From ‘R0’ to ‘k’: Applying the 80/20 Rule Towards Tackling Covid19

Pop quiz: Which is more dangerous for the country? Option A, ten popular spots recording a few positive Covid-19 cases each or option B, a cluster with 30–40 pax infected?

Most Malaysians don’t see a difference. Most of us (at least the public, not sure about the government) react similarly to news of KLCC Suria being infected with one person as with news about three dozen being infected from some gathering in Kedah. In fact, some will even claim that multiple malls being infected is a worse-off situation than a cluster.

But I want to suggest today that Option B is way more important than Option A (and since our ‘emo’ reserves are limited, we should channel most of our concern towards clusters rather than the one-off case in a popular hotspot). This is relevant not just because our evaluations of the relative seriousness of any particular scenario affect the national ‘mood’ (and thus solutions) towards the pandemic, but because understanding why also helps shed light on many other areas in life.

So why is Option B more serious than Option A? Why should all of us, according to this view I’m presenting, be less concerned about 1–2 cases breaking out in Paradigm Mall than, say, the discovery of a new cluster in Tropicana Golf Resort?

Our present way of tracking the infectivity level of Covid19 is to use the by now popular R0 (pronounced R-naught). This measures the average number of new cases that one case will create. However, some researchers are now suggesting that the critical number we should be looking at is ‘k’ i.e. the measure of the virus’ dispersion.

In a particular country or location, is Covid19 spreading in small steady increments or in large sudden bursts? Almost every piece of research suggests that it’s the latter i.e. this virus does NOT follow some steady ‘straight-line’ path of progress. Instead it grows in unpredictable jumps and spurts.

Thing is, if you’re looking at ‘R0’ your focus will be on the average…and the average is always tied to linearity. Yes, you’ll get a ‘picture’ but that picture won’t fit reality very well. On the other hand, if you look at ‘k’, your attention will be on the variability and the extremes, which is precisely what the experts are saying the spread of Covid19 looks like.

Just like the famous Pareto Principle, a majority of infections are caused by a minority of spreaders. This is most obvious in the case of ‘Patient 31’ from South Korea who was the starting point of more than 5,000 cases in a megachurch cluster back in March. Closer to home, the Sivagangga case in Kedah shows us that a few individuals may carry with them high ‘viral loads’, even as Datuk Mohd Khairuddin Aman Razali’s case (however unjustly and unfairly) shows that not everyone who breaks quarantine will create a cluster (see Note 1).

Likewise, as everybody knows, the Sabah clusters have ramped up our daily national average; and why our government didn’t close off the airports much earlier is anybody’s guess. Instead, because we didn’t take the Sabah cluster less seriously as we should have (was it because the ‘average’ was still relatively low?), it has now led to movement control orders in KL and Selangor.

Super-spreaders vs Non-super dispersion

My personal view, in light of the damaging effects the lockdown had on the economy, is to tighten and enforce the rules instead of mandating lockdowns. This is especially pertinent given the damaging effects lockdowns have on people’s livelihoods. At the risk of sounding simplistic, just because a mall had one or two positive cases, that should NOT require closing it. Firm SOPs’, sanitization, absolute social distancing and mask-wearing should suffice.

I know it’s almost impossible to remove the feeling of fear if you discover Mall A had one positive case but, logically, why would you feel safer in Mall B with no reported positive cases? Are you sure the chances of being infected in Mall A are ‘lower’? In fact, if Mall A is being sanitized and everyone’s taking extra precaution and suddenly crowds are much smaller, shouldn’t Mall A be a safer place than Mall B (to which more people may go to instead of Mall A!)?

A cluster, on the other hand, is already by definition a runaway train.

More and more people have already become infected, leading to a very strong likelihood of an outbreak. It would seem clear to me that the government should channel the bulk of their resources towards battling a cluster. Lockdowns and barricades should be used on super-spreader events; for ‘non-supe’ incidents, stricter SOPS’ and enforced rules, with some fortune, should result in lower or even zero numbers within a few days (eg, a majority of those mall incidents did not lead to new clusters).

Again, we must treat the ‘majority’ 80% (clusters) different from the way we handle the minority 20% (one-off positive cases).

I’m not an expert but I believe I’m echoing what many experts around the world are saying (check out the articles in the ‘Further Reading’ list below). I’ve also done a brief comparison of ‘R0’ vs ‘k’ solutions. Whilst Malaysia’s methods certainly overlap, there are nevertheless some differences if we address the pandemic with ‘R0’ in mind as compared to thinking about ‘k’.

I wouldn’t pretend to be able to say anything new to the Ministry of Health regarding how to handle our country’s pandemic situation. I’m just somewhat concerned that googling turns up not a single instance of ‘k’ being discussed by Health Director-General Datuk Dr Noor Hisham Abdullah nor the Ministry of Health (see Note 2). Thus, I hope this piece generates more conversation about the relative importance of the unequal spread of the virus vis-à-vis the daily ‘positive cases’ everyone receives in WhatsApp around 6pm.

Like much of life itself, Covid19 comes at us with a high degree of randomness. It’s almost like guerilla warfare. Needless to say, when we fight unpredictable insurgents — who don’t fight according to a fixed schedule — we need to reduce one-size-fits-all approaches and start being, well, creative?

Note 1: To be very clear here, like almost every Malaysian, I am incensed that political leaders can break SOPs’ with impunity. What Khairuddin did cannot be justified. The point of this article, though, is that thankfully not all irresponsible behavior produces disastrous consequences.

Note 2: My googling turned up just one result in which the ‘k’ indicator was discussed within the Malaysian context. It’s an article by two paediatricians, Dr Musa Mohd Nordin and Dr Husna Musa from early October and it makes essentially the same argument I’m making here (albeit with more technical finesse).

Further Reading

Adam, D.C., Wu, P., Wong, J.Y. et al. Clustering and superspreading potential of SARS-CoV-2 infections in Hong Kong. Nat Med (2020). https://doi.org/10.1038/s41591-020-1092-0

Endo, A., Centre for the Mathematical Modelling of Infectious Diseases COVID-19 Working Group, Abbott, S., Kucharski, A. J., & Funk, S. (2020). Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China https://doi.org/10.12688/wellcomeopenres.15842.3

Hartfield, M., & Alizon, S. (2013). Introducing the outbreak threshold in epidemiology. PLoS pathogens, 9(6), e1003277. https://doi.org/10.1371/journal.ppat.1003277

Kurchaski, A. (2020) The Rules of Contagion: Why Things Spread and Why They Stop, London: Wellcome Collection

Lloyd-Smith, J., Schreiber, S., Kopp, P. et al. Superspreading and the effect of individual variation on disease emergence. Nature 438, 355–359 (2005). https://doi.org/10.1038/nature04153

Edu-trainer, Žižek studies, amateur theologian, columnist.