Once I was requested to calculate the overall quantity of SARS-CoV-2 on the planet for the BBC Radio 4 present Extra or Much less, I’ll admit I had no concept what the reply can be. My spouse urged it might be the scale of an Olympic swimming pool. “Both that or a teaspoon,” she stated. “It’s normally one or the opposite with these types of questions.”
So tips on how to set about calculating an approximation of what the overall quantity actually is? Fortuitously, I’ve some type with these types of large-scale back-of-the-envelope estimations, having carried out a lot of them for my e book The Maths of Life and Loss of life. Earlier than we embark on this specific numerical journey, although, I needs to be clear that that is an approximation based mostly on probably the most affordable assumptions, however I’ll fortunately admit there could also be locations the place it may be improved.
So the place to start out? We’d higher first calculate what number of SARS-CoV-2 particles there are on the planet. To do this, we’ll must understand how many individuals are contaminated. (We’ll assume people relatively than animals are probably the most vital reservoir for the virus.)
In response to stats web site Our World in Knowledge, half 1,000,000 individuals are testing optimistic for COVID daily. But we all know that many individuals is not going to be included on this rely as a result of they’re asymptomatic or select to not get examined – or as a result of widespread testing just isn’t available of their nation.
Utilizing statistical and epidemiological modelling, The Institute for Well being Metrics and Evaluations has estimated that the true variety of individuals contaminated every day is extra like 3 million.
The quantity of virus that every of the individuals at the moment contaminated will carry round with them (their viral load) is determined by how way back they have been contaminated. On common, viral masses are thought to rise and peak about six days after an infection, after which they steadily decline.
Of all of the people who find themselves contaminated now, those that bought contaminated yesterday will contribute somewhat to the overall rely. Those that have been contaminated a few days in the past will contribute somewhat extra. These contaminated three days in the past somewhat extra nonetheless. On common, individuals contaminated six days in the past could have the very best viral load. This contribution will then decline for individuals who have been contaminated seven or eight or 9 days in the past, and so forth.
The ultimate factor we have to know is the variety of virus particles individuals harbour at any level throughout their an infection. Since we all know roughly how viral load adjustments over time, it’s sufficient to have an estimate of the height viral load. An unpublished research took information on the variety of virus particles per gram of a spread of various tissues in contaminated monkeys and scaled up the scale of tissue to be consultant of people. Their tough estimates for peak viral masses vary from 1 billion to 100 billion virus particles.
Let’s work with the upper finish of the estimates in order that we get an overestimate of the overall quantity on the finish. Once you add up all of the contributions to the viral load of every of the three million individuals who turned contaminated on every of the earlier days (assuming this 3 million price is roughly fixed) then we discover that there are roughly two quintillion (2×10¹⁸ or two billion billion) virus particles on the planet at anybody time.
This feels like a very massive quantity, and it’s. It’s roughly the identical because the variety of grains of sand on the planet. However when calculating the overall quantity, we’ve bought to do not forget that SARS-CoV-2 particles are extraordinarily small. Estimates of the diameter vary from 80 to 120 nanometres. One nanometre is a billionth of a meter. To place it in perspective, the radius of SARS-CoV-2 is roughly 1,000 occasions thinner than a human hair. Let’s use the common worth for the diameter of 100 nanometres in our subsequent calculation.
To work out the quantity of a single spherical virus particle we have to use the components for the quantity of a sphere that’s, little doubt, on the tip of everybody’s tongue:
V = 4 π r³/3
Assuming a 50 nanometre radius (on the centre of the estimated vary) of SARS-CoV-2 for the worth of r, the quantity of a single virus particle works out to be 523,000 nanometres³.
Multiplying this very small quantity by the very giant variety of particles we calculated earlier, and changing into significant items provides us a complete quantity of about 120 millilitres (ml). If we needed to place all these virus particles collectively in a single place, then we’d must do not forget that spheres don’t pack collectively completely.
Shut sphere packing
If you consider the pyramid of oranges you may see on the grocery retailer, you’ll do not forget that a good portion of the house it takes up is empty. In reality, the most effective you are able to do to minimise empty house is a configuration known as “shut sphere packing” wherein empty house takes up about 26% of the overall quantity. This will increase the overall gathered quantity of SARS-CoV-2 particles to about 160ml – simply sufficiently small to suit inside about six shot glasses. Even taking the higher finish of the diameter estimate and accounting for the scale of the spike proteins all of the SARS-CoV-2 nonetheless wouldn’t fill a Coke can.
It seems that the overall quantity of SARS-CoV-2 was between my spouse’s tough estimates of the teaspoon and the swimming pool. It’s astonishing to suppose that each one the difficulty, the disruption, the hardship and the lack of life that has resulted over the past yr may represent just some mouthfuls of what would undoubtedly be the worst beverage in historical past.
Christian Yates doesn’t work for, seek the advice of, personal shares in or obtain funding from any firm or organisation that might profit from this text, and has disclosed no related affiliations past their tutorial appointment.