Rolling the COVID Dice in Ireland
Tags: Covid-19, Data Science, Ireland, Pandemic

Notice too that there are disproportionate benefits arising from deploying multiple mitigations, even if imperfectly. For example, deploying all 4 mitigation strategies, but with an effectiveness of just 85%, offers a CPF of 63, which cannot be achieved with just 1 or 2 mitigations no matter how perfectly they are deployed, and can only be beaten using 3 mitigations if they are perfectly deployed, and only then for a specific combination of 3 mitigations (HH, SD, MW).

It is important to put these CPF numbers into context. When we talk about a CPF of 100 we literally mean that our risk of infection is reduced by 100 times. To put it another way, with a CPF of 100 we are assuming the same risk over a 2 year period (100 weeks) as someone with no mitigations assumes over a single week.

The message should be clear: we should deploy as many mitigations as possible as consistently as possible. If we do we will be safe and our loved ones will be safer too. Think of it this way, we are in the worst heat-wave in more than a century, are you really planning to go the beach with the whole family, insisting on nothing more than a hastily applied layer of factor 5 sun-cream for everyone, or are you loading with the factor 50 and bringing a sun hat and umbrella too?

Conclusions

We know we are all exposed to some degree of infection risk with this virus but what is the level of risk? The daily readouts of confirmed cases don’t really help us to evaluate this, because the numbers go up and they go down, and we don’t have an intuitive sense of the relationship between 255 new cases today and the chances of coming into contact with an infected individual tomorrow.

When left to our own devices, some people perceive a greatly exaggerated level of risk, and may experience an inflated sense of fear and a lower quality of life as they react to this. Others may underestimate the risk and their actions, as a result, may be harmful to themselves and others. For this reason, we believe that the data on the virus should be communicated to the public, but the raw data should also be accompanied by some estimate of the level of realistic risk that exists, so that we can all calibrate our behaviours accordingly.

This article has described one approach for translating daily case numbers into the odds of coming into contact with an infected individual and into the probability that such a contact will lead to virus transmission. As usual there are lots of assumptions and lots of unknowns, so the estimates are, at best, crude estimates, but they should be good enough to help us to judge the level of risk that exists.

Today in ireland we have a certain probability of becoming infected over the next week but if we reduce our contacts, maintain good hand hygiene, keep a 2m distance from others, and wear our masks in public, and even if we don’t do all of this perfectly, we can still reduce this by a factor of 100 if not more!

Probabilistically, the bottom-line is that we can roll the COVID dice every single one of the 100 weeks or so until a vaccine has been safely created, tested, and fully deployed, hoping our number never comes up, or with a few precautions, we can roll the dice once. Oh, and by the way only the house can win this game: we don’t win when our number doesn’t come up, we only lose when it does. So why would anyone want to play such a rigged game more than they have to?

Regardless of what is happening with the virus, and no matter what other people do around us, we can choose to reduce our own risk significantly. And if we make this choice, and if others do too, then we will all reap the rewards that come with falling cases, just as we did in the summer.

We should aim for this over the coming months because it is the right thing to do, and because we know we can do it. After all we have done it before, and back then we were still learning on the job. Now that we know what is required, we should be able to do it without the on-the-job training-wheels that lockdowns had to provide. Remember, mitigations today avoid lockdowns tomorrow.

Addendum

One issue with the original version of this article was that it estimated the probability of infection over a one week period by scaling up 15 contacts per day to 105 contacts per week, so that the probabilities scaled accordingly; the weekly probability was estimated as 1 in 56 based on this. In retrospect this was not the best way to proceed, because it created the impression that these 105 weekly contacts were as unique as the 15 daily contacts, which they most certainly are not.

It is far more likely that we come into contact with similar groups of people each day so our 15 contacts per day might be 105 contacts per week but with 30–40 unique people. So why not compute the weekly probabilities based on 2x or 3x close contacts? Even then it is not that simple, because different clusters of close contacts may have different infection biases. Moroever, a given close contact might become infected at some later stage during the week, so shouldn’t treat them as a single contact event. In short, it is likely that the weekly probability of infection will increase more slowly than a simple scaling of daily probabilities would suggest, and it would make for an interesting data science project for someone to consider extending this approach to model this more precisely; that’s my way of saying, “this is left as an exercise for the interested reader.”

In the end, the approach taken here is to focus on daily probabilities, rather than weekly ones, which neatly side-steps these issues while remaining just as valid as the basis of the relative risk and CPF metrics that followed. And in any event none of the above changes the relative risk or the CPF calculations, since these are both are relative measures rather than absolute ones.