The pareto principle and stochasticity in COVID-19

Most of you know difference between parameters such as mean and standard deviation. Or, that distributions have variable dispersion or multi-modalities. Standard stuff.

In relation to COVID-19 it was clear early on that “superspreader events” were critical. That in fact, these events were driving the pandemic in some deep way, with there being huge variance in the number of people individuals have spread the disease to if they were infected.

Readers of this weblog will not be intimidated by a word like kurtosis. But it is different for readers of The Atlantic, notwithstanding the fact that they have the pleasure of imbibing the deep insights of America’s foremost public intellectual, Dr. Ibram X. Kendi. But rather than the august Dr. Kendi, I want to point you to Zeynep Tufekci, now at The Atlantic, but originally hired by The New York Times in March of 2015. Her piece, This Overlooked Variable Is the Key to the Pandemic, is probably what you should share with less statistically literate members of your family.

Tufekci’s piece is strewn with gems of fact. For example, ~70% of people infected with COVID-19 may not transmit it to anyone else, even if the mean number of transmissions is closer to 3 individuals. The explanation of what’s going on is that like many social science phenomena, but unlike influenza, the spreading of COVID-19 occurs through a minority of big transmitters. That is, it follows a power-law distribution and adheres to the Pareto principle.

Last spring I read that Japan was focused on super-spreader events, and was somewhat skeptical of this strategy. How could they identify superspreader events? Well, it turns out that these events tend to adhere to some necessary, though not sufficient, conditions. Large crowds, enclosed spaces, and poor ventilation. But, Tufekci also points out that superspreader events occur stochastically. Not all, or even most, instances, where conditions are met, will produce an outbreak. Some will. This is not surprising, but as she admits in the piece it’s a really difficult thing for people to accept and internalize. Sometimes we can’t always ascertain a specific cause. Stuff just happens.

Anyway, pass the piece on to your relatives and friends.

Using 23andMe/Ancestry/Family Tree DNA to identify risk allele for respiratory failure with COVID-19

Several people have asked about the risk haplotype in the post below. If you have been genotyped on Ancestry, 23andMe, and Family Tree DNA (unless you are on 23andMe after summer of 2017) there is one SNP in high LD with the causal variant you can look up. It’s rs10490770. The risk allele is C and non-risk allele T. If you download the raw data from any of these services you can find rs10490770 with a search, and look for your genotype (if by some chance it is a reverse strand, the risk allele may actually be G and the non-risk allele A).

What does risk vs. non-risk mean? You can read the original paper, Genomewide Association Study of Severe Covid-19 with Respiratory Failure. They say: “We identified a 3p21.31 gene cluster as a genetic susceptibility locus in patients with Covid-19 with respiratory failure and confirmed a potential involvement of the ABO blood-group system…”

It looks like in their sample CT = 1.75 times greater chance of severe respiratory problems, and CC = 3 times greater chance. The frequency is ~10% or less in Western Europeans, so very few people are CC (~1%). But in South Asians the risk allele is 30-40%, which means that 10-15% of people have the CC genotype!

Here are the results. Focus on rs11385942 at locus 3p21.31 (the top one):

Living in a time of COVID-19

We’ve come really far over the past month or so in relation to coronavirus. There are lots of resources online and people should be making recourse to them. medRxiv and bioRxiv are great. If I were you, I would at least read the Report of the WHO-China Joint Mission on Coronavirus Disease 2019 (COVID-19). But, please read everything with skepticism and a grain of salt.

I’ve been “monitoring the situation” since January…with alarm beginning in the first week of February. My own family’s actions have moved from “social distancing” to isolation. Work-from-home, cancellation of playdates, and keeping children out of the schools. All of these actions exhibit guesswork and decision-making on incomplete information. In the WHO-China report, they note that “people interviewed by the Joint Mission Team could not recall episodes in which transmission occurred from a child to an adult.” And yet children do seem to shed RNA after infection, and many experts do think they can transmit.

Unless you’ve been sleeping under a rock, you’ve seen this table:

AGE
DEATH RATE
confirmed cases
DEATH RATE
all cases
80+ years old
21.9%
14.8%
70-79 years old
8.0%
60-69 years old
3.6%
50-59 years old
1.3%
40-49 years old
0.4%
30-39 years old
0.2%
20-29 years old
0.2%
10-19 years old
0.2%
0-9 years old
no fatalities

 

But strangely many older people I know did not know about the age profiles of the fatalities. Many people are promoting the idea that this is as risky as a bad flu season. This is wrong. The case fatality rate for flu pandemics seems to be in the ~0.1% range. The initial case fatality rates for coronavirus seems to be closer to 1%, though I assume that we can drive that down some. But, I have a hard time imagining that it will be as low as the flu. With its spread, with R0 going above 1, one can imagine a large proportion of the population being infected in the United States, resulting in hundreds of thousands of deaths. And yet many people are complacent, going on vacations and not altering their behavior in any manner.

After spending a fair amount of time reading papers and data I think there will be some patterns that will play out.

  • Age is a huge factor. Therefore, societies which are very young-skewing will probably not see the chaos and suffering that societies with many older people (China and Italy) will experience.
  • There are mixed reports from the analysis of spread in regards to temperature and humidity. But I suspect that on the margin there will be some effect of warmer temperatures, though please remember that many of these pandemics with seasonal patterns come back in waves in subsequent years.
  • Men seem to be more susceptible than women, and most definitely to dying from the disease. One of the preprints I read shows that boys are more likely to be infected than girls. This rules out, to me, smoking as driving the sex difference. Please note that the ACE2 gene which is responsible for the receptor in which coronavirus targets is on the X chromosome.
  • I assume there is some difference between ethnic groups, and if there is some difference East Asians are possibly more vulnerable since it was selected in that population first. We won’t know for a long time yet, and Whatsapp chains arguing there is an “African gene” or “Indian gene” which is protective are clearly misguided (the one paper I saw which looked at allele frequency differences showed a fair amount of overlap between populations).

There are lots of people with lots of information. You make your own decisions. Until the government makes it for you. But, I have to say that one thing that is really disturbing is the message out of Fox News and its penumbra of pundits that people are trying to create a panic to destroy the economy and undermine the Donald Trump. I have been having discussions with Right-leaning people since January about the virus, and most of us have been getting progressively more alarmed by the week. It is true that some people see a political opportunity in the crisis, but this is not a manufactured pandemic, and it will have a massive impact on life and liberty in this country. The median age of the Fox News viewer is 65. Many of the people who are being told that this is just like a bad flu season are the highest risk of dying. I am pretty sure that people in my orbit will die unexpectedly within the next 3 months of coronavirus.

Michael Brendan Dougherty writes in National Review, I Fear the Coronavirus. He says that people have told him “It’s just like the flu, but not as bad.” I hope that these people are correct, but I’m 99.9% they are wrong.

Meanwhile, certain groups of liberal intellectuals seem to periodically become more focused on anti-Asian racism, or see the virus as an opportunity to make fun of enemies.

My own take is that we’ll have time for culture wars after the suffering and deaths of the next few months. Let’s pause on that for a moment.

Anyway, I’ll let readers leave their comments here.

Of Plagues and Prehistory

The Fate of Rome: Climate, Disease, and the End of an Empire is an excellent book. I highly recommend it! But one of its assertions, which I accepted at face value at the time I read it, now seems to be less certain (likely wrong). The author contends that the network of trade and interaction facilitated by the emergence of the Pax Romana was instrumental in the rise of periodic pandemics. There was the Antonine Plague, the Plague of Cyprian, and the Plague of Justinian. In contrast, Neolithic Europe, and earlier civilizations may have been subject to endemic diseases. But not pandemics.

A new paper in Cell seems to falsify this view. Emergence and Spread of Basal Lineages of Yersinia pestis during the Neolithic Decline:

Between 5,000 and 6,000 years ago, many Neolithic societies declined throughout western Eurasia due to a combination of factors that are still largely debated. Here, we report the discovery and genome reconstruction of Yersinia pestis, the etiological agent of plague, in Neolithic farmers in Sweden, pre-dating and basal to all modern and ancient known strains of this pathogen. We investigated the history of this strain by combining phylogenetic and molecular clock analyses of the bacterial genome, detailed archaeological information, and genomic analyses from infected individuals and hundreds of ancient human samples across Eurasia. These analyses revealed that multiple and independent lineages of Y. pestis branched and expanded across Eurasia during the Neolithic decline, spreading most likely through early trade networks rather than massive human migrations. Our results are consistent with the existence of a prehistoric plague pandemic that likely contributed to the decay of Neolithic populations in Europe.

The plot to the right shows that Yersinia pestis in Swedish Neolithic farmers, who are genetically similar to modern Sardinians, is basal to the Yersinia pestis in Bronze Age steppe pastoralists, which is basal to later outbreak strains. The point here is that Yersinia pestis seems to a dynamic part of the broader Eurasian pathogenic landscape. The Plague of Justinian was not something new, but the latest manifestation of a reoccurring phenomena. The conditions for its flourishing existed before the rise of Rome.

What was probably different in the case of the Roman Empire was a matter of frequency and rapidity. As the paper, and David of the Eurogenes blog note, there was a massive demographic and social regression in late Neolithic Europe. It is hard to disentangle the variables though because they are all connected. When you read the impact that plague had in the New World on native societies, one of the key elements is that societies on the Malthusian margin often collapse when mortalities go above expectation. Crops go unharvested, and people have to tie up their labor in taking care of the ill. This leads to malnutrition and further susceptibility to the plague.

Or, you can imagine a system where a warm and rainy climatic regime increases primary productivity (e.g., medieval climatic optimum), which leads to greater population density and therefore specialization and economic activity and trade. Then, you might be subject to a climatic shift, in which case productivity drops, and famine ensues. This famine results in increased susceptibility to disease, and plague spreads through the preexistent trade networks established during times of plenty.

The decline is partially endogenous to the system of human societies. External climatic shocks are going to happen now and then. But there are internal dynamics, such as population density, which are going to impact how resilient a society is to an external shock.

It seems likely that the first dense agglomerations of humans were likely going to run up against the limits scale no matter what. Disease serves as a natural Malthusian check, and it was likely inevitable due to the vicissitudes of the circumstances that there would be spikes in mortality so that the population was reduced back to its carrying capacity.

This is a general point. Early societies were subject to random shocks, and those shocks knocked them down a peg for quite some time. But eventually social systems became less fragile, and total collapse and cultural amnesia was generally avoided. The socio-economic complexity of the Roman Empire declined precipitously in the 5th century, with the post-Roman world having to slowly wind itself back up during the “High Middle Ages” (in Western Europe at least). But the ideological superstructure of the Roman world, Christianity and such, maintained an intellectual and cultural continuity, so that Roman institutions and forms could be resurrected when social and economic complexity necessitated it (e.g., Roman civil law). The post-Roman Europeans were primitive in many ways compared to Rome, but their society had not be totally obliterated, so they did not have to reinvent the wheel, so to speak.

More specifically in this instance, it seems that the arrival of the Eurasian agro-pastoralists in the third millennium BC into Northern Europe was not due to their inadvertent biological weaponry. The diseases they brought. The Neolithic societies descended from those who introduced farming were already in collapse, and likely very vulnerable to the predations of agro-pastoralists. This is almost certainly a common event in prehistory, which we will become much more aware of in the near future due to science. For example, I predict pestilence will be associated with the end of the Uruk Period in the Near East.