You are the weakest link!
Tags: Overdispersion, Ireland, Covid 19, Lockdown

It is true that prevalence was >3x higher on October 18 (median prevalence was 281 compared with 82 cases per 100k on October 5) because there was plenty of transmission happing during Level 3. However, by October 18 transmission rates had fallen in more than 80% of counties, compared to the start of Level 3. On October 7, 61% of counties (16 counties) were in the top-right quadrant (high and growing transmission) but by October 17 only 26% of counties (7 counties) remained in this quadrant, and most of these were on the right trajectory to get them to the lower-left quadrant, eventually.

County Cavan is a good example to highlight. Back on October 7 it had a prevalence of 155 cases per 100k and it was registering very high transmission ratio values (~0.6) that were growing quickly. Sure enough these transmission rates drove prevalence to 993 per 100k by October 18, but fortunately, by then, its transmission ratio had fallen from 0.6 to just over 0.1 and it was continuing to fall.

Why we couldn’t stay in Level 3?

If these data show us that Level 3 was working, then why did we need to move to Level 5? Although the data show that transmission rates were mostly falling, there were still some counties that were bucking this trend, or where improvements were much slower to materialise. By October 18 only two counties (Donegal and Clare) had make it to the lower-left quadrant, for example, which is necessary for case numbers and prevalence to begin to fall.

But surely with a bit more time, falling transmission rates would have brought the remaining counties into this lower-left quadrant? Perhaps, but one of the early contradictory signs came from Dublin. In this graph we see the transmission ratio for Dublin after its early Level 3+ started on September 18. Although the transmission ratio fell during the last week of September, it grew steadily during the first 10 days of October, thereby undoing the Level 3+ gains that had been made. The fact that transmission rates were able to increase, despite Level 3+, suggests that the restrictions were not sufficient to produce the type of sustained behaviour changes that were needed to control case numbers. And if this could happen in Dublin then there was a risk it would happen elsewhere too.

The good news is that when we moved from Level 3 to Level 5 most counties were moving in the right direction, with falling transmission rates. This means that we entered Level 5, not from a standing-start, but with some significant positive momentum.

What are the implications for Level 5?

It’s important to realise that the limited efficacy of Level 3 is not a criticism of its restrictions per se. After all, the various levels are simply an effort to nudge us into a pattern of behaviour that limits virus transmission. When we conclude that Level 3’s nudge didn’t work, what we really is that we did not change our behaviours sufficiently. In other words, it is more accurate to say that we failed Level 3, than it is to say, Level 3 failed us!

Now, if Level 3 was a nudge, then Level 5 is a hard shove in the back! And many of us have treated it as such, none too happy about it but recognising that if we resist it, then it too will prove to be ineffective, and we will quickly run out of road. Let’s face it, nobody wants to be in Level 5 — nobody — but the fastest way to exit it is to do what we are being asked to do, as if our lives and livelihoods depended on it, which, of course, they do.

The problem is that most of us can’t imagine doing more than we already have been doing, and it is not surprising, therefore, that the move to Level 5 has been met with a sense of exasperation and frustration. It just seems wrong that we have to be in full lockdown when, by all accounts, the majority of us have greatly limited our social contacts and have been staying put as asked. If we do have to go out, then we keep our distance. And if we can’t keep our distance, then we always wear a mask. In fact, most of us will say we have been doing this for many weeks if not months, so why then are we in a second wave of the virus? If most people are doing what has been asked of them then why are cases still growing? And is a Level 5 lockdown really the only answer?

Overdispersion & the Unevenness of Transmission

One of the reasons that cases continue to grow, despite our best efforts, may have to do with an important characteristic of this virus, which has serious implications for how things are likely to unfold. It isn’t just that this virus is highly transmissible, it is that the transmission turns out to be extremely uneven n the way it transmits. Let’s discuss what this means, why it matters, and how we can take advantage of it.

Seasonal influenza is an equal-opportunity transmitter, in the sense that its transmission is evenly spread across a population of susceptible individuals. The median R number for seasonal influenza is 1.28 — remember R is the average number of people than an infected individual goes on to infect — and because influenza transmission is so even this means that most people go on to infect 1 or maybe 2 others.

The first indications that SARS-CoV-2 was different came from the so-called super-spreading events, which can significantly accelerate transmission in certain settings. For example, we have seen this effect in our own nursing homes and meatpacking plants, and, elsewhere, returning college students, protests, and political rallies have also proved to be rather excellent amplifiers of this virus. These super-spreading events are characterised by an explosive growth in the number of transmissions that is far more than we might expect from SARS-CoV-2 given that its R number is about 2–3.

There are many reasons why some people (or settings) might be responsible for more transmission than others, at least some of the time: an infectious individual might have a high viral load; or they might cough more or wear their mask incorrectly, if at all; they might be more sociable; or they might work in a less well ventilated office; they might be asymptomatic or unable or unwilling to isolate; or maybe they sing in a choir and their weekly practice takes place in a constrained, indoor space. The point is that the transmission of SARS-CoV-2 is especially sensitive to a host of biological, behavioural, and environmental factors to produce very uneven transmission characteristics, which can be measured.

This phenomenon is known as overdispersion and epidemiologists measure it using the fraction of individuals who are responsible for 80% of cases, indicated by k. The k-value for seasonal influenza is thought to be about 1, which corresponds to a even transmission pattern, but k for SARS-CoV-2 is estimated to be much lower, approximately 0.1, which means that about 10% of people are responsible for 80% of cases.

This means that the R number is not telling us the full story about SARS-CoV-2 transmission, because if 10% of people are responsible for 80% of cases, then some individuals must be infecting lots of people, while most others are infecting far fewer. The R number is useful for understanding the trajectory of transmission, but because it is an average it hides the unevenness of SARS-CoV-2 transmission.

This has some very important implications for how we might think about SARS-CoV-2 and how we might do a better job of controlling its spread, but first let’s get one thing straight: if 10% of people produce 80% of cases then this does not mean that just because 90% of people account for only 20% transmissions, then most of us don’t need to worry about transmitting the virus. For a start we have no way of telling whether we are in the 10% or the 90% — and it’s probably as much about the setting as it is about the individual anyway — and if 90% of people drop their guard then this would provide even more transmission opportunities and cases will grow even faster.

Why does overdispersion matter?

First, the good news. A low k-value means that most infections will fail to produce a transmission chain. For example, only 19% of virus imports into New Zealand resulted in more than one new infection. In other words, most imports produced either no new infections or just one new infection, instead of the 2–3 average infections that R predicts. Thus overdispersion actually helped to slow the spread of the virus and stop it taking hold.

However, when transmission does take hold, then overdispersion can lead to an explosion of new cases, which far exceeds what might be expected based on R. This is exemplified by the recently reported case of an individual returning home from a trip overseas, who failed to restrict his movements, per HSE guidelines, and went on to infect 56 others (directly or indirectly), but even this pales in comparison to the cluster of more than 1,900 South Korean cases traced back to only 6 identified cases. Thus, once clusters do emerge overdispersion can very quickly expand their reach.

This uneveness of SARS-CoV-2 transmission may change the way that we think about controlling the virus in at least two important respects. Up until now the focus has been on R, and the messaging has been about getting the majority of people to do what they can to limit transmission. From time to time there have been some very public examples of groups ignoring the recommendations — and most of us can see smaller examples of this in our own locales — but I think it is fair to say that the official line has been that these isolated incidents, while frustrating to see, will not have a big impact on cases. But that may not be true if 10% of people produce 80% of cases.

In other words, while it is necessary for the vast majority of people to follow the regulations, this is not sufficient to control transmission, because the minority that don’t follow the regulations can produce a disproprotionate number of infections. This minority is the weakest link in our defence against transmission and it means that we can no longer afford to simply lament this non-compliant minority, in the hope that the good behaviour of the majority will make up for their indiscretions. Indeed, perhaps this is why we find ourselves in a second wave and a Level 5 lockdown today, even though most of us feel sure that we have been following the guidance to the letter for months now. It also means that although the brute-force nature of Level 5 will go a long way to suppressing transmission, transmission will rebound when we exit in December even if most of us continue to act responsibly, as long as there are a few who don’t.

This uneveness of SARS-CoV-2 transmission also has important implications for contact tracing. When a new case is discovered — the index case — the contact tracing process starts by obtaining the close contacts of the index case via interviews and/or digital traces etc. Conventional (forward) contract tracing usually targets downstream individuals. These are people who may have been infected by the index case; those who have been in contact with the index case after the index case became infectious (usually 2 days before symptom onset for COVID-19). However, because SARS-CoV-2 has a low k-value, it means that most cases don’t go on to infect many others, thereby limiting the ability of forward contact tracing to identify and avert future infections. Forward tracing, we will tend to find an average of R new cases for each index case, since R is defined to be precisely the number of new infections from a typical case.

The alternative is so-called backward contact tracing, which seeks to identify the upstream primary case (or setting) that led to the index infection. This means retracing the close contacts of the index case up to two weeks before the point of likely infection and recent studies suggest that this will lead to a primary case that generates 3–10x more infections than average, and a 2–3x increase in the proportion of cases averted.

It is not clear whether we are doing forward or backward contact tracing in Ireland. Given the recent stresses on the system I fear that it is the former, at best, which means we may be missing many cases that could be detected or averted. Moreover, the lesson from other countries is that comprehensive contact tracing is the cornerstone of any successful strategy for dealing with this virus. When we come out of Level 5, we will have much lower levels of prevalence and this presents a unique and ideal an opportunity for contact tracing to get on top of new infections, but this will only be effective if we take full advantage of the overdispersion characteristics of this virus.

Conclusions & Recommendations

Let’s suppose that Level 5 works and we get to a rate of transmission that is low enough for us to return to some semblance of normality before Christmas. Currently we don’t appear to have a plan for what happens next; a plan to bounce in and out of Level 5 is no plan at all. We are told that Level 5 will allow us to celebrate Christmas in a responsible, socially distanced way but isn’t it more likely that, after being cooped up for 6 weeks, many will lower their guards and embrace the season that’s in it? Then we will surely bounce ourselves right back into Level 5 soon after. Not to mention the potentially lethal consequences for the grandparents and the elderly who are visited upon by well-intentioned families who believe it is safe to celebrate with their loved ones because Level 5 will have successfully stopped transmission.

I don’t usually go so far as to make suggestions for what should be done in these posts. After all, what do I know. I have no public health expertise and no medical training. I’m just a data guy. But sometimes the data can shed light on possible solutions…and given the uncertainty that lies ahead here are my suggestions, for what they are worth: