Update: Apr. 9th, 2020
Covid-19: Romania has reasons for being optimistic
A bit over two weeks have passed since strict social distancing measures were imposed in Romania and a bit over a week since I first discussed what the early data looked like (see my previous article).
As of April 9th, two weeks after the first reported death from coronavirus, Romania has accumulated 220 total deaths, while Italy had counted 463 and Spain 1043 (according to data from this source). This difference is very important, especially taking into account that during the first week since the first reported death, Romania's death count was higher than in Italy and Spain. As I argued in my first post, this is evidence for the success of the strict social distancing measures taken very early on in Romania.
To take a closer look at what the current data implies for the next few weeks and when we should start seeing light at the end of the tunnel, I've taken one of the standard epidemiological models, the SIR model and fit it to available data.
The SIR model tracks the number of Susceptibles, number of people who are healthy but might get sick (most of us), Infected, number of people who are sick, and Removed, number of people who were infected and are not infected any more, most of them recovered. Every day, the new number of susceptibles decreases by the number of new infected, the new number of infected increases proportional to the number of encounters between susceptibles and infected and decreases by the number of removed, and the new number of removed increases proportional to the number of infected.
The model is certainly a simplification. It glosses over details as to how people encounter and how these encounters vary in time, whether there are infectious focuses, like, unfortunately, some hospitals in Romania, demographical gradients of both density of people and age distributions, etc. It is not meant to perfectly work in detail, but as a useful effective description of how the disease spreads.
The model has four parameters that determine the full evolution of the spread: the size of the susceptible population, the initial fraction of infections, the initial doubling time (how long it takes to double the infections early in the spread), and the resolution time (how long it takes for an infection to be resolved as a recovery or a decease).
While the resolution time is a parameter that should be approximately shared by spreads in all countries, the rest depends on the country's population, the influx of initial infections, how measures of social distancing were implemented and many other social factors. They can all be directly extracted from the data.
I will skip the technical details of my particular implementation of the model. I used an out-of-the-box differential equation solver in scipy and a Markov Chain Mote Carlo package to fit the observed data.
I've used data from Wuhan, Italy, Spain and Romania. Since Wuhan went through a full epidemiological cycle, these data are important to accurately measure the resolution time. I only considered the death count from Wuhan as testing and reporting practices for covid might have varied very quickly in the beginning of the spread. The resolution time I get from Wuhan is 5.6 +/- 0.3 days. Instead of injecting the resolution time measured from Wuhan into models for other countries, I implemented a simultaneous fit of all available datasets from the countries listed above.
The following figure shows the results. The epidemiological model compares very well with all data sets with the exception of the decease count from Spain where deaths increased much faster than the model prediction at the end of the second week. This could be a methodological difference in data reporting, a shift in spread demographics or many other reasons. It certainly reminds us of the limits of the model.
Regarding Romania, the data is barely visible in this scale, which is actually good news. So let's make a zoom:
It does come as a surprise, but Romania's model suggests that the peak of confirmed cases is occuring now, and the peak of decease cases will come near april 11th. This should be taken with a grain of caution since the model is as good as the data it's fed. It is certainly, though, good news and maybe light at the end of the tunnel?
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