S*tatistics are human beings with the tears dried off –* Paul Slovic

Collected into a single ball, the troublemaking viral material from all the confirmed COVID-19 cases in the world would weigh less than 2 grams and occupy the volume of a small marble.

Even if you took the whole virus and assumed that many more people are infected than have tested positive, you still only have a mugful weighing just over 300 grams.

So little to cause so much damage? Well, size isn’t everything.

If you took your mug of goo and strung all those individual coronavirus spheres end to end, a necklace of tiny spiky beads could wrap itself round the earth’s equator 14 times.

And if you unpicked the curled up viral RNA from inside each of the virus beads and laid the filaments end to end, then the virus RNA would stretch to the sun and back 12 times.

Tiny, powerful…and deadly.

**A thought experiment**

Last week, I came across a question on twitter

“*If all of the COVID-19 existing today could be magically collected in a single ball, how large might it be and how much might it weigh*?”

@GreatDismal 5:55 pm · 21 Sep 2020·Twitter for iPhone

I discovered the wonderful world of William Gibson (aka @GreatDismal) surprisingly late in life; a whole canon of joy stretches ahead of me. It was a family discussion about jet lag in 2018 that prompted my Los Angeles based son to recommend *Pattern Recognition*, a book which contains the best description of sleep deprived lethargy in literature along with an astonishing introduction to Curta calculators.

As the question came from a writing hero, I was keen to answer. So, I got out my trusty Curta calculator (and an excel spreadsheet and a search engine) and got to work.

Have a look at my calculation below. This is a thought experiment, so **do** try it at home and **please **tell me where you disagree.

*Fiona Erskine is author of engineering thrillers The Chemical Detective (2019) and The Chemical Reaction (2020), published by Oneworld. Her latest book, Phosphate Rocks: A Death in Ten Objects, will be published by Sandstone Press (2021*)

**My calculation**

Total Value = value individual copy x number of copies per person x number of infected people

Known cases COVID-19 (number people 29SEP2020) | 7,612,823 | 7.61E+06 |

Estimated cases COVID-19 (number people) | 46,764,484 | 4.68E+07 |

Weight RNA in SARS-CoV-2 (g) | 0.000000000000000032 | 3.20E-17 |

Weight Virus SARS-CoV-2 (g) | 0.0000000000000010 | 1.00E-15 |

Number copies per case (number of viruses per person) | 7,380,000,000 | 7.38E+09 |

Total weight RNA SARS-CoV-2 from known cases (g) | 1.8 | 1.8 |

Total weight RNA SARS-CoV-2 from estimated cases (g) | 11 | 11 |

Total weight Virus SARS-CoV-2 from known cases (g) | 56 | 56 |

Total weight Virus SARS-CoV-2 from estimated cases (g) | 345 | 345 |

RNA SARS-CoV-2 length (m) | 0.0000102 | 1.02E-05 |

Virus SARS-CoV-2 diameter (m) | 0.000000010 | 1.00E-08 |

Length (m) of string of beads of virus from known cases | 561,826,337 | 5.62E+08 |

Stretched out length (m) RNA from estimated cases | 3,520,243,308,338 | 3.52E+12 |

Earth circumference (m) | 40,075,000 | 4.01E+07 |

Earth to sun (m) | 150,100,000,000 | 1.50E+11 |

Wrap beads of virus from known cases round Earth’s diameter (times) | 14 | 14 |

Filament of RNA to sun and back of estimated cases (times) | 12 | 12 |

Explanation

**Number of infected people**

No one knows how many people are infected, but we do have some idea of how many have tested positive.

As of today (29^{th} September 2020) there are 7,612,823 confirmed active cases

Early research suggested that 86% of infections went undocumented, so for every confirmed case, lets assume there are about 86/14 = 6 unconfirmed cases.

Number of infected people = 7,612,823 confirmed or or x 7,612,823 x 86/14 = 46,764,484 estimated (confirmed and unconfirmed)

**Weight individual virus**

The virus looks like a spiky sphere – an orange stuck with cloves (great in mulled wine) or the 1980’s cocktail party special with toothpicks skewering alternating chunks of cheddar cheese and pineapple stuck in a melon. The weight of the whole kit and caboodle (membrane, envelope, spikes, nucleus and genome) is about 1 femtogram.

A femtogram (fg) is a fraction of a gram, 1/1,000,000,000,000,000 written as 10⁻¹⁵ grams.

But if we’re not so bothered about the delivery packaging, and only interested in the deadly contents, then it’s the weight of the single strand of RNA virus inside: a genome of 30 kilobases.

A kilobase is a length of single-stranded RNA containing one thousand bases. Each base contains one of the building blocks of life: adenine, thymine, guanine, or cytosine and 30 thousand of them weigh about 0.032 femtograms, or 3.2 x 10⁻^{17} grams

Weight individual virus = 1 x 10⁻¹⁵ grams containing 32 x 10⁻^{18} grams of RNA

**Number of viruses per person**

The hardest data to find in a form I could understand and quantify was the viral load.

A twitter correspondent (@londonsidi) suggested 1 million viruses per ml of blood times 5 litres (5000ml) of blood per person = 5 billion viruses per person.

That sounded plausible, except that initial reports in patients from Wuhan, China found a very low RNA concentration in the blood – between 100 and 1000 copies per ml.

But if you look at nose and throat swabbing, the average viral load was 7.00 × 10^{6} copies per ml, with a maximum of 2.35 × 10^{9 }copies per ml.

A single swab can only collect a fraction of the virus in the body.

Let’s assume each lung produces 20 – 30 millilitres (ml) sputum per lung per day – so average 25 ml per lung times 2 lungs is 50 ml and we get 7.00 × 10^{6} copies per ml x 50 ml = 350 million copies per person in the throat.

The nose produces an incredible litre (1000 ml) of mucus per day, so if the same concentration is present in the nose, that’s 7.00 × 10^{6} copies per ml x 1000 ml = 7000 million copies

The same report found 10,000 copies per ml of poo (stool).

Assuming we excrete up to 250 ml per day, that’s 25 million copies per person

Plus up to 1000 copies per ml in the blood x 5000 ml blood = 5 million copies per person in the blood.

Total 7000 +350+25+5 = 7380 million copies

7 billion copies per person. Amazingly close to the initial estimate of 5 billion! But for all the wrong reasons.

This is the most suspect part of the thought experiment – I really have no idea what I’m doing and I miss my mum who was a brilliant virologist. I hope there’s a proper scientist out there who has read this far and can correct me.

Until then, I’m stuck with my estimate 7 billion copies of virus per infected person.

All comment welcome!