Abstract
We introduce a novel methodology for predicting the time evolution of the number of individuals in a given country reported to be infected with SARS-CoV-2. This methodology, which is based on the synergy of explicit mathematical formulae and deep learning networks, yields algorithms whose input is only the existing data in the given country of the accumulative number of individuals who are reported to be infected. The analytical formulae involve several constant parameters that were determined from the available data using an error-minimizing algorithm. The same data were also used for the training of a bidirectional long short-term memory network. We applied the above methodology to the epidemics in Italy, Spain, France, Germany, USA and Sweden. The significance of these results for evaluating the impact of easing the lockdown measures is discussed.
Highlights
The novel coronavirus SARS-CoV-2 is the third coronavirus to appear in the human population in the past two decades, following the severe acute respiratory syndrome coronavirus SARS-CoV outbreak in 2002 and the Middle East syndrome coronavirus MERS-CoV outbreak in 2012
We implemented the following tasks associated with the epidemics in Italy, Spain, France and Germany: (i) we determined the parameters of the logistic, rational and birational formulae, by training the above formulae using only a subset of the data, namely data up to T + 25
For the epidemic of Germany, the logistic model predicts a plateau on 3 May 2020 with 154 334 reported cases; the rational model predicts a plateau on 13 May 2020 with 164 659 reported cases; the birational model predicts a plateau on 23 May 2020 with 174 356 reported cases and the bidirectional long short-term memory (BiLSTM) network predicts a plateau on 20 May 2020 with 175 357 reported cases
Summary
The novel coronavirus SARS-CoV-2 is the third coronavirus to appear in the human population in the past two decades, following the severe acute respiratory syndrome coronavirus SARS-CoV outbreak in 2002 and the Middle East syndrome coronavirus MERS-CoV outbreak in 2012. This raises the following natural question: is it possible to find a formula yielding more accurate predictions than the logistic one? We implemented the following tasks associated with the epidemics in Italy, Spain, France and Germany: (i) we determined the parameters of the logistic, rational and birational formulae, by training the above formulae using only a subset of the data, namely data up to T + 25 (the inflection point T was determined by fitting the logistic model over the whole dataset of each country, namely up to 24 May 2020). For USA and Sweden, we have presented the parameters determined with data up to 24 May 2020, with the understanding that we do not expect neither the associated analytical formulae nor the BiLSTM network to provide accurate predictions (for these two countries the following numbers provide rather inaccurate lower bounds: USA, plateau on 28 August 2020, with 2 264 338 reported individuals; Sweden, plateau on 9 October 2020, with 57 540 reported individuals)
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