As the readers of my blog know, the opinions I express here are strictly non-partisan and non-ideological. My main interest is to go where science leads. Ideological thinking is different from science in that in science data triumphs over theories. Ideologues, on the other hand, can ignore or twist facts to suit their theoretical predispositions (see, for example, An Anarchist View of Human Social Evolution).

But it doesn’t mean that everything coming from an ideological camp is wrong. Take Marxism. I realize that it is now used in certain quarters as a label for “bad people”, but here I mean by it just the philosophical ideas of Karl Marx, Friedrich Engels, and their followers.

My own attitudes towards it went through quite wild swings over my life time. I grew up in the Soviet Union, where I was force-fed Marxism in school, so I took a very dim view of the ideas of Marx and Engels. But when I switched from studying ecology to human societies, I realized that there were interesting and valid ideas in Marx’s theory. The main problem for Marx and Engels, I now tend to think, was that they worked with a very limited empirical material (for example, they didn’t have the Seshat Databank!). I now acknowledge Marxian contributions to the structural-demographic theory (together with other important thinkers, such as Malthus, Durkheim, Weber). Furthermore, I found ideas from a number of contemporary Marxian thinkers to be useful in illuminating various aspects of how our complex societies function. As an example, see my use of Kitty Calavita’s “structural model of the capitalist state” in Chapter 10 of Ages of Discord.

A more recent example is Angela Nagle’s The Left Case against Open Borders. This title seems to be a self-contradictory “oxymoron”. As Nagle notes,

In the heightened emotions of America’s public debate on migration, a simple moral and political dichotomy prevails. It is “right-wing” to be “against immigration” and “left-wing” to be “for immigration.” But the economics of migration tell a different story.

Of course, economics is only one of the considerations that should inform public policy on immigration. It has become a hugely emotional issue. As Nagle writes,

With obscene images of low-wage migrants being chased down as criminals by ICE, others drowning in the Mediterranean, and the worrying growth of anti-immigrant sentiment across the world, it is easy to see why the Left wants to defend illegal migrants against being targeted and victimized. And it should. But acting on the correct moral impulse to defend the human dignity of migrants, the Left has ended up pulling the front line too far back, effectively defending the exploitative system of migration itself.

What I want to do, as I often do in this blog, is to follow Nagle and look below the surface to structural issues—economics, but even more deeply, power.

The economic argument is very clear. Massive immigration increases the supply of labor, which in turn depresses its cost—in other words, worker wages. Clearly, such development benefits the consumers of labor (employers, or “capitalists”) and disadvantages the workers.

Of course, immigration is only one of the many forces affecting wages. I explore this issue in a blog series, Why Real Wages Stopped Growing, with the summary in the fourth post, Putting It All Together (Why Real Wages Stopped Growing IV). My conclusion is that immigration was a significant contributor to the stagnation/decline of the wages in the USA over the past several decades, although not the only one. Unless there are strong institutions protecting workers’ wages, an oversupply of labor is going to depress them—it is simply the law of supply and demand in action.

As Nagle points out, this was clear to Karl Marx, who

expressed a highly critical view of the effects of the migration that occurred in the nineteenth century. In a letter to two of his American fellow-travelers, Marx argued that the importation of low-paid Irish immigrants to England forced them into hostile competition with English workers. He saw it as part of a system of exploitation, which divided the working class and which represented an extension of the colonial system.

It was also clear to those, who were negatively affected—the workers and their organizations:

From the first law restricting immigration in 1882 to Cesar Chavez and the famously multiethnic United Farm Workers protesting against employers’ use and encouragement of illegal migration in 1969, trade unions have often opposed mass migration. They saw the deliberate importation of illegal, low-wage workers as weakening labor’s bargaining power and as a form of exploitation. There is no getting around the fact that the power of unions relies by definition on their ability to restrict and withdraw the supply of labor, which becomes impossible if an entire workforce can be easily and cheaply replaced. Open borders and mass immigration are a victory for the bosses.

In fact, popular opposition to unrestricted immigration goes farther back in the American history. In 1854 the anti-immigrant Native American Party (“Know-Nothings”) achieved a stunning victory in several states that were most affected by the arrival of immigrants from Europe, carrying 63 percent of the vote in Massachusetts, 40 percent in Pennsylvania, and 25 percent in New York.

This 1888 cartoon in Puck attacks businessmen for welcoming large numbers of low-paid immigrants, leaving the American workingman unemployed

And, not surprisingly, the American economic elites also were very well aware that a continuing influx of immigrants allowed them to depress worker wages and increase the returns on capital. Andrew Carnegie in 1886 compared immigration to “a golden stream which flows into the country each year”. During the nineteenth century the corporate community often used the American state to ensure that this “golden stream” would continue to flow. For example, in 1864 (during the Lincoln administration) Congress passed the Act to Encourage Immigration. One of its provisions was the establishment of the Federal Bureau of Immigration, whose explicit intent was “the development of a surplus labor force” (italics are mine).

The business leaders today are much more circumspect about these issues. But one wonders, how many of them think in the same terms, even if they don’t speak publicly about it, instead choosing to emphasize the humanitarian aspects of migration.

To strip Nagle’s main argument to its essence, globalization is wielded by the governing elites to increase their power at the expense of the non-elites. It redistributes wealth from workers to the “bosses”. Some of that extra wealth is then converted into greater political power for big business. Furthermore, antagonism between native and immigrant workers corrodes their ability to organize. As a result, Nagle argues,

Today’s well-intentioned activists have become the useful idiots of big business. With their adoption of “open borders” advocacy—and a fierce moral absolutism that regards any limit to migration as an unspeakable evil—any criticism of the exploitative system of mass migration is effectively dismissed as blasphemy.

Quite a number of people, here and on Twitter, asked me about how I came up with my forecast for 2020. Here’s the story.

By the early 2000s I had already delved into structural-demographic theory and its implications for historical societies. These results went into Historical Dynamics (2003) and in much greater detail into Secular Cycles (2009). But every time I gave a talk about this research, someone in the audience was sure to ask, where are we now in the cycle? So around 2006-2007 I started gathering data on the USA. I remember giving a talk about this research to Santa Fe Institute colleagues in 2008, when I was there for a sabbatical year.

In early 2010 Nature asked a number of scientists about their forecasts for the next decade. By that point I already had a fully developed computational model for forecasting structural-demographic pressures for instability. Frankly, the results for the USA scared me. So I sent them my rather pessimistic forecast, which, somewhat surprisingly, they published. The Nature article had to be very short, so I later published the details of the approach, model, and data in a much longer article, Modeling Social Pressures Toward Political Instability. I’ve been publishing such scientific predictions (see my blog post on how this differs from “prophecy”) from the beginning of my scientific career, because this is the main way we can really test our theories.

In the years since 2010 a number of journalists interviewed me about this prediction, but the quality of resulting pieces were quite variable, from very good to rather bad. If you want to get the story right, better read what I wrote. In particular, here are two popular articles that I published in 2013:

Return of the Oppressed. From the Roman Empire to our own Gilded Age, inequality moves in cycles. The future looks like a rough ride. Aeon Magazine

Blame Rich, Overeducated Elites as Our Society Frays. Bloomberg View Op-Eds

Then, in January of this year I teamed up with another structural-demographic theorist, Andrey Korotayev, to revisit the forecast made in 2010. So far, this article has gone through one round of review at a scientific journal, and we have just resubmitted a revised version. Yesterday I posted the revised version on a preprint server; it also has supplementary materials with the data file and an R script that implements the model. If you want to delve into the details, here’s the link:

Turchin, Peter and Andrey Korotayev. 2020. “The 2010 Structural-Demographic Forecast for the 2010–2020 Decade: A Retrospective Assessment.” SocArXiv Preprint. 

Abstract

This article revisits the prediction, made in 2010, that the 2010–2020 decade would likely be a period of growing instability in the United States and Western Europe [1]. This prediction was based on a computational model that quantified in the USA such structural-demographic forces for instability as popular immiseration, intraelite competition, and state weakness prior to 2010. Using these trends as inputs, the model calculated and projected forward in time the Political Stress Indicator, which in the past was strongly correlated with socio-political instability. Ortmans et al. [2] conducted a similar structural-demographic study for the United Kingdom. Here we use the Cross-National Time-Series Data Archive for the US, UK, and several major Western European countries to assess these structural-demographic predictions. We find that such measures of socio-political instability as anti-government demonstrations and riots increased dramatically during the 2010–2020 decade in all of these countries.

America is burning. Dozens of cities across the United States remain under curfews at a level not seen since riots following the 1968 assassination of Martin Luther King Jr. Most commentary is focusing on the immediate causes of this wave of violence that has already continued for six days. And indeed, it is difficult to watch the video of George Floyd being slowly strangled to death without feeling rage and sorrow. But my job, as it were, is to look beyond the surface of the events to the deep structural causes.

Protesters overtaking and burning the Minneapolis Police’s 3rd Precinct Source

I have written elsewhere that the causes of rebellions and revolutions are in many ways similar to processes that cause earthquakes or forest fires. In both revolutions and earthquakes, it is useful to distinguish “pressures” (structural conditions, which build up slowly) from “triggers” (sudden releasing events, which immediately precede a social or geological eruption). Specific triggers of political upheavals are difficult, perhaps even impossible to predict with any precision. Every year the police kill hundreds of Americans: black and white, men and women, adults and children, criminals and law-abiding citizens. The US cops have already killed 400 people in just the first five months of 2020. Why was it the murder of George Floyd that sparked the wave of protests?

Unlike triggers, structural pressures build up slowly and more predictably, and are amenable to analysis and forecasting. Furthermore, many triggering events themselves are ultimately caused by pent-up social pressures that seek an outlet—in other words, by the structural factors. Readers of this blog are familiar with the chief structural pressures undermining social resilience: popular immiseration, intra-elite conflict, and the loss of confidence in state institutions. More details are available in my Aeon article and in The Double Helix of Inequality and Well-Being (and of course the most comprehensive treatment is in Ages of Discord).

These structural trends, that became obvious to me in the early 2000s, resulted in the forecast, which I published in 2010: “The next decade is likely to be a period of growing instability in the United States and western Europe” (see also A Quantitative Prediction for Political Violence in the 2020s).

This forecast was not simply a projection of the contemporary (in 2010) trend in social instability into the future. Social instability in major Western countries had been, in fact, declining prior to 2010 (see the graphic below). Rather, the basis for this forecast was a quantitative model that took as inputs the major structural drivers for instability (immiseration, intraelite competition, and state (in)capacity) and translated them into the Political Stress Index (PSI), which is strongly correlated with socio-political instability. The rising PSI curve, calculated in 2010, then, suggested growing socio-political instability over the next decade.

Recently, Andrey Korotayev and I revisited my 2010 forecast (in a manuscript in review in a scientific journal). We analyzed the data on a variety of instability indicators and found that, indeed, the trends for almost all of them went up after 2010 (our data series stops in 2018, but the numbers for 2019 should be available soon). Here’s the result for the incidence of riots in six major Western countries:

Focusing on the United States and looking over a longer time period, we see that the current wave of instability has already reached similar levels to the previous one, which peaked in the late 1960s:

Our conclusion is that, unfortunately, my 2010 forecast is correct. Unfortunately, because I would have greatly preferred it to become a “self-defeating prophecy”, but that clearly has not happened.

What does it mean for the current wave of protests and riots? The nature of such dynamical processes is such that it can subside tomorrow, or escalate; either outcome is possible.A spark landing even in abundant fuel can either go out, or grow to a conflagration.

What is much more certain is that the deep structural drivers for instability continue to operate unabated. Worse, the Covid-19 pandemic exacerbated several of these instability drivers. This means that even after the current wave of indignation, caused by the killing of George Floyd, subsides, there will be other triggers that will continue to spark more fires—as long as the structural forces, undermining the stability of our society, continue to provide abundant fuel for them.

Sweden and Denmark are both Nordic countries speaking similar languages, sharing a lot of culture and a lot of common history. But they followed very different approaches to managing the Covid-19 pandemic. Denmark was among the first in Europe to shut down schools, restaurants and other businesses like beauty salons. Sweden, in contrast, allowed businesses to stay open and street travel to continue unimpeded. These two countries, thus, offer us a natural experiment to investigate the effectiveness of lockdown in controlling Coronavirus. This question is quite important, as lockdown is hugely disruptive both socially and economically.

Currently it looks bad for Sweden. It’s deaths per 100,000 population due to Coronavirus are about three times as high as in Denmark. Here’s a good (although week-old) summary of evidence: Sweden says its coronavirus approach has worked. The numbers suggest a different story.

Of course, Sweden and Denmark, despite their strong similarities, differ in some ways. This is a problem with natural experiments. For example, Denmark’s population density is much higher than in Sweden. But that should make Denmark’s epidemic harder to control, so this consideration only strengthens the conclusion that a lack of lockdown hurt Sweden. In Norway and Finland, which, like Denmark, closed themselves down, but have population densities comparable to Sweden, death rates have been even lower than in Denmark, making the contrast with Sweden even more striking.

Still, a comparison of death rates, while useful, doesn’t really get at the most important question: how differently did Sweden and Denmark manage to depress the rate of spread of the epidemic? After all, one thing we learned recently is that death rates per 100,000 differ dramatically among countries, much more than expected, and we don’t know why. So a direct comparison of disease transmission rates and the resulting exponential growth rate of the epidemic is in order.

A month ago, as part of the CSH-Vienna initiative on Covid-19, I developed a model-based approach to analyzing epidemic trajectories (see How Effective Are Public Health Measures in Stopping Covid-19?). So let’s see what it tells us about Sweden versus Denmark.

Let’s first look at Denmark. Most of the charts below are self-explanatory. In (a) through (f) data are indicated by points, and model trajectory is shown by the curves. The interesting parts are in the bottom tier. Thus, beta(t) in panel (g) shows how the disease transmission rate responded to the lockdown. It started quite high, around 0.3, which means that the number of infected grew by 30% every day. After March 15 it dropped to 0.1, and the gradually declined to half that, although with fluctuations.  In (h) delta(t) is the death rate about which I will talk a little later. The most interesting is (i) r(t). This is the exponential rate of increase. The goal is to bring it below 0 at which point the epidemic starts to subside. Denmark succeeded in this by April 15. This is good news.

Denmark

Now let’s look at Sweden:

Sweden

Swedish dynamics are surprisingly similar to those in Denmark. There was also a rapid decline in the transmission rate, beta(t), by March 15, but not as deep as in Denmark. After that beta continued to decline, but again ,more slowly than In Denmark. As a result, the exponential rate of disease growth approached the zero-level veeery slowly and has just touched it yesterday (we don’t yet know whether this will be sustained).

So the verdict seems clear, although perhaps not as clearcut as might be expected. The approach of Denmark clearly worked, rapidly bringing an end to the epidemic there. But Sweden didn’t do as poorly as I expected. Somehow, despite a lack of lockdown, they are depressing the transmission rate down.

Let’s now look at death rates. Note that these are not death rates per 100,00 which conflate two processes: what proportion of population is infected and what proportion of infected dies. This is a look at just the second part.

Surprisingly, we find that for most of April, Coronavirus patients in Sweden had nearly twice as great probability of dying than in Denmark. I’ll offer a possible explanation below, but it is clear that it made a rather large contribution to the difference between death rates per 100,000 in Sweden and Denmark.

I started this analysis expecting to demonstrate clear support for the wisdom of lockdown. Make no mistake, I continue to be a strong proponent for comprehensive shutdown as the best currently available method of controlling the Coronavirus pandemic. In personal life my preference, definitely, is to endure sharp pain now to solve the problem in the long term. In line with this philosophy, I think we should drive Coronavirus to extinction.

But in science one needs to set one’s personal preferences aside. It turns out that the comparison between Sweden and Denmark has some hidden complexities that we shouldn’t ignore. Let’s rerturn to the difference in delta, the death rate. If it’s real, then it weakens the case for comprehensive lockdown. On the other hand, Sweden has tested a much lower proportion of population for the virus. What if the elevated death rate there is a result of a larger number of unknown infecteds? These are the kinds of complexities that need to be resolved.

We are now in the mid-game of the Covid-19 pandemic and it is a good time to take stock of where we are and where we might be going. It is already clear, for example, that the effect of the pandemic on demography is going to be slight—because much less than 1 percent of population will die and the mortality from Coronavirus is heavily biased towards those who are already in retirement. The epidemic has already killed 40,000 people in the United States alone, but from the overall population point of view this is not going to change much, or anything.

The epidemiological outlook in the mid-term (the next few years) is still uncertain. Will we be able to drive the virus to extinction? Or will it become endemic and return every Fall-Winter? Will the virus evolve to less lethal forms, as is usually the case? In my view, getting rid of coronavirus in the next 2-3 years is quite possible. The question is how much we collectively are willing to adjust our behavior to achieve such an end. It will require massive testing of all travelers and other possible disease carriers, aggressive quarantining of any virus hot spots, and cordons sanitaires around countries that are unwilling or unable to control the epidemic themselves.

Given the focus of this blog on social dynamics, however, let’s talk about the implication of this pandemic for the health of our societies. As I discussed in my previous post, the likelihood of novel lethal pandemics is quite high, given the current degree of globalization and popular immiseration. Thus, Covid-19 and any future, yet unknown, diseases are part of internal dynamics at the level of the world-system. But at the level of an individual country, which is the focus of my state-centered research framework, Covid-19 is an external shock. Its long-term impact depends primarily on the social resilience of systems that it hits.

On one hand, Coronavirus is an external enemy, and external threats tend to increase internal cohesion of societies. This effect is strongest with such external threats as interstate wars. There is a substantial body of research showing that war increases social cooperation (of course, within, not between, societies). An epidemic is readily conceptualized as a war (and has already been done so), and thus can serve as unifying force.

On the other hand, too strong an external shock shatters, not unifies. As we know, the social resilience of the US has been declining over the past four decades. By 2019 a number of fault lines polarizing our society have developed. Two of these fault lines, the one between the poor and the rich, and the one between the liberal coasts and the conservative heartland, have been deepened by the Corona shock.

Epidemics tend to hit poor people more strongly, and Covid-19 is no exception. The majority of Americans have very little savings, and many survive (barely) from one payday to the next one. The massive increase in unemployment, resulting from the need to control the spread of the virus, has become a personal catastrophe for millions of American families. Many are literally on the brink of starvation (as long lines for free food handouts show). Furthermore, the poor who still have jobs are at a higher risk of becoming infected because many of them cannot afford to avoid travel using public transportation. And the poor are more likely to die from Coronavirus, because general increase of immiseration has the consequence of undermining the ability of many to resist the virus.

In principle, these negative effects could be mitigated by a strong collective, government-led response. The Fed needs to print massive amounts of money to keep those who lost jobs and small business owners afloat. We need massive production of protective gear to keep safe those who must move around. Massive testing for virus will enable us to quarantine the hot spots, so that only the affected areas need to be shut down, allowing the rest of the country to operate normally. What needs to be done is quite clear; whether it will be done is in question.

An initial moment of relative unity, which enabled the two parties to quickly pass the coronavirus bill, is largely over. Our political class is back to internal bickering, and worse. The most visible sign is the rift between the president in Washington, who was largely elected by the heartland, and the governors of the coastal states.

The shock of Coronavirus has the potential both to create social solidarity within a country, and to break the country apart. In my estimation, two Nordic countries, Norway and Denmark, have the best chance to follow the first route. Twenty years ago, I would have no doubts predicting such a response. But in the last decade there have been signs that the Nordic model may be fraying at the edges.

For the United States my forecast is rather gloomy. Our governing elites are selfish, fragmented, and mired in the internecine conflicts. So my expectation is that large swaths of American population would be allowed to lose ground. Government debt will still explode, with most of the money going to keep large companies and banks afloat. Inequality will rise, trust in government decline even more, social unrest and intra-elite conflict will increase. Basically, all negative structural-demographic trends will be accelerated.

I very much hope that this pessimistic forecast is wrong.

After I published my last post on Coronavirus and Our Age of Discord, I’ve been looking through various lists of major epidemics in world history, both on resources such as Wikipedia and in academic articles. I know that there is a strong (although not perfect) association between crisis periods and disease outbreaks (see my 2008 article). The question is, how strong is this correlation?

Below is a table that I put together, based on the data I found. It is not a definitive test of the hypothesis that major epidemics tend to strike during Ages of Discord. The comparison is not systematic enough, it’s too qualitative, and there is a definite Eurocentric bias (or, at least, a bias towards western Eurasia). Still, this is my blog, not an academic article that requires much higher rigor (and we will do a proper job when we complete building the Seshat Crisis Database).

In any case, here’s what I came up with so far. Comments are welcome!

The plague of the Philistines at Ashdod. Oil painting by Pie Wellcome

As readers of this blog know well, I don’t claim to be a prophet and I think that prophecy is, in any case, overrated. But I make predictions. A scientific prediction, unlike a prophecy, is not about a future, but about a theory — it’s a way to find out how good is our understanding of the way the world works. I explain more in my 2013 post Scientific Prediction ≠ Prophecy.

As an example of this general philosophy, here’s what I wrote in the final paragraph of an article published in 2008:

Are there any lessons from this history for the current globalization through which we now live? I think there may be, but with two very important caveats. First, as I emphasized repeatedly throughout this chapter, we still have very sketchy understanding of the causes underlying previous world-system pulsations. Much more modeling and empirical research is needed before we could determine just what the history’s lessons are. Second, the world has changed dramatically over the last two centuries. Thus, our understanding of pre-industrial globalizations cannot be mechanically transferred to make predictions about the current one. Our models will have to be greatly modified in order to apply to the modern world. Still, several of the empirical trends associated with the globalization of the twentieth century bear an uncanny resemblance to what has come before. Most obviously, the second half of the twentieth century was a period of massive population growth that has slowed down in the last decade, suggesting that we may be approaching the peak of global population. On the epidemiological front, human emerging infectious diseases have dramatically increased in incidence during the twentieth century, reaching the peak during the 1980s (Jones et al. 2006). The cholera incidence has been on the rise (Figure 11). The AIDS pandemic (Figure 11), as terrifying as it has been, may be the harbinger of even worse diseases to come. These and other trends (for example, the growth of the global inequality of wealth distribution during the last two decades) raise the possibility that studying previous globalizations may not be a purely academic exercise.

For better or worse, these predictions I’ve made have a tendency to eventually become realized (the biggest one is, of course, A Quantitative Prediction for Political Violence in the 2020s). When I wrote of “even worse diseases to come” twelve years ago I, of course, had no idea of Covid-19, or that it would coincidentally hit in 2020, just as other pressures for a structural-demographic crisis are building up to a peak. Rather, this prediction was based on a strong macrohistorical pattern: major pandemics tend to happen during Ages of Discord. For details, see the 2008 article; here I will summarize the main ideas in a nontechnical way.

There are several general trends during the pre-crisis phase that make the rise and spread of pandemics more likely. At the most basic level, sustained population growth results in greater population density, which increases the basic reproduction number of nearly all diseases. Even more importantly, labor oversupply, resulting from overpopulation, depresses wages and incomes for most. Immiseration, especially its biological aspects, makes people less capable of fighting off pathogens. People in search of jobs move more and increasingly concentrate in the cities, which become breeding grounds for disease. Because of greater movement between regions, it is easy for disease to jump between cities.

Elites, who enjoy growing incomes resulting from low worker wages, spend them on luxuries, including exotic ones. This drives long-distance trade, which more tightly connects distant world regions. My 2008 article is primarily about this process, which we call “pre-modern globalizations.” As a result, a particularly aggressive pathogen arising in, for example, China, can rapidly jump to Europe.

Finally, when the crisis breaks out, it brings about a wave on internal warfare. Marauding armies of soldiers, rebels, and brigands, themselves become incubators of disease that they spread widely as they travel through the landscape.

This description is tailored to pre-modern (and early modern) Ages of Discord. Today, in 2020, details are different. But the main drivers — globalization and popular immiseration — are the same.

In my 2008 article I discuss previous waves of globalization (although the early ones are better called “continentalizations” as they primarily affected Afro-Eurasia, rather than the whole world). There is a very strong (although not perfect) statistical association between these globalizations, general crises, and pandemics, from the Bronze Age to the Late Medieval Crisis. The famous previous pandemics such as the Antonine Plagues, the Plagues of Justinian, and the Black Death all coincided (and, typically, helped trigger) prolonged secular crises.

The last two complete crisis periods, the Crisis of the Seventeenth Century and the Age of Revolutions, were truly global in nature. As our data become better for the Early Modern period, we can trace the two pandemics more quantitatively:

The first cycle is traced by resurgent plague, but it should be supplemented by the devastation of the Americas due to such diseases as measles. The second cycle reflects the recurring pandemics of cholera. According to the Encyclopedia of Plague and Pestilence, the great cholera epidemic of 1849 carried away up to 10 percent of the American population. And we shouldn’t forget the Spanish Flu Pandemic, which hit in 1919.

And now it looks like our Age of Discord got its own pandemic.

Last week my analysis of the Covid-19 epidemic in Italy yielded a very depressing result: despite all the measures taken by the government, there was no sign that they were making a difference. The epidemic was still growing exponentially with dire implications for the overall number of deaths it could cause.

My approach to tracking Covid-19 dynamics in various countries is explained in a technical publication and, less technically, in my previous blog post, How Effective Are Public Health Measures in Stopping Covid-19?

Rerunning the analysis on the more recent data (up to March 31) results in a much more optimistic conclusion. There are now clear signs that Italy has turned the corner. Here are the results:

The most visible sign of change is the decline of New Cases. Less visibly, other curves also have started to bend down. The change in dynamics is driven primarily by declining transmission rate of the disease:

At the beginning of the epidemic (in early February) the transmission rate, beta, was almost 0.4, which means that the number of infected grew at the rate of nearly 40% per day (but this explosive rate of growth was invisible to the public or the authorities, see below). The decline in beta was very slow and late (the inflection point of the curve is at March 13). This suggests that it took a while for the exhortation of the Italian government to change the behavior of its citizens. We know this also anecdotally. As late as on March 21, the Chinese Red Cross vice president, Sun Shuopeng, was reported saying “Here in Milan … public transportation is still working and people are still moving around, you’re still having dinners and parties in the hotels and you’re not wearing masks. I don’t know what everyone is thinking.” More amusingly (and we need some humor in these trying times), the latest run-away hit on YouTube has been videos of small-town mayors in Italy raging at people flouting the lock-down. But clearly the gravity of the situation — over 13,000 deaths as of today, has finally impressed itself on the Italians. The transmission rate has been declining — slowly, but is heading in the right direction.

Note the second graph (on the right). It shows quantitatively what we all know: the initial detection rate (the probability that an infected person would become known) started low and then increased. What this means is that we cannot simply use the reported numbers to accurately trace the dynamics of the epidemic. As the detection rate increases (first due to the general awareness that we are in an epidemic, and later as a result of massive testing of asymptomatic people) it would inflate the number of new cases, artificially increasing the transmission rate. To see what is actually happening we need to factor out this change in the detection rate, which is what my model does.

I’ll continue reporting my analysis results as more data come in. I was actually, hoping to run the data from New York, but yesterday they were not available as the team at Johns Hopkins (many thanks to them for putting together and updating the data) changed the way they report USA data.

As many of my readers know, I have accepted the position of research group leader at the Complexity Science Hub (CSH) in Vienna (and I continue as University of Connecticut professor, so right now I am in Connecticut).

A week ago the Austrian government asked CSH to conduct research that would help formulate better policies for dealing with the Covid-19 epidemic. As an aside, I find it incredibly refreshing that a national government would actually ask scientists for help (and have a research institute ready to provide such assistance). In any case, CSH decided to put other research on hold and redirect all of its scientific power to deal with the challenges that the Corona crisis poses to our society.

As a result, last week I have been contributing to a working group that asked the following question: how effective are various public health measures in slowing down, or even stopping the spread of the Covid-19 epidemic? There is quite a lot of variation in how different countries have decided to deal with Corona, ranging from highly Draconian measures implemented by China to (at least, initially) laissez-faire approach of United Kingdom. Of particular interest could be pairwise comparisons between such similar countries as Denmark and Sweden, which have adopted very different Covid policies.

The goal of my research last week, thus, was to estimate the effects of various measures implemented by national governments to slow down and reverse the spread of the Covid-19 epidemic. A direct approach to answering this question is to track the growth rate of epidemic (with the severity of epidemic estimated by the number of “Active Cases”, that is, the number of people known to be currently infected) and then observe how various interventions affect this growth rate. For example, one could use the “basic reproductive number” (R₀) — the average number of cases directly infected by a sick individual. The goal of an intervention is to bring down the reproductive number below 1, which will result in the epidemic dying out.

However, one potential problem with such direct approaches is that a large proportion (at least 50%) of people infected with Corona are “asymptomatic”, meaning that they themselves don’t know they are carrying the disease. As a result, they are not included in the disease statistics. Even worse, the proportion of known infected individuals tends to increase with time, as people become more aware of the epidemic and governments may decide to massively test asymptomatic individuals. Changes in the disease detection rate will, then, tend to mask changes in the epidemic growth rate.

So what can be done? My idea is that we should model both the dynamic process of how disease grows (and eventually declines) and how the numbers of actual infections are translated into official statistics. If we have a good process model (and for epidemics, we do) then an analysis of data based on such a mechanistic model will work better than using a purely data-driven approach. The reason is that we can build into the model what is known which enables us to efficiently use the precious data to estimate what is unknown.

For the technically minded I posted a document that describes exactly what I have done (GitHub:pturchin/Covid19). But in this blog, I will simply illustrate the approach with one specific example using non-technical language, which (hopefully) should be understandable to all readers (ask me questions in comments, if anything is unclear).

Important disclaimer: these results are quite preliminary and should be taken with a grain of salt. I often use my blog to air new ideas in order to find out any problems with them at an earlier, rather than later stage. And I certainly don’t speak for any organization (including CSH) or a government.

The illustrating example I use is the Covid-19 epidemic in South Korea. First, let’s look at the data. The chart below shows the progression of the disease, as measured by the number of “Active Cases” (people known to be infected).

Next, let’s see how fitting a model to these data can clarify the internal mechanics of the epidemic. I use a variant of a standard epidemiological model, known as SIRD (so named for the first letters of the variables it tracks: the numbers of Susceptible, Infected, Recovered, and Dead). We want to make sure that the model does a good job approximating a variety of different angles from which an epidemic can be viewed. The next series of charts show whether the model succeeds in this. Points are the actual data, while curves depict model predictions.

In fact, the model does a very good job. This increases our confidence that it has captured the essential mechanisms driving the epidemic. And we only need to add two additional features to the basic SIRD model to do this.

The key parameter in the model is the transmission rate, which determines how fast the disease spreads from the infected population to that of susceptibles. The second important parameter is the detection rate. Both of these parameters changed during the epidemic. As is well known, once the South Korean officials realized that they have an epidemic to deal with, they massively expanded their testing program and imposed vigorous quarantine measures. These measures should have increased the detection rate and decreased the transmission rate. Building these changes into the model, we can estimate when and how much these two rates changed. Here’s what I got:

Panel (a) shows how the transmission rate (beta) changed with time. Initially the infection rate was very high, with the exponential rate of increase of around 0.4 day^–1 (in other words, every day the number of infected increased by 40%). This parameter began declining after day 25 (mid-February), but reached low levels only close to day 50 (early March).

Panel (b) shows the detection rate. It is estimated as 0 until day 30, which suggests that initially, and for quite a while, the epidemic was growing “below the radar screen”. People were getting sick in growing numbers, but the society as whole was not yet aware of it.

South Korean authorities started testing for Covid-19 in early February, and the scale of testing was massively expanded after Feb. 20, which closely corresponds to day 30 when model-predicted detection rate began increasing. Eventually it reached a very high level of nearly 70%, suggesting that aggressive testing of asymptomatic people is bearing fruit.

Overall, then, this analysis of South Korean data makes a lot of sense in light of what we know about the course of the epidemic there. There are some caveats, which I discuss in the technical document, but the model fits exceedingly well and provides us with numerical estimates of the effectiveness of the measures taken by the SK government. The intervention was highly effective.

A future post will report on the analysis I’ve done for China. The situation there was more complex, and the model fit was not as excellent as for the SK epidemic. But it still yields very interesting and instructive insights. Stay tuned.

Added (21:00 23.III.2020): I have posted the document providing technical details and the R-script on my GitHub directory