Projections for SARS-Cov-2 spread in Greece
What to expect in a few lines and some Data Analysis…
A special bulletin, prepared by the Data Science dept. of E-ON INTEGRATION S.A.
As a private – independent initiative, we, at E-ON INTEGRATION S.A. (www.e-on.gr) are planning to examine on a daily basis the evolution of the phenomenon, to process data from reliable sources and present the most recent and educated forecasts about the short-to-medium potential course of the pandemic. The model output and results are a product of interdisciplinary work and are based on published data.
“Exponential or Sigmoid/Logistic mathematical modeling result in more optimistic or pessimistic projections. The coming days will show clearer trend”
In the following diagram, we see today’s situation regarding the spread of the virus SARS-Cov-2 in Greece, based on the latest data that have been released by Johns Hopkins University, Center for Systems Science and Engineering
In this graph, we see lines for confirmed cases (blue line), deaths (orange), cured cases (green) and active cases (current patients – red).
At E-ON, through mathematical modeling, we constructed the last two functions, exponential and logistic, with purple and brown color respectively, in order to assess future cases and, ultimately, to understand how Greece is affected by the pandemic.
From this study, we reach the following conclusions:
1. Based on the recorded data, the doubling time of cases is approximately 4 days considering the data from 13/03 to 17/03.
2. If the measures that were put in effect in 12/03/2020 are applied meticulously, then Greece will follow the Logistic (brown) line and the cases will reach 639 in 5 days. Ιt seems that the confirmed cases are reaching a plateau and that the doubling time increases thus slowing down the spread ratio for the infection.
3. Else, that is if Greek inhabitants do not exercise the necessary discipline to the measures and there is intense crowding, then the cases will follow an exponential increase (purple line) and the cases will reach about 1.222 in the same time frame of 5 days.
It is noted here that this prediction is based on recorded cases in Greece. In these predictions, there may errors resulting from non-recorded cases due to the lack of relevant detection tests or due to asymptomatic behaviour of the disease. In the following days, we will be obtaining new data, which will allow us to do more accurate and complete analysis.
In the following figure, you may see the evolution of the pandemic, in Greece, in 10 days from now.
Now, the difference between the two simulations is evident:
1. The Logistic line consists of an exponential part in the beginning, a linear part after that and finally it reaches a plateau. In the case where the measures are accurately followed, the cases approach the plateau in 10 days, with their number approaching 738. This means that probably in 10 days from now, we may see a decrease in the rapid spread of the pandemic and thus have a very optimistic development. Of course, the new cases will not be zero but they will follow a linear - predictable path until the pandemic is eliminated.
2. Otherwise, if Greece follows the exponential trend, next week we are looking at about 3.500 cases. Beyond that, one possible scenario is that the spread will continue at an exponential rate, implying that in 20 days from today we may have reached around 8 to 10 thousand cases. However, even with an exponential increase in the cases over the next 20 days, it is certain that the outbreak will eventually reach a plateau and follow the logistic function.
The main goal of the implementation of the measures is the reduction in the increase rate of the incidents so that the health care system is able manage the needs of the patients. Nevertheless, the recording of cases within the next few days and our subsequent simulations will answer these scenarios.
In order to better understand the results, it is worth examining the neighboring countries of Italy and Spain and how the pandemic is evolving in them, following the same trends as in Greece.
Virus evolution in Italy
As shown in the figure above, our model running the exponential and accounting functions on the published data for Italy, predicts about 52 thousand cases with the logistic function or 78.4 thousand cases with the exponential function on 22/03. Moving in one or the other direction depends on the effectiveness of the Italian government's lockdown measures. It is a nightmare to imagine that the outbreaks may reach hundreds of thousands over the next 15 to 20 days if the outbreak follows the exponential path.
It is also disappointing that there is no sign of a plateau at the moment according to our model, even if we examine the logistic scenario, which is the most optimistic between the two.
Italy ordered a general lockdown on 9172 cases, forcing it to remain in the exponential phase for a much longer period. However, it seems that Italy has begun exiting the exponential phase and entering the linear part of the logistic function.
We want to believe that in a few days the plateau will start showing in our estimates.
Virus evolution in Spain
As for Spain, we see that it too has been slow to act on 16/03/2020 and we expect it to follow a path similar with Italy, with possibly fewer deaths as it has a lower distribution of the population aged 65+ (19.4% in Spain against 22.8% in Italy). Please note that this cannot be said with certainty since there are other factors such as the differences in the healthcare of the two countries. Spain seems to be entering the logistic function’s plateau in 10 days as we have seen that in the last days the number of days has increased from one in 12/03-13/03 to four in 13/03-17/03. Therefore, it is evident that the rate of spread slows.
The main conclusion that can be drawn from the above graphs is that Greece acted correctly by taking measures so early. Greece ordered partial lockdowns, closing cafes, issuing instructions as well as urging citizens to reduce crowding, at a rate of 9 cases per million, while Italy at 164.4 cases and Spain at 213, respectively.
E-ON INTEGRATION executes Big-Data & Analytics projects for its clients. It has developed systems and expertise to gather data, analyze them through Machine Learning techniques and produce accurate and tangible results for the end-user and the higher management. It believes that companies and organizations have already gathered a valuable volume of data and it tries to assist them in harnessing the power of data analytics, artificial intelligence and big data.