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.