Coronavirus: A Personal Risk Assessment
One issue that almost everyone seems to be struggling with right now is deciding how concerned to be over the risk posed by the coronavirus.
How worried should you be? You will have heard how thousands of people have been infected in many countries, with the global total running into the hundreds of thousands. But with this number changing so rapidly, it can be challenging to weigh up the risks posed to yourself and to others around you. If there are ten times more cases in your country than there were last week, should I be ten times more scared?
Disclaimer: I’m a statistician. I’m not a virologist or an epidemiologist. In terms of actions, my recommendation is simply to pay attention to the advice being offered by experts in public health (and ignore anyone else). The aim of this article is to help you understand why you are being asked to take these actions, and why you should be carrying out these actions without undue concern.
Daily risks
One of the difficulties we face when attempting to rationalise risks is we often end up talking about very large numbers which are hard to keep in perspective: the numbers involved can run into the hundreds, thousands, and millions. To make the numbers easier, we’re only going to talk in terms of numbers of dice.
Imagine throwing a handful of dice. What are the chances that they all land on a six? If you have two dice in your hand, the chance of that happening is just one in 36, or 2.8%. If we roll more dice at the same time, the numbers rise very quickly. If we have six dice, the chance of rolling six ‘6’s is a little over one in 50,000. I will refer to risk levels in terms such as this: ‘two-dice risk’ and ‘six-dice risk’. Notice that a risk of throwing six dice is much lower, and hence safer, than when throwing just two. The more dice you have in your hand, the safer you become.
Every day of our lives we expose ourselves to some degree of risk. That’s inevitable and unavoidable. But it would be futile and counterproductive to sit around and worry about tiny risks. Every task you can think of carries some risk. Most tasks — such as commuting to work — lie below our threshold of acceptable risk. They are considered safe enough that we will go ahead with it without any significant concern — (although we still ought to take sensible precautions such as putting on a seat belt when you enter a car). How high are these daily risks? Some examples of risks most of us take for granted include:
Flying. Taking a commercial air flight exposes yourself to a 9-dice risk. That’s an incredibly small probability, at around ten million to one. Yet many of us develop a fear a of flying at some point in our lives. It’s a good illustration of how hard it can be to maintain a rational assessment of the risks involved. [source]
Driving. If you travel one hundred kilometres by car, then you expose yourself to a nine-dice risk. Again, on it’s own it is tiny. But if you were to do this journey each weekday over the course of a year, this cumulative risk works out at the equivalent of throwing six dice. [source]
Canoeing. If you enjoy canoeing, you are typically exposed to a risk equivalent to throwing six dice each year. [source]
Drinking or smoking. If you are a moderate drinker or smoker, you are slightly increasing your chances of developing conditions such as heart disease and cancer. Over the course of each year, this typically puts your life at risk with six dice. For heavy smokers and drinkers, this risk becomes stronger, so they are playing with fewer dice. [source ]
Personal risk associated with COVID-19
All activities carry some amount of risk, a risk that we can count in terms of the number of dice. The more dice you hold in your hand, the lower the risk. So when it comes to the coronavirus, how many dice do you hold at the moment? To answer that question, we can break the sources of risk down into two parts: (1) the risk of catching the virus, (2) the risks once someone has the virus. The total risk can then be found by adding the dice from each part. For example, if each of these parts is a three-dice risk, then the total risk is six-dice.
Risk of catching the virus
The risk of you catching the coronavirus partly depends upon your behaviour, and partly on your environment: how many sick people are in your vicinity. This environmental risk varies from region to region, from country to country, and from one week to the next.
At the very early stages, when the virus is first beginning to spread through a country, then perhaps only one in ten million people catch the virus each day. This means that if you go about your daily life as usual, you face a nine-dice risk each day, just for catching the virus. That’s an incredibly low risk. However, if the virus spreads in an uncontrolled manner, the pace of infection increases. At week 1 (defined by the infection rate of one in ten million people catching it per day) then you started with nine dice in hand. But in week 2, the virus has spread to roughly six times as many people compared to the week before (a rate seen in many countries), so you would then have eight dice. In week 3 you have seven, and by week 4 you would have only six. Remember, a six-dice risk is still very low, not something people tend to worry about. But if the virus continues to spread, then by week 6, you would potentially be facing a four-dice risk. This would mean that around one in 1,300 people are contracting it each day. For a country the size of the United Kingdom or Italy, that would be over 40,000 new infections each day.
How many infections per day are happening in your country right now? The real number is tricky to pin down, especially if your country is not performing extensive testing like South Korea. We can use the number of deaths per day, rather than cases per day, as a slightly more reliable indicator. There is quite a significant lag between infection and death, so the death rate in your country is telling you the infection rate from about two weeks ago. But even if spreading at its fastest, we can put an upper limit on how many infections could be occurring today.
When will a country hit the daily four-dice level? Where cases are rising in an uncontrolled manner, that point is when a country rises above one death per million people per day. Italy hit that point on March 8th — the day before the country went into quarantine. [They only recorded 1,492 new cases that day, but (a) there is a substantial delay between infection and diagnosis, largely due to the incubation period of the virus and (b) many less severe cases are never tested]. Statistics for other countries can be found here.
The UK will hit an equivalent point when it breaches 66 deaths per day, and the USA will hit the four-dice level when it reaches 327 deaths per day. If no action is taken, the risk will increase to three-dice the following week: odds of just 200 to 1. However it seems likely that stricter measures will be imposed before a country reaches that point. Once a country enacts a lockdown on their population the infection rate begins to fall, and so the associated risk falls with it. You will find that the dice in your hand gradually begin to replenish. [source]
Risks after infection
Sometimes, when someone catches the virus, they may not develop any illness at all. If they do develop symptoms, then in most cases, they will recover within a few days. A small proportion of people die from complications. The risks of fatality suggests that for those that are under 18, the risk is around one in twenty thousand. That’s a five-dice risk. For those in their thirties, it’s four-dice risk, and for those in their sixties it’s a two-dice risk [source]. These figures may improve over time with the arrival of better treatments such as antivirals.
Many younger people are less concerned about their own well-being, and are more concerned about the possibility of passing on the virus to someone more vulnerable than themselves. So if we include that risk — the risk of passing it on to someone older — then in a sense, everyone’s risk after infection can be thought of as a two-dice risk. That is roughly the chance that an infection will lead to a fatality (either the person who catches it, or a person they immediately pass it on to).
If the risk after infection is represented by two dice, and your risk of catching the virus is (say) five dice (depending on your country’s current situation), what do these two risks mean in combination? To find the total risk, we simply need to add the two sets of dice together. So for example, Italy on the day of its lockdown was a four-dice risk of infection. Now we need to combine those dice with the two-dice risk from infection. So overall, a typical Italian was subject to a six-dice risk in one day. That’s still a very small probability, but marginally higher than most other daily risks we face.
Mitigating the risks
Once a country reaches a four-dice level (which means one thousand people being infected each day per million in the population), the coronavirus still poses a small risk to any one individual, but it has crept above other daily tasks. And if left unchecked, the risk will rise even further the following week. These risks have understandably caused many people some degree of worry and concern. But you can reduce your own personal risk. By reducing your contact with other people, you can reduce your chances of infection. If you change your lifestyle such that you come into contact with ten times fewer people each day, then your risk falls by a factor of ten. Frequently washing your hands will also reduce your risk of catching the virus. By reducing your risks in this way, you can earn yourself extra dice.
If you are worried about transmission, the good news is that social distancing is even more effective than you might think. As you reduce your human contact, the risk of catching the coronavirus falls. At the same time, the risk of passing on the coronavirus falls with it. What this means is that if you make a ten-fold reduction in human contact — for example coming into contact with only ten people per week instead of one hundred — you are making a hundred-fold reduction in your risk of acting as an intermediary.
With these extra dice that can be gained from social distancing, it is possible for anyone to reduce their overall risk to at least the six-dice level. Provided you adhere to the measures recommended by public health experts, your overall coronavirus risk level can be kept manageable even at the height of an outbreak. In fact, the long term risk you face need not be any higher than it is for many other everyday activities.
Most of us regularly take these ‘six-dice’ risks without any concern at all. By being in control of your level of risk, you can take precautionary steps without being unduly worried and stressed about the possible consequences. Much like putting on a seat belt when you enter a car.
Isolation Risk
You might ask — why take any unnecessary risks with the virus at all? Why don’t we all just confine ourselves to our homes?
There is a source of risk that has received relatively little attention, compared to the direct risk from the virus, and that is the risk associated with social isolation. The adverse effects of prolonged periods of social isolation have already been well studied. Essentially, if you are isolated, you are at increased risk of developing health problems, such as a stroke, cancer, heart disease, or dementia. Another factor is your diet may also suffer if you live off long-lived foods instead of frequently travelling to the shops to pick up fresh fruit and vegetables.
How big is this risk? How many dice are you throwing when you stay in lockdown? According to an analysis led by Julianne Holt-Lunstad in 2015, a lack of social connection raises health risks as much as smoking 15 cigarettes a day. This suggests the annual risk imposed by isolation could be as high as four-dice for many people, especially the elderly. An annual four-dice risk is equivalent to taking a seven-dice risk each day.
The negative impact of isolation on public health will be much more prolonged, and much harder to measure than the pandemic of COVID-19. Yet it will be just as real. During the very early stages of the spread of the virus, the risk of infection is so low that the risks associated with social isolation is very much higher than the threat from the virus itself. In fact, the virus’ threat to public health only significantly exceeds the threat posed by isolation once it has become as widespread as it was when Italy went into lockdown. It would therefore not be surprising if many other countries chose to follow a similar path. The progression of the virus in the UK is around two weeks behind Italy, so this point will probably be hit by around March 23 (although this relatively high infection rate will not be immediately visible in hospitals).
It may be possible to mitigate the risks from the virus and isolation at the same time. The adoption of ‘social rationing’ might be sufficient to prevent the spread of the virus spread , while allowing enough human contact to stave off the worst consequences of isolation. This would involve greatly reducing our social contact, but not eliminating it. How much would we have to reduce our contact? If we can reduce the number of people we come into contact with, down to perhaps one quarter of what we are used to, then overall transmission of the virus would potentially be reduced by a factor of 16. Whether such restrictions would be adhered to, or can be enforced, is a different matter.
Summary
This article is not intended to guide your actions or behaviours — that is the responsibility of public health experts. The intention of this article is to demystify the risks posed by the coronavirus. By better understanding the risk levels we face, my hope is that the recommended precautionary measures (such as social distancing and frequent hand washing) can be carried out without unwarranted levels of concern.
Following public health guidelines can keep you well within a comfortable level of risk. Conversely, if you ignore these recommendations when the infection rate in your country is high — which is indicated by having more than one recorded death per million people per day — then you may be taking a risk that is substantially greater than any other activity you do.
