Benedetta Cerruti & Xavier Roca-Maza
While Italy is slowly exiting its second wave, and struggling to keep the new cases at a manageable level, vaccinations have started worldwide. While in Europe the vaccinations, started the 27th of December 2020, still do not reach a significative percentage of the population, Israel has vaccinated 90% of >60 years old, and around the 40% of total population (1). We propose here a possible proxy for monitoring the vaccine effects on the epidemics.
Italy’s first and second wave: a comparison
We have previously shown that different containment measures in different countries may lead to quite similar epidemics figures (2). The robustness of the results led us to try a similar approach to compare the two waves in Italy. The first wave was fought through a harsh national lockdown, starting the 9th of March 2020. When the new cases started to rise again in autumn, the government choose to try to avoid a hard lockdown, and set in place a color code for the different regions of the country instead, according to the combined values of a few KPIs (3). There are three possible levels of alert, namely yellow, orange, and red, corresponding to increasing hardness in the containment measures. We will refer also to this set of measures as ‘lockdown’ for simplicity.
At the beginning of the second wave, the vital question in Italy then was: is this system as effective as a harsh lockdown? will it invert the curve slope? To this purpose, we designed the lockdown-O-meter: we compared the data in a similar way as for same wave/different countries problem explained before (2). The only difference is that we have now a same country/different waves framework.
Lockdown starting dates are here:
- 9th of March 2020 for the first wave
- 6th of November 2020 for the second wave.
The data of the two waves in Italy before the shift and the normalization look quite different (fig.1): in particular, the second wave in Italy arose much slower than the first one, thanks to the widespread use of face masks, social distancing, and other containment measures that were in use at that time, but not in the ascending branch of the first wave . This also led to a much slower slope down for the second wave.
Since the number of deaths for the starting date were this time consistently different, we also now subtracted the number of deaths of the respective first days for each series (97 for the first wave, 446 for the second one, data from ref.(4)). Results are shown in figure 2.
Despite the frequent changes in the colors of the regions, the containment measures proved to be equivalent to the first lockdown. Aside of the normalization and shift that make compatible the initial conditions, the curves are indistinguishable within the error bands. No free parameter is involved.
What about Israel?
Israel is now in lockdown. Also in this case the measures were not taken all at once. On the 27th of December 2020 some measures were taken, and on the 8th of January the lockdown tightened (5). We will consider the following dates for the lockdown: the 8th of January 2021, and in analogy, the 23rd of September 2020 for the earlier wave, when the 18th September 2020 measures were tightened. Israel ‘first’ wave in March was almost negligible and we will not consider it here. The relative equivalence of the second and third wave lockdowns will be tested below using our approach.
In the meanwhile, Israel has vaccinated 90% of >60 years old, and around the 40% of total population (1), and results of the vaccination will hopefully start to be visible at some point on the death toll.
Nevertheless, the overlapping of vaccinations and the lockdown risks to make difficult a timely identification of the effects of the vaccinations on the drop of the new cases and/or death toll. In fact, the peak of the deaths arrived at the expected time after the lockdown (around 20 days after the lockdown day). So we can conclude that it was essentially caused by the lockdown itself.
We thus propose a similar construction as the one shown for Italy. For Israel, we would like to see a clear difference in the descending part of the curves, that would likely be and effect of the vaccination campaign (see figure 3).
What will happen in the descendant part of the curve? We hypothesize here that the containment measures are similar enough to see the same qualitative behavior for the two curves, as observed until now for Israel, and for the entire wave in Italy. There are thus three possibilities:
- New variants (or some other ‘negative’ effects) will dominate, and the red curve will go down slower than the black one.
- Vaccine effects (or some other ‘positive’ effects) dominate, and the red curve will go down faster than the black one.
- None of the previous.
The outcome number 3. can be due either to a failure of our hypothesis, a competition between 1. and 2., or to no visible effects of the vaccines on the death curve, at least in the observed time interval.