Today there was a COVID-19 press conference, with the Prime Minister Boris Johnson, and Sirs Chris Whitty and Patrick Valance. It is on YouTube. At about 38 minutes LBC’s Ben Kentish asked a couple of questions. Sir Chris Whitty gave what sounded to me like an excellent answer on vaccines, clear, authoritative, from the heart, and useful. Impressive. He was also also asked about some healthcare workers not getting FFP3 masks. Maybe the question was a little vague but the answer was certainly vague and he did imply that there was a debate about where an FFP3 was useful and where they are not.
How long does SARS-CoV-2 survive outside the body?
It may not be obvious that there is a connection between the air-conditioning units of Boeing airliners, and the survival of viruses, but there is. In the 1960s, an engineer called Proschan, while working for Boeing, was studying the failure statistics of the air-conditioning units in airliners. He was a pioneer of what is often called survival analysis – the branch of statistics that deals with failure/death. The same statistics applies both to failure of a machine, or death of an organism — and to the demise of a virus, which is perhaps somewhere between a machine and an organism.
The standard, and simplest, model for survival assumes two things. The first is a constant failure/death rate, and the second is that for all the machines/living organisms, this rate is the same. Then the fraction of air-conditioning units, infectious virus etc decays exponentially
% remaining = 100*exp(-kt)
for k the failure/death rate.
Unfortunately, both these assumptions are usually wrong, even air-conditiong units are more complex than this, and living organisms are much more complex than this simple model admits. Proschan considered the case when the failure rate of each individual machine (air conditioning unit in that case) is constant, but varies from one unit to another. Then he showed that the % remaining decays more slowly than exponential. Data is then often fit with what is called a Weibull function
% remaining = 100*exp(-k’tβ)
When the exponent β < 1 the % remaining decays more slowly than exponentially.
This is shown in the plot at the top of the post. The red circles are data from Oswin and coworkers on the survival of mouse hepatitis virus (MHV), a surrogate coronavirus for the other coronavirus: SARS-CoV-2. This is in aerosol droplets – which is how COVID-19 is transmitted. The blue curve is a fit of a Weibull function, with a best-fit value of β = 0.49. This is a very different function from an exponential – the bestfit exponential is shown as the orange curve.
The Weibull fit implies that as time goes on the average rage at which viruses cease to become infectious becomes slower and slower. This matters. Exponentials decay fast, for exponential decay, there is a well-defined lifetime and after about ten lifetimes then there is none left. But for the much slower decay of the blue curve above, there is no well defined lifetime. And at long times, there is much more left than with the exponential. Note that the exponential fit underestimates the data at the longest time (10 minutes). So if you want to know, for example, how long you need to wait for 99% of the virus to be no longer infectious, then it really matters which of a Weibull or an exponential is the better model.
Something surgical masks can do: stop you spraying someone with your bugs
Many people are wearing surgical masks, even though SARS-CoV-2 is airborne and so a better fitting mask, eg FFP2, would offer a lot more protection. But surgical, and cloth, masks are not useless, if you are infected they are good at stopping you breathing virus-laden particles directly onto to anyone you are talking directly at, and are close to. This is nicely illustrated in a recent work by Bourrianne and coworkers. The basic point is simple, we need to breathe in and out, about once every couple of seconds. When we breathe out we push out a litre or two of air in about a second. This goes through some combination of our nostrils, and a typically mostly closed mouth. This is quite a small area, perhaps a few square centimetres. Basic geometry says that to expel 1 litre through holes say 10 cm2 in area, you need a speed of 1 m/s. This is quite fast and results in a cone of air shooting out from your mouth/nose towards anyone you are facing*. The cone rapidly dissipates in the room air but still you are imparting momentum to your breath which carries it and any nasties it may be carrying towards anyone you are facing.
Open the windows, and let the carbon dioxide and virus out
Above is a plot of prevalence of COVID-19 in children versus the concentration of carbon dioxide (CO2) in their classrooms. Prevalence is defined as being number of children who test positive for COVID-19 per 100, so 0.01 means one in 10,000 children has COVID-19. Cumulative CO2 concentration is obtained by integrating CO2 concentration over something like a school day, I think. The data is from a study by Empa (part of the Swiss university ETH), of classrooms in Graubünden, a canton of Switzerland. As they say, this is very preliminary, but although of course the data is noisy there does seem to be a trend. The R in the plot is Pearson’s correlation coefficient, and a value of 0.72 suggests a significant correlation between the amount of CO2 in the air children are breathing in classrooms, and how many are becoming infected with COVID-19.
Beards and mask wearing: Dos and don’ts
Back in the carefree year 2017, the USA Centers for Disease Control (CDC) produced the above guidance for healthcare workers who needed to wear masks for work, but favoured facial hear. It was motivated by Movember. The green ticks mean that the style of facial hair is compatible with wearing a fit-tested mask, the red crosses indicates that the style is not allowed, and those healthcare workers who need to mask-up at work will need to get the razor out. Most moustaches are allowed but almost all beards are banned as there is then facial hair where the mask has to fit tightly to the skin (see top left of image) to get a good seal and prevent air leaking around the edges.
When your lecture notes are out of date two days after you wrote them
On Wednesday I updated my biological physics lecture notes, for a course I am teaching. I added a few new sentences to my notes, including:
“We are watching the evolution of the spike protein [of SARS-CoV-2] very carefully as vaccines use this protein, and so if a new variant arises with a heavily mutated spike protein, vaccines may then be much less effective against it, than they are for current variants.”*
The topic of the lecture is on evolution, including a long-standing (i.e., written pre-pandemic) section on the rapid evolution of viruses and bacteria. That was Wednesday, yesterday (Friday) the World Health Organisation announced the naming of a new variant of concern: Omicron. A variant with a heavily mutated spike protein, which makes scientists worried that vaccines may be much less effective against. Something that was mentioned in today’s press conference with Boris Johnson, Chris Whitty and Patrick Valance.
Why, in a pandemic caused by a virus, are so many people wearing masks made to protect surgical patients against bacteria?
The bar graph compares examples of the three basic types of mask: a cotton mask (as in the fabric ones you can wash), a surgical mask (these are typically blue and are disposable), and a mask that meets the USA standard for personal protective equipment (PPE) – this is called the N95 standard. The height of the bar quantifies the amount of protection offered, for example, a ten on this scale means a reduction in dose of particles by a factor of ten. In other words, 90% of the particles are filtered out. Masks are just air filters we wear on our faces. Note that the y axis is a log scale – there are large differences in the amount of protection! The data is from Duncan, Bodurtha and Naqvi.
Is it time we wore properly regulated masks?
As a 50-year-old guy I find it a bit weird to recommend a YouTube channel, but I am going to recommend Aaron Collins’ YouTube channel on masks*. Back in Spring/Summer 2020 we were (rightly I think) urged to avoid the sophisticated masks used by healthcare workers, because there was a shortage of these masks and these frontline workers needed them more. But now there is no shortage, so we should wear the best mask we can. See Aaron Collins’ channel for him testing masks and recommending the best masks. Not all masks are the same, some offer much more protection than others. The filtration properties of cotton fabric are generally pretty poor (colleagues and I have a preprint on that), but the best masks are made from sophisticated filtration medium which is much much better.
Welsh independence seems to mean independent of the scientific consensus
Although I have been at Surrey for over 20 years I grew up in South Wales, where my mother still lives. In fact she lives in the Neath Senedd constituency of the Welsh government’s Minister for Education, Jeremy Miles. The Welsh government, under Jeremy Miles has had a bit of a brain fade and planned to introduce ozone machines into Wales’ classrooms. These don’t work, essentially because ozone is toxic so you can’t run machines while children and teachers are in them. But as the virus is breathed out by infected people, you have to purify or refresh the air while people (including possibly an infected person) are actually in the room. Running an ozone machine at 7 am in an empty classroom is a waste of everyone’s time, and protects no one.
If you know what you are doing you get the same result from a 1940s differential analyser and a modern computer running Python
Above is an aircraft wing which has picked up ice on the leading edge of its wing. This is of course is not ideal, especially for an aircraft in the air. You don’t want large amounts of ice forming along the leading edge of the wing in flight, it will add weight and make the wing less able to generate lift. I think there were particular worries about this during the Second World War, possibly because planes were flying higher and faster as the war drove rapid advances in aircraft design and performance. So the United States Army Air Force turned to the dream team of a Nobel-prize winner, Irving Langmuir, and the first woman to obtain a PhD in physics from the University of Cambridge, Katherine Blodgett. They worked to understand the following problem.
Chance & Necessity 