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- Christine Yates
- （Christian Yates）
Image source,fake images
The BBC Radio 4 program “Roughly Like This” asked me to calculate the total amount of the new coronavirus that is currently ravaging the world and endangering all of humanity. I have to be honest, I don’t know the answer. My wife believes that the total amount should be the size of a lap pool. She said, “Or just a teaspoon. Very few people would ask such a question.”
So how should we proceed to calculate an approximate value of the total number of new coronaviruses in the world?
Fortunately, for large-scale rough calculations, I already have some models, and in my book “The Mathematics of Life and Death” (The Mathematics of Life and Death), I used these models to estimate some good numbers. But before I embark on this special digital journey, I must clarify that this is only a rough calculation based on the most reasonable assumptions, and I am happy to admit that there is room for more precise calculations.
So where should we start? I think it is better to first calculate how many particles of the new coronavirus there are in the world. To get this number, we need to know how many people in the world are infected. (We assume that the most important host of the virus is humans, not animals, that is, it is not considered the new coronavirus that resides in animals).
According to the statistics website “Our World in Data”, 500,000 people test positive for the new corona virus every day. However, we know that there are many virus carriers who are not included in these statistics because they do not have symptoms or choose not to be tested, or because comprehensive testing is difficult to obtain in their country.
The Institute for Health Measurement and Evaluation uses statistical and epidemiological models to estimate that the actual number of people infected every day in the world is approximately 3 million.
Image source,fake images
It is necessary to roughly calculate the viral load of each person infected with the new coronavirus.
Currently, the amount of virus that each infected person carries, that is, the viral load calculated based on the number of viruses per milliliter of blood, depends on when the patient was infected. On average, the viral load of patients after infection showed an upward trend, reaching a peak in about 6 days and then steadily decreasing.
Among all infected people, the viral load of those infected yesterday only represents a small percentage of the total load. The proportion of people who have been infected for two days will be higher than the first. More people were infected over three days. Patients who were infected for six days had the highest viral load and then began to decline. For patients who have been infected for seven, eight, or nine days, the viral load ratio will decrease. The longer the days of infection, the greater the decrease.
The last thing we need to know is the number of virus particles that a patient carries at any stage of the infection process. Since we already know approximately that viral load changes with the time of infection, we can estimate the viral load at the peak of infection. An unpublished study collected data on the average number of virus particles per gram from different organs and tissues in infected monkeys, and then enlarged the monkey’s organs to the size of the human body, so that it can be roughly estimated that human infection is in the peak stage. The virus has between 1 billion and 100 billion particles.
Let’s take the median (geometric mean) in the middle, which is 10 billion. Assuming that the infection of 3 million people is approximately constant, and that these 3 million people are sequentially infected with different viral loads, and then we add the viral loads of each of them, and we will find that humans carry them at any time . The number of new coronavirus particles is approximately 200 quadrillion (i.e. 2 x 10¹⁷, 2 times 10 to the 17th power).
It sounds like an astronomical number and it is true. This is roughly equivalent to the total number of grains of sand on earth. But when calculating the total volume, we must remember that the new coronavirus particles are extremely fine. The diameter is estimated to be 80 to 120 nanometers. A nanometer is one billionth of a meter. From this perspective, the radius of the new coronavirus is about 1,000 times smaller than the radius of human hair. In subsequent calculations, we use the average diameter of the new coronavirus, which is 100 nanometers, to calculate.
Image source,Reuters
Like stacked citrus, spherical particles will not stack perfectly and smoothly.
Assuming that the radius of the new coronavirus is 50 nanometers (the mean value of the estimated range), the volume of a single spherical virus particle is estimated to be 523,000 cubic nanometers.
Multiplying this small volume by the astronomical number of virus particles that we have calculated before, and then converting it to significant units, we conclude that the total volume of the new coronavirus carried by 3 million patients is approximately 120 milliliters. But if we want to stack all these new coronavirus particles together, we must remember that spherical objects cannot stack perfectly and smoothly.
Think about the piles of citrus you see in the store and you will remember that there are many gaps in the piles of citrus that are not full. In fact, the way to minimize the voids in the accumulation of spherical objects is a structure called “closer packing of spheres”. In this structure, the voids represent 26% of the total accumulation space. Calculating with this structure, the total volume of 3 million new coronavirus particles will increase to about 160 ml. It is so small that it can easily be stored in six small wine glasses. Even taking into account the upper limit of the estimated diameter and protein size of the viral peak, the accumulation of all the new coronaviruses in the world is still not enough to fill a soda can.
Facts have shown that the total capacity of the new global coronavirus is actually between my wife’s rough teaspoon and pool estimate. The shocking thing is that the culprit for all these problems, destruction, suffering and loss of life in the last year may be just a few sips, but it is without a doubt the scariest drink ever.
An earlier version of this article incorrectly stated that the total number of new coronavirus particles in the world at any one time is approximately 2×10¹⁸. But this number is wrong, it should be 200 quadrillion (2 x 10¹⁷). This bug did not affect the calculation results and has been corrected.
* Christine Yates is Senior Lecturer in Mathematical Biology at the University of Bath and author of the book “The Mathematics of Life and Death”.
