All of the world’s coronaviruses could fit in a can of Coke, with plenty of room to spare

When I was asked to calculate the total volume of SARS-CoV-2 in the world for the BBC Radio 4 show More or Less, I admit I had no idea the answer. My wife suggested it would be the size of an Olympic size swimming pool. “Either that or a teaspoon,” she said. “It’s usually one or the other with these kinds of questions.”

So how do you calculate an approximation of what total volume actually is? Fortunately, I have some form with these kinds of large-scale estimates, having done a number of them for my book The Maths of Life and Death. Before we embark on this particular digital journey, however, I should be clear that this is an approximation based on the most reasonable assumptions, but I will gladly admit that there may be places where it can be. be improved.

So where to start? We’d better calculate the SARS-CoV-2 particle number in the world first. To do this, we need to know how many people are infected. (We’ll assume that humans rather than animals are the virus’s most important reservoir.)

According to the statistics website Our World in Data, half a million people test positive for COVID every day. Yet we know that many people will not be included in this tally because they are asymptomatic or choose not to get tested – or because widespread testing is not readily available in their country.

Using statistical and epidemiological models, the Institute for Health Metrics and Evaluations has estimated that the actual number of people infected each day is over 3 million.

The amount of virus that each of the currently infected people will carry with them (their viral load) depends on when they were infected. It is believed that on average, viral loads increase and peak around six days after infection, after which they decrease steadily.

Of all those infected now, those who were infected yesterday will contribute a little to the total tally. Those who were infected a few days ago will contribute a little more. Those infected three days ago a little more. On average, people infected six days ago will have the highest viral load. This contribution will then decrease for people infected seven, eight or nine days ago, and so on.

The last thing we need to know is the number of viral particles that people harbor at any time during their infection. Since we know roughly how viral load changes over time, it is enough to have an estimate of the peak viral load. An unpublished study collected data on the number of viral particles per gram from a range of different tissues in infected monkeys and increased the size of the tissues to be representative of humans. Their rough estimates of peak viral loads range from 1 billion to 100 billion virus particles.

Let’s work with the upper end of the estimates so that we get an overestimate of the total volume at the end. When you add up all the viral load contributions from each of the 3 million people who have been infected on each of the previous days (assuming that rate of 3 million is roughly constant), we find that there is about two quintillions (2 x 10¹⁸ or two). billions of billions) of virus particles around the world at any given time.

It sounds like a very large number, and it is. This is roughly the same as the number of grains of sand on the planet. But when calculating the total volume, we must remember that the particles of SARS-CoV-2 are extremely small. Diameter estimates range from 80 to 120 nanometers. A nanometer is a billionth of a meter. To put it in perspective, the radius of SARS-CoV-2 is about 1,000 times thinner than a human hair. Let’s use the mean value of the diameter of 100 nanometers in our further calculation.

To calculate the volume of a single spherical viral particle, we have to use the formula for the volume of a sphere which is, without a doubt, on the tip of each one’s tongue:

V = 4 π r³ / 3

Assuming a radius of 50 nanometers (at the center of the estimated range) of SARS-CoV-2 for the value of r, the volume of a single viral particle is 523,000 nanometers³.

Multiply that very small volume by very large particle number that we calculated earlier, and converting to significant units gives us a total volume of about 120 milliliters (ml). If we wanted to collect all of these virus particles in one place, we have to remember that the spheres do not come together perfectly.

Close the packaging of the sphere

If you think about the pyramid of oranges that you might see in the grocery store, you’ll remember that a significant portion of the space it takes up is empty. In fact, the best you can do to minimize void space is a configuration called “closed sphere wrapping” in which the void space takes up about 26% of the total volume. This increases the total collected volume of SARS-CoV-2 particles to about 160 ml – small enough to fit in about six shot glasses. Even taking the high end of the diameter estimate and factoring in the size of the spike proteins, not all of the SARS-CoV-2 would still fill a can of Coke.

Turns out the total SARS-CoV-2 volume was between my wife’s rough estimate of the teaspoon and the pool. It’s amazing to think that all of the problems, disruptions, hardships and loss of life that have resulted over the past year could be just a few bites of what would arguably be the worst drink in the world. history.