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Mathematician claims all the world's coronavirus would fit in can of soda

  • Published at 01:29 pm February 12th, 2021
Soda cans
File photo: Regular and mini cans of Coke and Pepsi are pictured in this photo illustration in New York August 5, 2014 Reuters

Radius of SARS-CoV-2 is roughly 1,000 times thinner than a human hair

All the SARS-CoV-2 virus particles in the world would fit inside a can of soda, according to Christian Yates, senior lecturer in mathematical biology at the University of Bath.

Yates writes for The Conversation: “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 will admit I had no idea what the answer would be. My wife suggested it would be the size of an Olympic swimming pool."

“Either that or a teaspoon. It’s usually one or the other with these sorts of questions,” his wife had said.

The calculation

Around half a million people are testing positive for Covid-19 every day, but it should also be noted that countless cases are excluded from this count as many people are either asymptomatic or choose not to get tested, Yates remarked.

“Using statistical and epidemiological modelling, the Institute for Health Metrics and Evaluations has estimated that the true number of people infected each day is more like 3 million,” he mentioned. 

Meanwhile, the viral load, or amount of virus that each currently infected person would carry around with them, is contingent on how long ago the person had been infected.

“Of all the people who are infected now, those who got infected yesterday will contribute a little to the total count. Those who were infected a couple of days ago will contribute a little more. Those infected three days ago a little more still,” Yates said. 

“On average, people infected six days ago will have the highest viral load. This contribution will then decline for people who were infected seven or eight or nine days ago, and so on.”

The final key to the puzzle, he said, is the quantity of virus particles a patient carries at any point during the infection. 

According to an unpublished study, peak viral loads range from one billion to 100 billion virus particles, Yates said. 

“When you add up all the contributions to the viral load of each of the 3 million people who became infected on each of the previous days [assuming this 3 million rate is roughly constant], then we find that there are roughly 200 quadrillion virus particles in the world at any one time,” the mathematician estimated. 

Drawing a parallel, he said: “It is roughly the same as the number of grains of sand on the planet.”

“But when calculating the total volume, we’ve got to remember that SARS-CoV-2 particles are extremely small … the radius of SARS-CoV-2 is roughly 1,000 times thinner than a human hair.

“Assuming a 50-nanometre radius [at the centre of the estimated range] of SARS-CoV-2, the volume of a single spherical virus particle works out to be 523,000 cubic nanometres.

“Multiplying this very small volume by the very large number of particles we calculated earlier, and converting into meaningful units gives us a total volume of about 120 millilitres.”

It is also to be noted that spheres don’t pack together perfectly.

Taking this into consideration, the total gathered volume of SARS-CoV-2 particles go up to about 160 millilitres.

Even using the upper end of the diameter estimate and accounting for the size of the spike proteins, all the SARS-CoV-2 particles on Earth still would not fill a can of soft drink, Yates said.

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