suggests that most transmission of COVID-19 is occurring from symptomatic people to others in close contact, when not wearing appropriate PPE.”
The acronym PPE stands for “personal protective equipment” such as medical masks and respirators used by health care professionals. With respect to the widespread use of masks by the general public in the community setting, the WHO notes that a recent review of available studies, which mostly relate to other respiratory viruses, found that surgical masks or multi-layered cotton masks are associated with protection, but these studies also suggest that healthy individuals “would need to be in close proximity to an infected person in a household or at a mass gathering where physical distancing cannot be achieved to become infected with the virus.”
The WHO further emphasizes that, “At present, there is no direct evidence (from studies on COVID-19 and in healthy people in the community) on the effectiveness of universal masking of healthy people in the community to prevent infection with respiratory viruses, including COVID-19.”
The WHO guidance on masks, updated on June 5, reiterates that, while many governments have recommended (or ordered) the use of cloth face coverings for the general public, “At the present time, the widespread use of masks by healthy people in the community setting is not yet supported by high quality or direct scientific evidence and there are potential benefits and harms to consider.”
In other words, executive mask-wearing orders are not evidence-based.
The harms include the “potential increased risk of self-contamination due to the manipulation of a face mask and subsequently touching eyes with contaminated hands”; the “potential self-contamination that can occur if non-medical masks are not changed when wet or soiled”, which “can create favourable conditions for microorganism to amplify”; and “potential headache and/or breathing difficulties, depending on type of mask used”.
Weighing the potential benefits and harms, the WHO sensibly advises that, to preserve the supply of medical masks for health care workers, members of the public should wear a cloth face mask “in specific situations and settings” where “physical distancing cannot be maintained”, such as “while on public transport”. The purpose of the mask, the WHO also notes, is not to protect the wearer but to serve as “source control”, meaning to prevent an infected wearer from spreading virus-laden respiratory droplets to others.
As Zhang et al. correctly note, aerosols have been considered “as a potential route for the spreading of the disease.” (Emphasis added.) They further acknowledge that, “Currently, the mechanisms to spread the virus remain uncertain, particularly considering the relative contribution of the contact vs. airborne transmission routes to this global pandemic.”
Here, they cite an article in Nature discussing the controversy surrounding the question of whether SARS-CoV-2 is airborne transmissible in the community setting. Assuming so, questions also remain about the dose that would be required for there to be a significant risk of infection, which risk is also related to the duration of exposure. A reasonable assumption is that airborne transmission might occur in confined areas with poor ventilation and where prolonged close contact is unavoidable—such as on public transportation. However, as the Nature article acknowledges, there is an “absence of evidence” that SARS-CoV-2 is airborne (which, the article emphasizes, doesn’t necessarily mean it isn’t occurring).
Nevertheless, Zhang et al. attempt to overturn the consensus view that the virus is spread mainly through larger respiratory droplets by claiming that airborne transmission is not merely occurring in the community setting but is the predominant route by which the virus spreads.
While scientists should question prevailing opinion and challenge consensus views, in this case, the study authors do so by means that suggests that they set out to prove a predetermined conclusion rather than to follow the evidence wherever it might lead.
To establish a foundation for their conclusion about airborne transmission, they cite an experimental study “showing that the virus remains infectious in aerosols for hours”. However, their source, a study published in the form of a letter to the editor of the New England Journal of Medicine, is the same study the WHO is referring to when it notes that experimentally generated aerosols containing viable virus “do not reflect normal human cough conditions”.
Lacking direct evidence of widespread airborne transmission in the community setting, Zhang et al. sought instead to demonstrate its occurrence by logical deduction.
To make their case, Zhang et al. examined data from three pandemic epicenters: Wuhan, China; Italy, and New York City. They note that the numbers of cumulative confirmed cases and deaths globally and in the US have continued to increase with “striking linearity” from the beginning of April through early May.
They also show that the infection curves in Wuhan, Italy, and New York City did not continue linearly upward indefinitely but began to flatten over time. Zhang et al. attribute this flattening to the issuance of mask-wearing orders in those locations, whereas the linearity of cumulative cases globally and in the US is “due to the nonimplementation of face-covering measures”.
To try to prove this, they focus on Italy and New York City. I will focus solely on New York City because that data was readily accessible to me (as I had previously accessed it for another purpose), because my time is limited as is the time of my readers, and because doing so renders it superfluous to look also at Italy.
It is important to emphasize that their conclusion is entirely dependent on the assumption that if mask-wearing orders had not been issued, cumulative cases would have continued upward in a straight line rather than flattening over time.
They visualize this assumption for us in the following graphs included in their paper.
In addition to presenting graphs of cumulative cases, as shown in the following graph, Zhang et al. also attempt to show that mask-wearing orders effectively reduced transmission by presenting a graph showing a steeper decline in a linear trendline for daily cases after the mask order in New York City compared to the downward linear trendline after the implementation of a stay-at-home order but before the mask order.
Having attributed the flattening of cumulative cases in Italy and New York City to mask-wearing orders, Zhang et al. further argue that, “With social distancing, quarantine, and isolation in place worldwide and in the United States since the beginning of April, airborne transmission represents the only viable route for spreading the disease, when mandated face covering is not implemented.” (Emphasis added.)
The “linear increase in the infection prior to the onset of mandated face covering in Italy and NYC” compared to the flattening after the orders indicate that masks “block atomization and inhalation of virus-bearing aerosols” and “that airborne transmission of COVID-19 represents the dominant route for infection.” (Emphasis added.)
The fundamental problem with this study, though, is that the authors’ conclusions do not follow from their findings and, furthermore, the assumption upon which the authors’ conclusions is premised is falsifiable. That cumulative cases had already been flattening by the time mask-wearing orders were issued is easily demonstrable by examining the data from New York City.
The first glaring fallacy of the study is that its authors equate correlation with causation. Just because cumulative cases flattened after the mask-wearing order does not necessarily mean that the order is what caused the flattening.
Relatedly, even if masks are an effective means of source control, it does not follow that it is necessary to mandate their use among the public. As rightly indicated by the WHO’s guidance, such orders are not evidence-based, and individual circumstances as well as the potential harms of mask usage must be taken into consideration. Therefore, the appropriate policy response would be to recommend mask use depending on the individual and the situation.
Ordering individuals to wear a mask as opposed to issuing a reasonable recommendation accompanied with explanations as to who should wear one along with when, where, why and how could potentially be counterproductive, prompting people to choose not to do so even when it would be appropriate strictly out of defiance of an unreasonable policy that violates individuals’ right to exercise their own judgment given their own unique circumstances.
Also, the authors’ argument implicitly assumes that there was little or no mask use among New Yorkers prior to the order and strict compliance afterword, but it may have been that large numbers of people were already wearing masks when going out prior to the order and that many people dissented from the order after it was issued. In other words, there are confounding factors that they did not consider.
When the New York Times reported the executive order two days before it went into effect, it featured an image of two men walking down a sidewalk already wearing masks, with a caption suggesting that masked faces were “bound to become an inescapable sight” due to the order. In fact, New York City Mayor Bill de Blasio had already issued a recommendation two weeks earlier for New Yorkers to wear cloth masks if out in public and “near other people”. An Associated Press (AP) article reporting the recommendation featured a photo of two women standing on the sidewalk in front of a store entrance wearing masks and rubbing sanitizer on their hands.
Obviously, some if not many New Yorkers were already wearing masks and had been doing so for weeks prior to the mandate.
Another AP article published more than three weeks after the mask order reported that “many denizens of New York City prefer to go their own way” instead of strictly complying. The article featured a photo with the caption, “A jogger wears a face mask on Monday on the Williamsburg Bridge in New York, but a bicyclist and a pedestrian prefer not to.” Apart from being outdoors where the risk of transmission is low, the two men not wearing masks are not near anyone else in the photo, and any close contact they might have had with others who can be seen in the background crossing the other way would have been fleeting. As the article noted, “while the rule is clear, New Yorkers have adopted their own interpretation of when masks are required.” Mask use was also inconsistent and potentially counterproductive among those who did choose to use one. “It isn’t unusual”, the article remarked, “to see groups of parkgoers and essential workers—even police officers—leaving their masks dangling as they squeeze past people on sidewalks or chat with friends.”
Consequently, the assertion that the date upon which the executive order went into effect can be singularly identified as the turning point in the epidemic is dubious. While mask use may have played some role in reducing transmission, the idea that the executive order was something like a flipped switch turning effective widespread mask use from “off” to “on” is totally unrealistic. And, again, even if the specific date of the order were correlated with an observable shift in the data, it would not prove that it was the order that caused the change.
In sum, the authors employ a dual fallacy to establish their premise. It is a non sequitur fallacy because it does not follow from the observation that cumulative cases flattened after the mask-wearing order that therefore the order caused the reduction in the rate of increase. It is also a petitio principii fallacy (circular reasoning or “begging the question”) because they presume the proposition to be proven—that the mask-wearing order caused a reduction in transmission—as the premise from which to draw their headline conclusion that airborne transmission is predominant.
The second glaring fallacy is another non sequitur, which is that, even if we assume that the mask order did cause the flattening of cumulative cases, the conclusion still does not follow that airborne transmission is the primary means by which SARS-CoV-2 spreads.
That argument, too, is unrealistic inasmuch as it assumes that, prior to the mask order, New Yorkers were strictly observing social distancing guidelines and otherwise behaving in such a way that it would have resulted in a cessation of transmission if aerosols were not a significant mode of transmission.
The authors’ assertion that with lockdown policies in effect there was no viable route for spreading the virus other than airborne transmission is patently absurd.
The truth is that there were plenty of opportunities for transmission to occur even with the extreme “lockdown” policy of an executive “stay-at-home” order in place. It is not as though prolonged close contact with others was always avoidable for everyone everywhere in New York City. The use of public transportation, for example, represents one obvious means by which larger respiratory droplet or fomite transmission could occur even if people did their best to socially distance. Another possible route is nosocomial infections, which refers to infections acquired at the hospital (that is, people became infected because they went to the hospital). Another is infections in nursing care homes, where potentially infected staff would necessarily be in close contact with elderly residents to provide for their care. Another obvious route is transmission within households.
The implicit assumption underlying this argument by Zhang et al. is that New Yorkers were infecting each other without close contact happening, that they were doing so at a distance through aerosol transmission. But even if airborne transmission from asymptomatic individuals were a significant route of viral spread in the community setting, it is likely that prolonged close contact would still be required for someone to become infected.
For example, among the documented instances in which aerosol transmission might have occurred was when 53 members of a 122-member choir in Washington state developed COVID-19 after attending a choir practice. While it’s unclear how the CDC determined that transmission through larger respiratory droplets is insufficient to explain this outcome, the agency investigated the “superspreader” event (as events such as this have been described) and concluded that airborne transmission was likely. But this conclusion came with the caveat that “unique activities and circumstances”—like 122 choir members standing closely together singing loudly for an extended duration—were required for aerosol transmission to occur.
That prolonged close contact would still be required even with airborne transmission was also implicit in the CDC’s conclusion that people in the community setting should maintain six feet of separation and wear a cloth mask if social distancing could not be maintained.
That prolonged close contact would still be necessary for infection to occur was precisely the conclusion of a study published in April in Nature Medicine. The purpose of the study was to examine the effectiveness of surgical masks at reducing forward shedding of common human coronaviruses, which are a cause of common colds, through large respiratory droplets and aerosols from exhaled breath. Researchers showed that most infected individuals who didn’t wear a mask shed no detectable virus despite collecting breath samples for thirty minutes. As the authors noted, this implied that “prolonged close contact would be required for transmission to occur, even if transmission was primarily via aerosols”. (Emphasis added. Also, it should be noted that they did not determine whether shed virus was infectious.)
The fact that the available evidence indicates that prolonged close contact would still be required for infection to occur even if by the airborne route completely undercuts the ludicrous assumption made by Zhang et al. that with social distancing measures in place, only airborne transmission could have been occurring.
Another problem with the authors’ argument is the thin evidence for the effectiveness of masks at preventing aerosol transmission of SARS-CoV-2—especially cloth face coverings, which are the type of mask that the public has been ordered to wear in order to preserve medical masks, which include N95 respirators and surgical masks, for health care workers.
While the Nature Medicine study found that masks did significantly reduce forward shedding of aerosols containing viral RNA of common human coronaviruses, a study published in April in Annals of Internal Medicine tested mask effectiveness with COVID-19 patients and found that “Neither surgical nor cotton masks effectively filtered SARS-CoV-2 during coughs by infected patients.” (Emphasis added.) Counterintuitively, they found a heavy viral load on the outside but not the inside of the mask, which they hypothesized was due to a “turbulent jet due to air leakage around the mask.”
A study published on the Cornell University preprint server arXiv in May drew inferences about the effectiveness of surgical or cloth masks at preventing transmission of aerosol particles by examining air flow dynamics from breathing or coughing into the mask. They confirmed that both types of mask produced a “potentially dangerous leakage jet” that had “the potential to disperse virus-laden fluid particles by several metres”. Consequently, there is “a false sense of security that may arise when standing to the side of, or behind, a person wearing a surgical, or handmade mask”. (Emphasis added.)
Moreover, while Zhang et al. assert that masks are effective at preventing “inhalation of virus-bearing aerosols”, the European Centre for Disease Prevention and Control (ECDC) points out in a technical report on the use of masks to prevent transmission of SARS-CoV-2 that “There is no evidence that non-medical face masks or face covers are an effective means of respiratory protection for the wearer of the mask.” (Emphasis added.)
The Food and Drug Administration (FDA) notes that since surgical masks, unlike N95 respirators, are loose fitting and don’t form a seal around the face, they “create a physical barrier between the mouth and nose of the wearer” but “do not provide full protection from inhalation of airborne pathogens, such as viruses.” Non-medical masks such as homemade cloth masks “may not provide protection from fluids or may not filter particles, needed to protect against pathogens, such as viruses.” Since they likely offer little or no protection to the wearer, cloth masks “are not considered personal protective equipment [PPE].” (Emphasis added.)
The Occupation Safety and Health Administration (OSHA) under the US Department of Labor states that surgical and cloth masks “Will not protect the wearer against airborne transmissible infectious agents due to loose fit and lack of seal or inadequate filtration.” Surgical masks are considered PPE because they at least “protect workers against splashes and sprays (i.e., droplets) containing potentially infectious materials.” Cloth masks, on the other hand, “Are not considered personal protective equipment (PPE).” (Emphasis added.)
In sum, the conclusion drawn by Zhang et al. that airborne transmission is the predominant route by which SARS-CoV-2 spreads does not logically follow from the premise that the mask-wearing order effectively reduced transmission. Furthermore, that premise itself begs the question and does not follow from the observation that cumulative cases increased at a declining rate after the implementation of the mask order.
The third major problem with the PNAS study—and the most important one—is that the correlation the authors claim to have shown is illusory. The fundamental assumption upon which their conclusions depend, that cumulative cases in New York City would have continued linearly upward had it not been for the mask-wearing order, is not just counterfactual but falsifiable.
To illustrate the sleight-of-hand employed by the authors of this study to support their evidently predetermined conclusions, it’s first important to understand conceptually the relationship between daily cases and cumulative cases.
For cumulative cases to increase linearly necessarily means that the numbers of cases reported daily remain relatively constant over time—a plateauing of cases. If we graph exactly 100 cases reported daily for a given period (e.g., the month of May), the line is perfectly straight and horizontal, which gives us a strictly linear increase when graphed in terms of cumulative cases. The can bee seen in the following two graphs.
If the daily case count starts at 100 on May 1 and steadily declines by two cases per day through the end of the month, the graph of daily cases is linearly downward while the cumulative case count is no longer strictly linear, but curves slightly toward the horizontal (it increases at a decreasing rate over time because each consecutive day there are slightly fewer cases being added to the cumulative total than the day before). This is shown in the following two graphs.
Of course, respiratory virus epidemics don’t look this way, with daily cases ongoing linearly. Instead, they tend to come and go in waves. If daily cases trickle in at the start of the epidemic and then explode into rapid growth followed by a leveling off at the peak and subsequent decline, the graph of cumulative cases takes on more of a flattened “S”-shaped curve, starting out fairly horizontal, then rapidly increasing in slope, and then gradually leveling off once again. This is shown in the following two graphs.
Now that the concept has been hypothetically illustrated, let’s look at real data.
Data for the US from the CDC show a trickle of cases in early March followed by an explosion of cases until an epidemic peak near the end of the first week of April. Daily case numbers since the peak have been highly variable, but with a clear overall trend of steady decline through mid-June. This results in a graph of cumulative cases that, as Zhang et al. observe, is strikingly linear—although, as we should expect given a declining trend, it does curve slightly toward the horizontal.
According to the reasoning of Zhang et al., the linearity of the increase in cumulative cases is due to a lack of mask-wearing orders around the country. The evidence presented to support this claim is the contrasted flattening of cumulative cases seen New York City after such an order was implemented.
However, a flattening of cumulative cases is exactly what we would expect to have seen in New York City regardless of whether there was widespread mask use among the public.
This is because the number of people who remain susceptible to infection is inversely proportional to the number of people who become infected and either die or acquire immunity and recover. As the number of susceptibles decreases, the rate of transmission also naturally declines. This is the main reason for the typical wave or hill shape of respiratory virus epidemics.
The assumption that there would have been no such flattening absent the order is unrealistic because it assumes the existence of an endless pool of susceptibles.
In truth, no mask order is required to explain the flattening of cumulative cases in New York City as compared with the linearity of cumulative cases for the US as a whole.
Rather, this trend in the data is easily enough explained by the fact that, while the pool of susceptibles in New York City has been greatly depleted, there remain vast swaths of the populated areas in the very large geographical territory of the United States where sustainable outbreaks can occur. As outbreaks come and go in any one location, new outbreaks can appear in other locations.
So, with that understanding, let’s look at the data from New York City, where an executive “stay-at-home” order went into effect on March 22 and an executive mask-wearing order went into effect on April 17.
In the following graph, you can see what the daily case count looks like from the end of February through mid-June. (Since the large weekly swings in variation are statistical artifacts from how testing and reporting was done, I’ve also included a seven-day moving average trendline.)
Next, the following graph shows what this same data looks liked graphed as cumulative cases.
There is nothing unexpected about this graph. It is precisely what we would expect to see, regardless of any political interventions. It is a smooth curve, with no clear point at which any shift occurs that could be attributed to the actions of politicians. If you had to guess on which days stay-at-home and mask-wearing orders were implemented, it would be a game of chance.
The following graph is the same except with vertical lines indicating the dates each of those orders was implemented.
We can also effectively reproduce what Zhang et al. show in their paper. In the following graph, I’ve added a linear trendline to fit the data points from the stay-at-home order (March 22) to the mask-wearing order (April 17), after which date there certainly is an observable flattening of cumulative cases (a decrease in the rate of increase).
But if you played our game of chance and tried to guess the date of the mask-wearing order just based on the raw graph of cumulative cases, you might have picked April 10. The following graph illustrates what happens if we choose that date for the start of our trendline.
Now recall also that Zhang et al. made their case by using March 22 as the starting point for their pre-mask-order trendline, even though their graph of daily cases showed that case numbers continued to increase thereafter until the peak on April 6. Naturally, as illustrated in the following graph, choosing a starting point while the epidemic was still growing results in a linear trendline that declines less steeply than a linear trendline fitted to data representing the tail end of the epidemic.
March 22 would make sense as the starting point if the stay-at-home order had coincided with the beginning of a sustained decrease in daily case counts. However, cases continued to increase, and it wasn’t until more than two weeks later that the epidemic began its steady climb downward.
If, however, we choose the epidemic peak of April 6 as our starting point, which marked the turning point at which the case counts thereafter began their steady decline, a different picture emerges.
As you can see in the graph above, if anything, the mask-wearing order is associated with a slowing of the rate of decrease in daily case counts. Applying the same logic as Zhang et al., we could argue that since daily cases declined less rapidly after the mask order compared to the decline observed prior to its implementation, therefore the mask order was counterproductive.
We can also observe what this looks like in terms of cumulative cases.
Clearly, before the mask-wearing order was implemented on April 17, the cumulative case numbers had already begun to slope less steeply. There is absolutely no reason to assume—as Zhang et al. do—that cumulative cases would not have continued to curve more horizontally without the mask-wearing order.
Furthermore, if we are to accept their argument, we must believe that the effect of the mask-wearing order was observable in the data immediately. However, cases reported in the several days after April 17 were improbably also infected after April 17. Rather, these cases had probably been infected at least several days prior to the mask-wearing order.
Cases that get reported are ipso facto those cases that come to the attention of public health officials. Individuals who were asymptomatic and therefore did not seek medical care are cases that would likely have gone undetected. Detected cases, on the other hand, would have been those who were experiencing symptoms and who therefore had sought medical care and received a diagnosis of COVID-19.
Therefore, we must account for the incubation period, which is the period from infection until the onset of symptoms. (Delays in people seeking care after the onset of symptoms is another factor Zhang et al. failed to consider, but we’ll set that aside.)
According to the WHO, “The time between exposure to COVID-19 and the moment when symptoms start is commonly around five to six days but can range from 1 – 14 days.” A study published in Annals of Internal Medicine estimated the median incubation period to be 5.1 days.
Therefore, it is highly unlikely that any effect of the mask-wearing order would have been seen in the data until at least five days later. The following graph presents the data with a linear trendline that takes the incubation period into account.
Obviously, the observable flattening of cumulative cases cannot reasonably be attributed to the mask-wearing order of April 17.
As a final illustration of just how ludicrous the argument presented by Zhang et al. is, we can apply their same logic to determine whether the stay-at-home order was effective for reducing transmission by graphing the trendlines for cumulative cases prior to the order and comparing it with the trendline after.
According to their own fallacious reasoning, the above graph proves that the stay-at-home order caused cumulative cases to climb upward at a higher rate than had been observed prior to its implementation.
The authors of the PNAS study purport to demonstrate with data that executive mask-wearing orders combined with stay-at-home orders are effective and, moreover, that airborne transmission is the predominant means by which SARS-CoV-2 spreads. However, these conclusions absolutely do not follow from the data that they present.
Their paper is riddled with logical fallacies and baseless assumptions, but chief among these are three fallacies that totally invalidate their argument.
First, they fallaciously equate an observed correlation in the data with causation, attributing to the executive mask-wearing order of April 17 the flattening observed in the graph of cumulative cases for New York City even though this is precisely what we would expect to see regardless of any actions taken by politicians. They also fail to consider voluntary mask use before the order and noncompliance thereafter.
Second, they ludicrously assume that only airborne transmission could explain the case numbers seen following the executive stay-at-home order of March 22 as though this couldn’t just as easily be explained by respiratory droplet transmission in circumstances where prolonged close contact with others was unavoidable, such as on public transportation, in hospitals or long-term care facilities, and within households.
Relevant to both of those major fallacies, they present no evidence that airborne transmission is occurring significantly in the community setting, much less evidence that masks are effective at preventing aerosol transmission of SARS-CoV-2, either as source control or to protect the wearer. In fact, their claim that masks protect against inhalation of aerosols is contradicted by statements from numerous public health authorities that neither surgical nor cloth masks effectively do so and that the types of cloth masks that people have been instead ordered to wear are so ineffective at preventing inhalation of either aerosols or larger respiratory droplets that they cannot be considered PPE.
Finally, and most importantly, their entire argument depends on the assumption that cumulative cases would have continued to climb linearly upward absent the mask-wearing order, yet that assumption is not only counterfactual but falsifiable. In truth, it is observable in the data that cumulative cases had already begun to flatten before the mask order could possibly have had any effect on the numbers.
In sum, this PNAS study amounts to nothing less than scientific fraud. Its authors may be scientists, but with this study, they have acted rather as professional propagandists by deceiving the public and thereby serving to manufacturing consent for extreme lockdown measures that are not evidence-based and that violate individuals’ fundamental human rights. These extreme measures include executive “stay-at-home” orders, which have caused extraordinary harm including mass unemployment, and orders for everyone to wear a mask when out in public regardless of whether it makes sense for individuals to do so after considering relevant factors given their own unique circumstances.
A key lesson for the reader is to always be wary of any “science” for which a political agenda is obviously being served. A corollary is to always be wary of any government bureaucrats who claim that their policies are based on “science”. Data might not lie, but plenty of scientists and politicians do.
 For examples of how the media serve this function, see: Jeremy R. Hammond, “SARS-CoV-2 Response: Imperial College Model and Lockdown Endgame”, JeremyRHammond.com, April 17, 2020, https://www.jeremyrhammond.com/2020/04/17/sars-cov-2-response-imperial-college-model-and-lockdown-endgame/. Jeremy R. Hammond, “COVID-19: What You Need to Know about Fatality Rates”, JeremyRHammond.com, April 25, 2020, https://www.jeremyrhammond.com/2020/04/25/covid-19-what-you-need-to-know-about-fatality-rates/. Jeremy R. Hammond, “Facebook “Fact Check” Lies about COVID-19 Fatality Rate”, JeremyRHammond.com, June 2, 2020, https://www.jeremyrhammond.com/2020/06/02/facebook-fact-check-lies-about-covid-19-fatality-rate/. Jeremy R. Hammond, “New York Times Laughably Lies That the Mask Debate Is ‘Settled’”, JeremyRHammond.com, June 5, 2020, https://www.jeremyrhammond.com/2020/06/05/new-york-times-laughably-lies-that-the-mask-debate-is-settled/. Jeremy R. Hammond, “Does SARS-CoV-2 Spread Through Poop? Fact Checking the NY Times”, JeremyRHammond.com, June 18, 2020, https://www.jeremyrhammond.com/2020/06/18/does-sars-cov-2-spread-through-poop-fact-checking-the-ny-times/. Jeremy R. Hammond, “How CNN Deceives about Asymptomatic Transmission of SARS-CoV-2”, JeremyRHammond.com, June 26, 2020, https://www.jeremyrhammond.com/2020/06/26/how-cnn-deceives-about-asymptomatic-transmission-of-sars-cov-2/.
 World Health Organization, “Advice on the use of masks in the context of COVID-19”, WHO.int, June 5, 2020, https://www.who.int/publications/i/item/advice-on-the-use-of-masks-in-the-community-during-home-care-and-in-healthcare-settings-in-the-context-of-the-novel-coronavirus-(2019-ncov)-outbreak.
 Zhang et al.
 Dyani Lewis, “Is the coronavirus airborne? Experts can’t agree”, Nature, April 2, 2020, https://www.nature.com/articles/d41586-020-00974-w.
 Zhang et al.
 Neeltje van Doremalen et al., “Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-2”, New England Journal of Medicine, April 16, 2020, https://doi.org/10.1056/NEJMc2004973. Cited in WHO, “Advice on the use of masks”.
 Elisabeth Buchwald, “Why do so many Americans refuse to wear face masks? Politics is part of it — but only part”, MarketWatch, June 28, 2020, https://www.marketwatch.com/story/why-do-so-many-americans-refuse-to-wear-face-masks-it-may-have-nothing-to-do-with-politics-2020-06-16.
 Luis Ferré-Sadurní and Maria Cramer, “New York Orders Residents to Wear Masks in Public”, New York Times, April 15, 2020, https://www.nytimes.com/2020/04/15/nyregion/coronavirus-face-masks-andrew-cuomo.html.
 Erin Durkin, “New York City urges all residents to wear face coverings in public”, Politico, April 2, 2020, https://www.politico.com/states/new-york/albany/story/2020/04/02/new-york-city-urges-all-residents-to-wear-face-coverings-in-public-1271059.
 Associated Press, “Despite 20,000 Dead, Some New Yorkers Reject Masks”, Courthouse News Service, May 13, 2020, https://www.courthousenews.com/despite-20000-dead-some-new-yorkers-reject-masks/. On the risk of transmission outdoors being low, see: Michael Levenson et al., “What We Know About Your Chances of Catching the Virus Outdoors”, New York Times, May 15, 2020, https://www.nytimes.com/2020/05/15/us/coronavirus-what-to-do-outside.html.
 Lea Hammer et al., “High SARS-CoV-2 Attack Rate Following Exposure at a Choir Practice — Skagit County, Washington, March 2020”, MMWR, May 15, 2020, https://www.cdc.gov/mmwr/volumes/69/wr/mm6919e6.htm.
 Seongman Bae et al., “Effectiveness of Surgical and Cotton Masks in Blocking SARS–CoV-2: A Controlled Comparison in 4 Patients”, Annals of Internal Medicine, April 6, 2020, https://doi.org/10.7326/M20-1342.
 European Centre for Disease Prevention and Control, “Using face masks in the community”, ecdc.europa.eu, April 8, 2020, https://www.ecdc.europa.eu/sites/default/files/documents/COVID-19-use-face-masks-community.pdf.
 Centers for Disease Control and Prevention, “About Cloth Face Coverings”, CDC.gov, updated June 28, 2020, accessed July 7, 2020, https://www.cdc.gov/coronavirus/2019-ncov/prevent-getting-sick/about-face-coverings.html.
 Food and Drug Administration, “Face Masks and Surgical Masks for COVID-19: Manufacturing, Purchasing, Important and Donating Masks During the Public Health Emergency”, FDA.gov, updated May 11, 2020, accessed July 7, 2020, https://www.fda.gov/medical-devices/personal-protective-equipment-infection-control/face-masks-and-surgical-masks-covid-19-manufacturing-purchasing-importing-and-donating-masks-during.
 Occupational Safety and Health Administration, “COVID-19 Frequently Asked Questions”, OSHA.gov, accessed July 7, 2020, https://www.osha.gov/SLTC/covid-19/covid-19-faq.html.
 Centers for Disease Control and Prevention, “Cases in the U.S.”, CDC.gov, updated June 15, 2020, accessed June 15, 2020, https://www.cdc.gov/coronavirus/2019-ncov/cases-updates/cases-in-us.html. At the time I accessed the page for the purpose of investigating the claims made in the PNAS study, data was available from January 1 through June 14. Cases in the US have since increased again, surpassing the peak number of cases in early April, but this is not relevant for our purpose here.
 Lourenço et al., “Fundamental principles of epidemic spread highlight the immediate need for large-scale serological surveys to assess the stage of the SARS-CoV-2 epidemic”, medRxiv, March 26, 2020, https://doi.org/10.1101/2020.03.24.20042291.
As Lourenço et al. state, “There is an inverse relationship between the proportion currently immune and the fraction vulnerable to severe disease.” While this inverse relationship alone explains the wave shape of the epidemic, seasonality may also play a role for reasons including lower humidity and more vitamin D deficiency during winter months.
There has been much fearmongering in the media that infection with SARS-CoV-2 may not confer immunity, but there’s no reason to believe it doesn’t, and studies have shown that it does, naturally—otherwise clearance of the infection and recovery would not be possible. The media focus on antibodies as though equivalent to immunity, but antibodies are neither always sufficient nor even necessary for immunity, and studies indicate that cellular, as distinct from humoral (or antibody) immunity, plays a critical role in immunity to this particular virus. While the question of the duration of immunity remains, cell memory may persist even after antibody levels wane so that the immune system will rapidly ramp up to protect against reinfection. There is also evidence that acquired immunity to common human coronaviruses that cause the common cold confers some cross-protection against SARS-CoV-2. Furthermore, herd immunity may be much more easily achievable than originally assumed.
A fuller discussion of immunity is beyond the scope of this article, but here are several relevant studies: Fan Wu et al., “Neutralizing antibody responses to SARS-CoV-2 in a COVID-19 recovered patient cohort and their implications”, medRxiv, April 20, 2020, https://doi.org/10.1101/2020.03.30.20047365. Julian Braun et al., “Presence of SARS-CoV-2 reactive T cells in COVID-19 patients and healthy donors”, medRxiv, April 22, 2020, https://doi.org/10.1101/2020.04.17.20061440. Tom Britton et al., “The disease-induced herd immunity level for Covid-19 is substantially lower than the classical herd immunity level”, medRxiv, May 14, 2020, https://doi.org/10.1101/2020.05.06.20093336. Abishek Chandrashekar et al., “SARS-CoV-2 infection protects against rechallenge in rhesus macaques”, Science, May 20, 2020, https://doi.org/10.1126/science.abc4776. M. Gabriela M. Gomes et al., “Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold”, medRxiv, May 21, 2020, https://doi.org/10.1101/2020.04.27.20081893. Davide F. Robbiani, “Convergent Antibody Responses to SARS-CoV-2 Infection in Convalescent Individuals”, bioRxiv, May 22, 2020, https://doi.org/10.1101/2020.05.13.092619. Nina Le Bert et al., “Different pattern of pre-existing SARS-CoV-2 specific T cell immunity in SARS-recovered and uninfected individuals”, bioRxiv, May 27, 2020, https://doi.org/10.1101/2020.05.26.115832. Alba Grifoni et al., “Targets of T Cell Responses to SARS-CoV-2 Coronavirus in Humans with COVID-19 Disease and Unexposed Individuals”, Cell, June 25, 2020, https://doi.org/10.1016/j.cell.2020.05.015. Takuya Sekine et al., “Robust T cell immunity in convalescent individuals with asymptomatic or mild COVID-19”, bioRxiv, June 29, 2020, https://doi.org/10.1101/2020.06.29.174888.
 Nathaniel Lash, “Don’t Be Folled by America’s Flattening Curve”, New York Times, May 6, 2020, https://www.nytimes.com/interactive/2020/05/06/opinion/coronavirus-deaths-statistics.html. Lauren Leatherby and Charlie Smart, “Coronavirus Cases Are Peaking Again. Here’s How It’s Different This Time.”, New York Times, July 2, 2020, https://www.nytimes.com/interactive/2020/07/02/us/coronavirus-cases-increase.html.
 New York City Department of Health and Mental Hygiene, “NYC Coronavirus Disease 2019 (COVID-19) Data”, case count by date, GitHub, updated June 12, 2020, accessed June 13, 2020, https://github.com/nychealth/coronavirus-data/blob/master/case-hosp-death.csv.
 As explained by the NYC Department of Health and Mental Hygiene, the dataset from which I obtained the case numbers reports “confirmed cases” of people “being treated in NYC” for COVID-19. Cases are reported “by date of diagnosis”. Specimens are collected from patients for laboratory testing, and as the department notes, “the Health Department is currently advising people with mild to moderate symptoms to stay at home and not seek testing. Many cases in the community, without laboratory testing, will not be included in these counts because they never had a positive laboratory test.” See the notes at https://github.com/nychealth/coronavirus-data. Obviously, those not being tested would also include those without any symptoms. Since cases include COVID-19 patients for whom diagnosis was confirmed through laboratory testing, we must account for the incubation period.
 World Health Organization, “Q&A on coronaviruses (COVID-19)”, WHO.int, April 17, 2020, accessed July 8, 2020, https://www.who.int/emergencies/diseases/novel-coronavirus-2019/question-and-answers-hub/q-a-detail/q-a-coronaviruses.
 Stephen A. Lauer, “The Incubation Period of Coronavirus Disease 2019 (COVID-19) From Publicly Reported Confirmed Cases: Estimation and Application”, Annals of Internal Medicine, May 5, 2020, https://doi.org/10.7326/M20-0504.