Covid-19 epidemiological models and the Lombardy data
As the epidemic of Covid-19 severely hit countries outside of China one-by-one, they have been taking increasingly harsh measures to enforce extreme social distancing. Several countries (including Italy, France, Spain, Belgium, Morocco) have gone so far as to put their whole populations under complete lockdown, where people are only allowed to leave their homes if absolutely necessary.
I will make no secret of the fact that I strongly disagree with the lockdowns both from the purely moral standpoint and from my belief that they are ultimately bound that they are going to cause a lot more deaths than they may possibly spare in addition to the already severe restrictions such as closing of schools and all the non-essential venues.
But here I would like to address one of the key factors that moved many governments to turn to such unimaginable measures. I am talking to epidemiological models of Covid-19 caused by SARS-CoV-2. Most people believe that epidemiological models are at their core about biology, in this case, viral biology. But this is only partly true.
What is known about SARS-CoV-2 is important. It causes a disease with a relatively long incubation period (median 6 days) to which few people are probably immune, which is asymptomatic or only mildly symptomatic in the vast majority of carriers but causes severe pneumonia and sometimes deaths in some patients. The category most at risk from the virus are older people with underlying pathologies. The virus seems to spread the easiest (perhaps, overwhelmingly) through.
Equally important, however, is the social aspect of epidemiology. It is how people tend to interact and with whom that will determine the course of a given epidemic.
Epidemiological models on which the harsh measures and much of the panic around Covid-19 are based seem to assume a constant average rate of transmission without external intervention. Here is a relevant quote from the Imperial College of London’s model paper:
“Based on fits to the early growth-rate of the epidemic in Wuhan, we make a baseline assumption that R0=2.4 but examine values between 2.0 and 2.6.” By “early phase here, they seem to mean the phase of the Wuhan epidemic in which there was no intervention.
The assumption of a constant average rate of transmission is highly implausible, however. As Stanford biophysicist Michael Levitt tells us:
“In exponential growth models, you assume that new people can be infected every day, because you keep meeting new people. But, if you consider your own social circle, you basically meet the same people every day. You can meet new people on public transportation, for example; but even on the bus, after some time most passengers will either be infected or immune.”
To which I would add that with the virus that spreads like SARS-CoV-2 what matters the most are prolonged close contacts between individuals, especially in confined spaces. It is not just that I am unlikely to constantly have such interactions with new people but also the people who I tend to closely interact with will tend to have overlapping circles of close interaction.
The Lombardy data and the rate of unchecked transmission
But theory is theory, can we look at some data? To judge the development of the epidemic, many people look at confirmed cases but there is a major reason why it is probably a poor indicator. Not just because almost everywhere the vast majority of cases goes unnoticed but also because different countries or even different regions within one country have different criteria for testing.
While almost all countries initially try to test as many people connected to the confirmed cases as possible, most don’t stick to this strategy for long. With multiplying cases, they may only test only people with underlying conditions or mostly medical personnel. But some countries like South Korea and Iceland (and probably also Germany, Singapore) test massively. With such a variety of approaches, it is probably better to largely ignore the ongoing case counts in severely hit countries.
The one indicator that is much more reliable, however, is the number of deaths. While we do not know what the real fatality rate of the virus is, given that the virus has not mutated significantly, it probably has similar impacts on large human populations. That said, some countries may, in theory, have significantly higher or lower fatality rates, although so far, this remains unproven. For instance, in Italy, there may be too many deaths because of how concentrated in the Lombardy region the outbreak is, and what pressure it put on the ICU units there and how many doctors it initially hit. Older patients may also be overrepresented in Italy because of the average age of the country, the fact that the virus initially hit villages and small towns and that the widespread practice of children living with parents long into adulthood. In contrast, with mass testing in South Korea, it becomes possible to treat a lot of symptomatic cases early and minimize complications like pneumonia.
This does not, however, imply that we cannot use the evolution of the number of deaths to try to infer the evolution of the infection’s spread and whether it remains the same in the baseline scenario without intervention.
In this regard, there is perhaps no better example than the Italian region Lombardy. Based on the fact that the first death there occurred on 22 February, this means that the outbreak there had probably started in late January. The reason for this is that it probably takes at least 20 days from the day of infection for someone to die, and probably 24 in the median case (6-day median incubation period plus 18 days from the start of symptoms to death).
It had been developing silently for more than three weeks and three weeks have passed since the end of the silent period. If the epidemiological models are right, then the average rate of growth of deaths per day corresponding to the silent period should show no clear trend. But that is not what the data from Lombardy reveal.
In Fig. 1, only the last several data points relate to the period when active suppression measures were taken against the outbreak. The strict quarantine of the initially hit communes, or “red zones,” in Italy (11 of 12 of them in Lombardy) was instituted just two days after the discovery of the epidemic, on February 23. If we add 20 days of the minimum time from infection to death, the first day on which we might see any impact of the quarantine is March 14.
The data clearly suggest that the epidemic growth had been trending down significantly even before the initial lockdown. They invalidate the fundamental assumption of the Covid-19 epidemiological models and with it, probably also the rationale for the harshest measures of suppression..