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On COVID-2019

Source: Wikimedia

I have been asked to put together some thoughts on the current COVID-2019 epidemic, and I hope you can find them useful:

So what is this COVID-2019? It is a virus, a tiny organism, a bit similar to flu viruses, but with some differences. I will not bore you with biology, but the most important things to know are:

  • It is tiny, but there are many of them, and they multiply very quickly so that you might be harbouring millions of them
  • It spreads very well, mainly on droplets from coughing, sneezing – or talking
  • It survives pretty well on surfaces like tables, door handles, windows
  • It does not respond to antibiotics, and there is no working vaccine yet
  • It likes to mutate so what we know about it now might not be accurate in the future

How can I get it? The main transmission is person-to-person by cough, sneeze, or touch. It looks like the highest risk is within 2 meters from an infected person. It also seems that – like a flu virus – you can also pick it up by touching a surface and then your face. The virus cannot walk or fly on its own, it needs to go from the source to you. The virus cannot pierce your skin, so the main entry into your body is your mouth and nose.

If it gets into my body, what is it going to happen to me? At first, nothing. The virus needs to get into your airways and then it starts to multiply. This might take several days, and it triggers a response from your organism. In many cases, the body can fight the virus successfully, and you might not notice anything and fully and quickly recover. It looks at the moment that most people only have very mild symptoms or none at all. If the virus starts multiplying without control, your organism will switch its response into a higher gear, with high temperature which slows down the virus and coughing to expel it. Of course, any coughing will spread the virus to other people!

Will I recover? Most people will; symptoms will disappear after a few days as the organism builds up immunity. For the ‘usual’ flu, most people will become immune to it, that is will not get it again in the future. It is not clear at present whether this is true for COVID-2019. It also looks at the moment that only a small proportion of people will develop more significant problems. This seems to be less than 1% for young people, but goes up to 15% for older people; more on it later.

What is all the fuss, it is like the usual flu, isn’s it? Indeed, the virus is similar to the flu, but there are some essential differences. Firstly, it seems that it spreads much quicker and thus can infect many more people.

To understand this, we will need to do a bit of math, so please bear with me for a moment. We know that for seasonal flu, each case of infection usually causes 1.3 new cases per week, at least in the worst periods of the epidemic. In other words, starting with three infected, in the next week we might get four new infections, then next week, five, then next week, almost seven, then nearly nine, so it will take about 4 weeks to triple the numbers of new cases. For COVID, we believe the number of new infections is between 3 and 4. Again starting with three infected, we get at least nine new infections in the next week. Thus, it will take 40 weeks for the flu to go from three to 100,000 new cases per week, but for COVID only 9 weeks (for illustration purposes I assumed that the infectious period for both flu and COVID is one week). This means that very quickly, we can end up with hundreds of thousands if not millions of people being ill. We have seen this rapid growth in China, and we see it now in Italy and in other countries. 

 Secondly, as many people have only very limited symptoms while spreading the virus, it is much more challenging to stop it from spreading. Thinking why this is important, think about the last time you had flu with high fever and extreme weakness which meant you very likely and very quickly went to bed. This limited the number of people you could contact and infect. This might not be a case for COVID, so you will go around unknowingly spreading it.

Thirdly, although the rate of severe complications and deaths seems to be lower than for seasonal flu, COVID appears to affect some people severely. Going back to numbers, if 100,000 people are ill, and 1% have serious complications, we suddenly have 1,000 severe cases that need intensive care. Even in the best prepared and developed countries, health systems are simply not ready to handle that many seriously ill people at one time. There is simply not enough intensive units, oxygen bottles, drips, doctors and nurses. So, doctors will have to prioritise. If – like myself – you are a high-risk person, this is not a very nice thought, as I might be the one for whom treatment is withheld if I happen to become ill.

And what about developing countries where a lot of people are hungry and where health service is inadequate or non-existent?

This brings us to the next question, am I safe from COVID? If you are a healthy young person, preferably living in an underground bunker, you are perfectly safe. If you are a young and healthy person and live in a city in a developed country or near transportation hubs, then you might become ill, but the chances of complications are low. If somebody has any immunological deficiency, or is 70 years old and older, and lives in high-risk areas, he or she is in danger. Remember that this might be your Mum, Grandma or Grandpa, or an elderly friend across the road. You might also have an underlying condition you are not aware of, and you might be the next person who requires oxygen that has just run out. Hence, you die gasping for air in a hospital corridor. Sorry to be brutal.

That’s all panic and hoax; be honest, you have no idea this will happen. Of course, I do not know this is going to happen. If I could predict the future accurately, I will be an investment banker, not a university lecturer. But, we are actually quite confident that something like this might be the worst-case scenario. Given what is at stake, it is probably better to play safe. We also have pretty good evidence things can go out of control, from countries like China and Italy.

So it is dangerous after all, isn’t it? For most of us, probably not. But if you care about others, you should try to do something to stop it. Most governments are now implementing compulsory measures to prevent the disease from spreading. We might not like them, we might consider them a result of fascist/communist/socialist conspiracy, but they do have some good reasons. Yes, the governments are currently in a panic mode. Still, they are simply afraid of being accused of not doing enough. If you are a politician, you simply do not want to have a health system collapse on your watch and people dying.

You convinced me, so what can I do protect myself and others? You might be (rightly or wrongly) distrusting governments and experts, but there is actually good advice out there. As the virus spreads through close contact between people or through touching surfaces, you should do your best to limit this. It might sound silly, but try to do (or not do) simple things. Do not shake hands, avoid large crowds, do not travel if you can avoid it (some governments make you do it anyway) and above all, wash hands. Make sure you strengthen your immunological system, so eat well, drink a lot of fluid.

What about face masks? You can see a lot of people wearing them, but the efficiency of the masks is actually minimal. They actually have two modes of action. Firstly, they filter what is going out and in doing so can actually be relatively efficient. So, if you are coughing or sneezing and absolutely have to go out, you can wear a mask to stop your viruses going out. The masks also are supposed to filter the incoming air and prevent the virus from reaching the person who wears them. For this, they are actually quite useless if not dangerous. Firstly, cheap masks do not stop viruses as they are not thick enough – remember that viruses are very tiny! Secondly, the mask must fully isolate the mouth and nose and so needs to be tightly fitted to the face. Any hole on a side, particularly if you wear a beard, is going to let the virus in. Thirdly, the mask actually collects germs on the outside material as you breathe in. So, when you take it off, you need to be very careful that the outer material does not touch your face. You also need to remember washing your hands very carefully after touching the mask. Needless to say, a mask used once should be disposed of correctly. On the other hand, washing hands or not going to the cinema does not cost much and is more effective.

Is my government doing enough/too much? You need to understand that a politician needs to carefully balance the pros and cons of any action they take, as the consequences might be massive. This means that they tend to either do nothing (President Trump before the 11th of March) or go into a full action (President Trump after the 11th of March). They will not want to be accused of needlessly spending money. Still, on the other hand, they do not want to see TV programmes about hundreds of people dying in hospitals. In fact, our own research shows that for people, there are two rational strategies, do nothing, or act with a full force. Economists call it a ‘bang-bang’ approach.  So, expect the governments to swing between different options as they face the biggest crisis since 2008.

I hope you find the above notes useful, please let me know if you have any comments or questions. A disclaimer: I am an epidemiological modeller (did I already lose you?), which means a scientist who uses mathematics, statistics and computers to understand how pests and bugs spread. 

As usual, if you have comments, please send them to me at info@statisticallyinsignificant.uk

Pi day (3/14)

Today is the Pi day, March 14th, i.e. 3/14 in the American notation. As a Mathematician and Statistician, it is difficult for me not to marvel about the ways in which special numbers like \pi appear in many different, apparently unrelated places in Maths, Stats and real life.

\pi is of course a ratio of a circle circumference and diameter.

The Wolfram’s Mathworld lists many different formulas, either infinite series or products, that produce the number \pi. I found some of these formulas amazing and some frankly bizzare. There is a part of my scientific background that is deeply rooted in Mathematics (thanks to my lecturers at the Jagiellonian University where I did my undergraduate and PhD studies) that causes me to stop and think, why:

\frac{2}{\pi}=\sqrt{\frac{1}{2}}\times \sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}} \times \sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}} \times\ldots

for example?

To me, there is an intrinsic beauty in such mathematical formulas, similar to art, e.g. Horse riders by Escher, or nature:

There is another, much more chaotic, side of \pi – the apparent unpredictability of its digits. \pi is supposedly a normal number in that if in its sequence of digits, all digits and all subsequences of digits are equally represented. Although it has not been proven that \pi is indeed normal, this property seems to be well supported. In other words, if I tell you that the fifth digit is 5, each of the 10 digits (0, 1, 2, …, 9) can come next and so I cannot really conclude that sixth digit is more likely to be 9 (3.14159…).

If we consider a ‘random’ walk governed by digits of \pi, i.e. at each time step a particle moving either to the left or to the right by how far the current digit is from the mean of 5:

  • if the digit is 3, move by 2 to the left;
  • if the digit is 1, move by 4 to the left;
  • if the digit is 4, move by 1 to the left;
  • if the digit is 5, move by 1 to the right;
  • if the digit is 9, move by 4 to the right;

we get the following graph:

which looks random!

I find it really amazing that there is so much to a humble number \pi and that it shows so much simplicity and at the same time so much complication, so much structure, and at the same time so much randomness and unpredictability.

If you want to see more information on the randomness aspects of \pi, please see the slides from my public lecture given at the University of Stirling in 2013. You can find it at SlideShare.

I better stop now, as it is time for lunch:

Broccoli picture by Jon Sullivan - http://pdphoto.org/PictureDetail.php?mat=pdef&pg=8232, Public Domain, https://commons.wikimedia.org/w/index.php?curid=95997