Wednesday, August 18, 2021

Masks redux

My previous post on Delta policy and masks led to some discussion that went off the rails, on twitter especially. An effort to summarize the point: 

From the literature I have read, masks can be moderately medically effective. The literature has pretty wide ranging estimates, from some studies and meta-studies saying no effect, and others saying substantial effects.  

Delta has a reproduction rate of 6. (Again, best guesses with varying estimates.) Even if masks are 50% effective -- which is wildly optimistic -- they reduce the reproduction rate to 3. That's more than the alpha covid with no masks. Each person who gets it passes it on to three people, about every two weeks. 

If one wishes to stop the virus, only one goal matters: Getting the reproduction rate below one. e to the 3 t is not a lot less exponential growth than e to the 6 t.  (With t in two-week or so intervals.) 

Thus a public policy response that focuses exclusively on fine-tuning mask mandates, depending on the current level of infection is bound to fail its stated goal. That is the point. 

If our policy makers were willing to say "we are passing the mask mandate so it rips through the population a little bit slower" I might not be so grumpy. 

I am glad to see vaccine incentives finally percolating out, too slowly and late. I don't know that vaccines bring R0 below one, but they're darn close. 

You beat exponential growth when case levels are low, not by waiting until there is a crush.  


  1. I understand the observations here and you have a point – masks are second order effect right now.

    However, I want to make a clarification. The basic reproduction number is not a rate – it is the average number of people infected by an infected person. The number infected does not grow as “e to R t”. In a branching model, R_0 and propagation time dynamics are linked through a renewal equation. The solution of the renewal equation determines the exponential growth rate, the Malthusian parameter. Alternatively, in a simple SIR model the contact time and the removal time can compete against each other to give different dynamics at the same R_0. Diseases with the same R_0 can propagate at very different exponential rates. In fact, a disease with a smaller R_0 can grow faster over time than one with a larger R_0.

  2. "Thus a public policy response that focuses exclusively on fine-tuning mask mandates, depending on the current level of infection is bound to fail its stated goal. That is the point." I agree as a logical statement, R >1 => problem! (it fits on a hat). The issue is that vaccines are a big part of the policy, and masks are a complement, which may help a little or a lot (meta-studies). This complement is more relevant when vaccination hits a wall and one needs to look for additional tools. In the GF episode from last week, HRM and NF make a more balanced case, basically saying no one has "given up" on vaccinations. Masks help at the margin, so they should be part of the conversation.

  3. City Journal has a new "review of the evidence" - "Do Masks Work?" -

    One observation: "Mask supporters often claim that we have no choice but to rely on observational studies instead of Randomized Controlled Trials, because RCTs cannot tell us whether masks work or not. But what they really mean is that they don't like what the RCTs show."

    1. A couple of other observations - 1) some (all?) of the RCTs mentioned in that City Journal article didn't involve COVID-19 - isn't it more readily transmitted via aerosol than many other "influenza-like" viruses; 2) there was no apparent standard for a mask. That doesn't necessarily make the article's conclusions wrong, but it also doesn't really provide them much actual support. RCTs are fine if they truly model the thing you're interested in, otherwise they're just more noise regardless if what they "show".

    2. Ironic that economists have decided that strict RCTs are the only way to infer policy recommendations when almost their whole profession is based on inferring conclusions on non-RCT data. Macroeconomists are sure going to be bummed about the new standards.

    3. Come on, now Eddie. I didn't say that and nobody else did either. Let us economists also lead the way by not putting words in people's mouths that aren't there. Yes, it would be lovely if the FDA and CDC got around to doing RCTs, given that masks are now going to be the only public policy response, and observational studies vary widely in their effectiveness. But that does not mean that observational studies are useless either, in health, economics and astrophysics. Read just bit before writing silly things like this, and let's also not accuse people of complete illogic before thinking just a bit too.

    4. @Anonymous - if SARS-CoV-2 is in fact "more readily transmitted via aerosol than many other "influenza-like" viruses" ", then that logically *lowers* the efficacy of cloth masks / face coverings against SARS-CoV-2 spread.

      The proposed mechanism for cloth mask effectiveness is that they block largely respiratory droplets - particularly as source control - and that these droplets carry infectious virus. Cloth masks aren't effective at blocking fine aerosols, because those are too small. Fine aerosols will go both through and around cloth masks (Well-fitted N95's will provide meaningful protection against fine aerosols, but virtually none of the general public wear those.)

      I strongly suspect that fine aerosols are in fact the main method of transmission of SARS-CoV-2. That suggests not only that cloth masks are ineffective mitigants but that better ventilation and/or air filtration (with HEPA filters) are far more useful areas of focus.

      Why do I think that respiratory droplets aren't that important as a mechanism for spreading SARS-CoV-2? The observed lack of outdoor transmission, with virtually all documented transmission occurring indoors. But people are surely often close enough to each other outside to sneeze, cough, and breathe on each other - i.e., exchange respiratory droplets. A respiratory virus being readily spread indoors with very little spread outdoors seems consistent with the primary mode of spread being fine aerosols. So these build-up to infectious levels indoors - particularly in poorly ventilated spaces - but are diluted outdoors.

  4. An aggressive virus cannot be controlled sufficiently to make a substantial difference in infection rates. Masks are deluding. Their effectiveness are minimal to useless. Quarantines work, but at the level needed, it could resemble cutting one's head off to loose weight. Fortunately, Covid 19, and is offspring, are not deadly to virtually 80 percent of the population who, at most, suffer the difficulty of a severe cold. The elderly near death, as well as people with compromised health are at risk, and can die about 5 percent of the time. Fortunately. effective treatments have been developed. Vaccinations suave massive fears, but immunity from the infected is as effective, and may be the natural road to herd immunity.

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  6. gosh it sounds as if you are making excuses to justify a rational decision.
    Masks mean people who do not have any of the symptoms but still have covid are unlikely to pass it on.

    That is pretty simple to understand.

    1. The point is there is no good data suggesting how 'unlikely' masks make it that you pass Covid on and nothing to suggest that the non-medical grade masks that 90 something percent of people use provide any benefit.

    2. Yet you have nevertheless managed to misunderstand it. Masks make such transmission less likely, not unlikely. The question is "how much less?" And the answer may well be "not that much," especially if the goal is to prevent a large outbreak.

    3. The important question is, if masks actually prevent your passing infection along at all, how well do they do it.

    4. But that's not what it means, that's the point of his post (or one of the points, anyway).

      Even if you assume masks are 50% effective (which is surely a dramatic overestimate of their effectiveness), it means you halve the reproduction rate - instead of giving Delta to 6 people, you give it to 3. That's not 'unlikely to pass it on'. That's 'half as likely to pass it on'.

      "Great!" you think - anything we can do to reduce the spread. But this only delays the spread, it doesn't stop it. Delaying the spread is worth something, but it would sure be nice if people acknowledged that we're merely delaying the inevitable, not stopping it.

  7. Challenge: find a mask study (pre Covid) that recommends cloth face masks (that are reused for days perhaps). Spoiler alert. You can’t. Masks are very likely making things (slightly) worse.

  8. Most masks don't work and neither do vaccines. The COVID virus is too small for masks to stop the virus and the COVID vaccines are weakening our immune systems and causing ADE (antibody dependent enhancements).

    Please look at the data and research concerning the experimental COVID vaccines.

    The vaccines we had as children went through rigorous testing on animals and then humans and the vaccines took years to develop and were thoroughly vetted. (In the past, we would never allow tens of thousands of people die and hundreds of thousands of people to be injured and still allow the vaccines to be used. More people have died from the COVID vaccines than all of the deaths from all of the vaccines combined since 1997.)

    The COVID vaccines/gene therapy bypassed animal testing/experiments and were rushed (we have never been able to develop vaccines for coronaviruses) and thus that is why we are having so many problems with the COVID vaccines. - COVID vaccines are weakening our immune systems and causing sickness and death with Dr. Dan Stocks - vaccine issues/ADE with Dr. Malone

    Vaccinated people are dying and being hospitalized everywhere especially Israel, England, Scotland, Singapore, Iceland, and even in the US. - ICU nurse says her hospital is full of vaccinated patients in kidney failure.

    The vaccinated are not protected from getting or spreading COVID or from getting seriously ill and dying from COVID. And the vaccines carry risks (16,000 to 55,000 dead and over 500,000 adverse events) so what is he point of the vaccine?

    Experimental vaccines, masks, and lockdowns don't work but therapeutics (a combination of ivermectin, Fluvoxamine, and Methylprednisolone along with Quercetin, zinc, vitamin D3 and C) are stopping/curing COVID. Therapeutics could be the answer to treating/curing COVID.

    Regeneron is also a very effective antibody therapy for treating/curing COVID. - early treatment guide for stopping/curing COVID.

  9. It shouldn't even be a discussion. Wear a mask. Maybe it won't stop it 100% but it reduces the chances of transmission and contraction. People indulging their selfish preferences is a formula for unnecessary self-inflicted pain and suffering.

    1. The COVID-19 virus is tiny and most masks are ineffective at stopping the virus because the diameter of coronavirus — is 0.13 microns (a micron is 1,000 times smaller than a millimeter). The best N95 standard mask filters down to 0.3 microns. Wearing a mask is like putting up a chain link fence to keep out mosquitos.

      But if you think masks work and you want to wear a mask then go ahead but do not force the rest of us to wear ineffective and unconstitutional masks.

      There are many scientifically based peer reviewed studies that show masks do not work and a few of those studies are listed below - bacteria, parasites, and fungi, including three with dangerous pathogenic and pneumonia-causing bacteria found on children’s masks.

      COVID is less deadly than the flu for those under age 70, and has a 99.9% plus survival rate and this is true for the variants too. It is absolutely insane the way we/society have reacted and continue to react to COVID especially when we have very effective therapeutics (a combination of ivermectin, Fluvoxamine, and Methylprednisolone along with Quercetin/HCQ, zinc, vitamin D3 and C) as well as Regeneron, an effective antibody therapy for treating/curing COVID.

      Could these therapies be the answer to treating/curing COVID rather than ineffective vaccines, masks, and lockdowns? And if we target the therapy to those who need it then we can get back to living and building a strong and healthy society and economy.

    2. I've just recovered from it and I'll pass on any masks.

  10. One thing that needs to be in the formula is that it is better to 3 weeks from now than to die now.

  11. A random user 12345August 19, 2021 at 2:21 PM

    Mask vs. no mask is not a very interesting question. KF94 mask vs. no mask is much more interesting, and I think that's evidenced by South Korea's numbers. Yes, it is true that SK has done a better job at _lots_of_things_ in the pandemic, so that confounds analysis, but if SK is so excellent why don't we follow their mask design guidelines? They are cheap, easy to produce and seem to do much better on every parameter that would plausibly impact viral spread. They are more breathable than most cloth masks I've used and tend to not vent steam into your glasses (hence more compliance).

    w.r.t. r0 and vaccines, keep an eye on the development of nasal delivery covid vaccines. While existing mRNA vaccines seem to give very good systemic immunity, they don't produce very good immunity in the mucosal system. Intranasal inoculation may be superior at delivering mucosal immunity, which would go a long way to driving down R0 in vaccinated individuals.

  12. If our policy makers were willing to say "we are passing the mask mandate so it rips through the population a little bit slower" I might not be so grumpy.

    If this is indeed the reality, why even be grumpy? Masks help slow transmission to some degree, it's just one piece of slowing transmission while we get vaccines distributed.

    As some other commenters have mentioned... isn't this common sense? Or is it some peoples' perspective that there is enough evidence of mask ineffectiveness that proves it's not even worth the hassle of putting one on?

  13. Is anyone else concerned that a narrowly focused vaccine will create a population that is overly dependent on it and vulnerable to the next virus or significant variation of Covid 19? I believe the medical term for this is vaccine-induced pathology and I know at least a few physicians that are concerned that is what we may be creating with these rushed vaccines.

  14. "Masks mean people who do not have any of the symptoms but still have covid are unlikely to pass it on."

    If that were true COVID would have been over a long time ago?

  15. Actual math notation would be helpful.
    e to the 6 t is not.

  16. It seems to me another reason to be grumpy is that mask mandates appear to be most likely to be found in places that need them the least. Would it be better if it was ripping through the south a little slower? perhaps, and perhaps not, its not pretty but they seem to be making do fairly tolerably? On the other hand we have northern states where it seems to me we'd be better off to let it rip faster, in the interest of letting people live there lives, and getting most people to be immune one way or another sooner rather than later.

  17. If you are looking for totally irrational NPI, what about the travel ban from European countries and UK?

    Since the prevalence of the virus is higher in USA than in most European countries, letting Europeans in will actually reduce the prevalence in USA.

    What's the "scientific reason" why you don't need a negative test to travel from Florida to Maine, but you need one traveling from Germany to Maine. After all, statistically speaking, a Floridian is more likely to have covid than a German is.

  18. To focus on the root cause start from the premise that we are living some distance from the "stone age", or the "iron age", but now in the "disinformation age". The innoculations, and masks, we need the most are against viruses transmitted through the internet.

  19. This is why NY, CA, other places are rolling out vaccine mandates for teachers and, in some cities, for indoor events in response to the delta wave.

  20. Can we apply "efficient market theory" to the question of masks? If cheap, cloth masks are helpful in reducing the spread of respiratory disease then why didn't the practice take hold until April 2020?

    Cheap masks working strikes me as equivalent to finding ten dollar bills on the sidewalk and no one picking them up. This is nonsensical, unless people have learned that the bills are fake and that explains why they walk past them. And so it is that the mood for masking today will evaporate once the perceived social and political benefits for masking are lifted. People who support masking now mainly do so for the social conformity and not for any health benefits.

    The behavior of the "elite" indicates they know masks are fake bills. For in private, they do not mask. But in public they are demonstrative maskers. In private the only reason to mask would be for the health benefits. And they don't do it!

  21. Can we just make masks voluntary? End of story.

  22. The AEA publication "American Economic Review: Insights", Vol. 3, Issue 3, September 2021, includes two articles which may have some relevance to the debate over social distancing and masking.
    1) Waning Immunity and the Second Wave: Some Projections for SARS-CoV-2 (#5)
    Chryssi Giannitsarou, Stephen Kissler and Flavio Toxvaerd;
    2) A Simple Planning Problem for COVID-19 Lock-down, Testing, and Tracing (#8)
    Fernando Alvarez, David Argente and Francesco Lippi.

    The first paper's abstract describes an open population with waning immunity in the presence of the novel coronavirus. The paper's on-line appendix presents the mathematical model and computational algorithms.
    1) "This paper offers projections of future transmission dynamics for SARS-CoV-2 in an SEIRS model with demographics and waning immunity. In a stylized optimal control setting calibrated to the United States, we show that the disease is endemic in steady state and that its dynamics are characterized by damped oscillations. The magnitude of the oscillations depends on how fast immunity wanes. The optimal social distancing policy both curbs peak prevalence and postpones the infection waves relative to the uncontrolled dynamics. Last, we perform sensitivity analysis with respect to the duration of immunity, the infection fatality rate, and the planning horizon."

    The second paper presents a simplified economic model of an economy that is in the throes of a novel coronavirus and has the option of closing part or all of the economy to slow the spread of the virus and its impact on the economy. The on-line appendix presents the mathematical model in detail and describes the discrete-time mathematical algorithm that solves the optimization problem.
    2) "We study the optimal lock-down for a planner who controls the fatalities of COVID-19 while minimizing the output costs of the lock-down. The policy prescribes a severe lock-down beginning a few weeks after the outbreak, covering almost 50 percent of the population after a month, with a total duration shy of 4 months. The intensity of the optimal lock-down depends on the gradient of the fatality rate with respect to the infected and the availability of antibody testing, which yields a welfare gain of 2 percent of GDP. We also study test-tracing-quarantine, which we show to be complementary to lock-down."

    Those with an interest that runs to mathematical models of economic phenomena and epidemiological models, these two papers may offer new insights.

  23. Yet another case of gross masking innumeracy: and

    This is from Texas Tech University Health Sciences Center. They posted their sources on Facebook, and it appears they’ve confused vaccines with masks.

    This infographic has been shared widely on Facebook, including by many other state health departments and physicians.

  24. This is the first RCT for masks. Surgical masks work.

  25. Look at the numbers. Masks work. A bit. They do not lower the reproduction rate from 6 to less than one. They do not make it "safe" to go out and about, to bars and nightclubs. They might mean you get the same spread in 10 days that without them takes a week. The story that a teacher gave children covid because he took his mask off for a few seconds is ludicrous. Vaccines work a lot better. Rapid tests work better. My point was and remains, that it is a grand forgetting of all we know about health policy that minutely adjusted mask mandates are the central policy response to the Delta variant. I actually admitted a lot more effectiveness than this RCT shows.


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