Dec 21 I keep forgetting to send out my columns on time! For Friday December 11, I wrote about a mathematical model that's designed to challenge this idea of social distancing. Well, not the distancing itself, but the widespread belief in a distance of six feet. The model instead seeks to estimate how safe you are from Corona infection in your particular situation - the size of the room you're in, how well it is ventilated, how many others are there with you and how many are masked ... the results are surprising.
Take a look: https://www.livemint.com/opinion/columns/is-the-six-foot-rule-enough-in-that-room-11607652477012.html . There's a link at the end of my text below where you can try the model out for yourself. If you do, or even if you don't, please let me know what happened. cheers, dilip --- Are you breathing, speaking or singing in that room? ------------------ Dilip D'Souza One of the pleasures - if that's the word I want - of this Corona time is noticing how it has been like a gold mine for mathematicians. So many have investigated so many interesting facets of the virus - its structure and what might fight it, how it spreads and what "herd immunity" means, for just three. And a new mathematical model seeks to answer questions you might have about meeting others in a time of a pandemic. We've all heard the rules about keeping six feet distant, and wearing masks and avoiding indoor gatherings. But some of us, for example, have to meet others indoors as part of our jobs - think of a shopkeeper or a dentist. Some of us cannot always observe the six-foot rule - think of bus conductors and commuters. Can such people at least get an idea of how safe they are, or what risks they are taking? If one person with you has the virus, how long are you safe? That's the question this mathematical model is designed to answer. The answer depends on many different factors. Consider how a friend queried the model. His normal work area - that is, before covid forced him to work from home - is a room whose area is 900 square feet. It has ceilings that are 20 feet high, but closed windows and doors; thus the circulation of air is not very efficient. There are often as many as 25 people working in the room. In a space of that size, 25 people can easily observe the six-foot rule. Actually, if you think about it, up to 36 can. That's because you can have a square room 30 feet on each side, which makes 900 square feet. This allows six rows of six people each, six feet apart: 36 people. So naturally, since it can accommodate 36 socially-distanced people, my friend assumed it would be safe for 25 people to work there indefinitely. But then he fed all these details and a few more to the model. The result, he said, was "very, very surprising." In a room like that, it said, the 25 people would be safe from the virus for just 62 minutes. Just over an hour. In fact, if he wanted to work there through a full morning of five hours before breaking for lunch - the way he and his colleagues usually did before the pandemic - the model said there should be no more than four in the room. Not 25. The catalyst for crafting this model was scepticism about the six-foot rule, particularly indoors. Of course it makes sense to maintain some distance from others around you, but why six feet? Why not more, or 56 inches, or an arm's length? After all, the generally accepted scientific fact about the virus is that it spreads through droplets in the air. Do we know for certain that they don't travel as much as six feet? Martin Bazant and John Bush, mathematicians at MIT, developed this model. Their aim was "to derive an indoor safety guideline that would impose an upper bound on the 'cumulative exposure time.'" (Beyond Six Feet: A Guideline to Limit Indoor Airborne Transmission of COVID-19, medRxiv, 26 August 2020). They assume you're part of a group of people in an enclosed space, one of whom has the virus. The virus-bearing droplets from this person are "sufficiently small to be continuously mixed" through the room. Therefore, they factor in the room's size, how it is ventilated and whether its air is filtered, how fast people are breathing, what proportion of its occupants are using face masks, and more such. Once you assign values to all these, the model gives you an estimate of how safe you are in that space. Naturally, this is too limited a space to explain all the mathematics in the Bazant/Bush model. But let me give you a flavour of just one aspect of it, the effect of respiratory activities on the spread of the virus. It's important to know the size of the droplets that are floating about in your room, courtesy the person who has the virus. The smaller they are, naturally, the longer they linger in the air before dropping to the ground. But why would the sizes vary at all? "The exhaled drop-size distribution," Bazant and Bush write, "depends strongly on respiratory activity." In fact, "one is at greater risk in rooms where people are exerting themselves in such a way as to increase their respiration rate and pathogen output, for example by exercising, singing or shouting." So we ask, what is the person with the virus doing, respiratorily speaking, in that room? Breathing through the nose? The mouth? Whispering? Speaking? Singing? And if singing, is it soft or loud? Each of these makes a difference to the chance that the virus will spread, and so each must be accounted for in the model. The paper has a graph explaining this, with different curves for each of these "respiratory activities". There's more in this vein. The authors point out that one parameter that's not easy to pin down is "the concentration of exhaled infection quanta by an infectious individual." That is, when the infected person expels droplets, whether while breathing or singing, can we estimate how much of the virus is actually in the air he exhales? Again, there's data and a fascinating graph that tries to do just that. When we breathe normally through our nose or mouth, we exhale about half a cubic metre per hour of air. When we sing, that rate doubles, to about one cubic metre per hour. How infectious are each of those cubic metres? Simply breathing through the nose emits just 1.1 "infection quanta" - think of that as bits of infective material - per cubic metre of exhaled air. Singing raises that into the hundreds of quanta per cubic metre. For a case at the other extreme, consider one of the earliest "super-spreader" events, the Skagit Valley Chorale's weekly rehearsal in Washington State in the USA on March 10 this year. 53 of the 61 singers in attendance contracted covid-19, and one died. Researchers estimate that the emission rate there was about 970 quanta per cubic metre. 1.1 vs 970: that gives you an idea of what is involved here, what this model must take into account. Between those two extremes are such activities as "whispered counting" (37 quanta/cubic metre) and "loud speech" (142). To put this all into some perspective, the graph also has estimates of other notable virus-spreading episodes. The Wuhan and the Diamond Princess cruise liner outbreaks had emission rates of about 30. In January, a single infected person on a poorly-ventilated bus in Ningbo, China, infected nearly two dozen others; the emission rate there was later estimated to be about 90. Bazant and Bush offer two case studies to show their model's findings, a classroom in a school and a home for the elderly. "Our analysis sounds the alarm," they write, "for elderly homes and longterm care facilities" in particular. Needless to say, such homes have already seen a lot of Corona-related hospitalizations and deaths. In the end, the great value of their model is that it challenges our reliance on the six-foot rule. It offers what they call "a rational, physically-informed alternative for managing life in the time of covid-19." Managing life: makes sense to me. (Run the Bazant/Bush model yourself here: https://tinyurl.com/CovidSafetyModel) -- My book with Joy Ma: "The Deoliwallahs" Twitter: @DeathEndsFun Death Ends Fun: http://dcubed.blogspot.com -- You received this message because you are subscribed to the Google Groups "Dilip's essays" group. To unsubscribe from this group and stop receiving emails from it, send an email to dilips-essays+unsubscr...@googlegroups.com. To view this discussion on the web, visit https://groups.google.com/d/msgid/dilips-essays/CAEiMe8onGAA5fKEcvESdQUgrfcEV%3D7xdpKnKOnpVd2GRQVX2hA%40mail.gmail.com.