Figure 1
Methodology overview diagram. In this figure, we focus on the main steps to treat the data, choose the model parameters and validate the model with an statistical imputation method.
Figure 2
Brazil has a low level of daily COVID tests according to Coronavirus Pandemic (COVID-19) publication data (Roser et al. 2020ROSER M, RITCHIE H, ORTIZ-OSPINA E & HASELL J. 2020. Coronavirus Pandemic (COVID-19). Our World in Data ).
Figure 3
COVID-19 daily cases evolution for critical group countries in log scale. Source Roser et al. 2020ROSER M, RITCHIE H, ORTIZ-OSPINA E & HASELL J. 2020. Coronavirus Pandemic (COVID-19). Our World in Data .
Figure 4
COVID-19 daily cases evolution for attention and impact group countries in log scale. Source Roser et al. 2020ROSER M, RITCHIE H, ORTIZ-OSPINA E & HASELL J. 2020. Coronavirus Pandemic (COVID-19). Our World in Data .
Figure 5
COVID-19 daily cases evolution for successful group countries in log scale. Source Roser et al. 2020ROSER M, RITCHIE H, ORTIZ-OSPINA E & HASELL J. 2020. Coronavirus Pandemic (COVID-19). Our World in Data .
Figure 6
Rolling window sub-sampling method. In (a) we show the rolling window sub-sampling, this method allows us to choose the window size (m), that is, the size of input data to get the prediction horizon (h), that is, the prediction output. In (b) we show how this sub-sampling method runs through the entire time series, setting the inputs and prediction outputs.
Figure 7
LSTM Model for Daily Coronavirus Cases Predictions.
Figure 8
Number of daily cases in Brazil and USA.
Figure 9
The confirmed cases reported in Brazil (black dots), line with an 80% confidence interval (green band), and the importance of outliers is annotated based on how far the dot is from the boundary of the confidence interval.
Figure 10
The confirmed cases reported in the USA (black dots), line with an 80% confidence interval (green band), and the importance of outliers is annotated based on how far the dot is from the boundary of the confidence interval.
Figure 11
The components plot of weekly seasonality for both countries.
Figure 12
Outliers identification in data of COVID daily cases in Brazil using the Median Absolute Deviation (MAD).
Figure 13
Characterization of the distribution and percentage of the missing data in daily cases of Brazil.
Figure 2
Brazil has a low level of daily COVID tests according to Coronavirus Pandemic (COVID-19) publication data (Roser et al. 2020ROSER M, RITCHIE H, ORTIZ-OSPINA E & HASELL J. 2020. Coronavirus Pandemic (COVID-19). Our World in Data ).
Figure 3
COVID-19 daily cases evolution for critical group countries in log scale. Source Roser et al. 2020ROSER M, RITCHIE H, ORTIZ-OSPINA E & HASELL J. 2020. Coronavirus Pandemic (COVID-19). Our World in Data .
Figure 4
COVID-19 daily cases evolution for attention and impact group countries in log scale. Source Roser et al. 2020ROSER M, RITCHIE H, ORTIZ-OSPINA E & HASELL J. 2020. Coronavirus Pandemic (COVID-19). Our World in Data .
Figure 5
COVID-19 daily cases evolution for successful group countries in log scale. Source Roser et al. 2020ROSER M, RITCHIE H, ORTIZ-OSPINA E & HASELL J. 2020. Coronavirus Pandemic (COVID-19). Our World in Data .
Figure 6
Rolling window sub-sampling method. In (a) we show the rolling window sub-sampling, this method allows us to choose the window size (m), that is, the size of input data to get the prediction horizon (h), that is, the prediction output. In (b) we show how this sub-sampling method runs through the entire time series, setting the inputs and prediction outputs.
Figure 7
LSTM Model for Daily Coronavirus Cases Predictions.
Figure 8
Number of daily cases in Brazil and USA.
Figure 9
The confirmed cases reported in Brazil (black dots), line with an 80% confidence interval (green band), and the importance of outliers is annotated based on how far the dot is from the boundary of the confidence interval.
Figure 10
The confirmed cases reported in the USA (black dots), line with an 80% confidence interval (green band), and the importance of outliers is annotated based on how far the dot is from the boundary of the confidence interval.
Figure 11
The components plot of weekly seasonality for both countries.
Figure 12
Outliers identification in data of COVID daily cases in Brazil using the Median Absolute Deviation (MAD).
Figure 13
Characterization of the distribution and percentage of the missing data in daily cases of Brazil.
Figure 14
Validation results of LSTM models for daily COVID-19 cases predictions for countries (Brazil (a), USA (b), India (c), Russia (d) and South Africa (e)) of Critical group.
Figure 15
Validation results of LSTM models for daily COVID-19 cases predictions for countries (Portugal (a), Italy (b), Switzerland (c), Australia (d) and China (e)) of Impact group.
Figure 16
Validation results of LSTM models for daily COVID-19 cases predictions for countries (New Zealand (a) and South Korea (b)) of Successful group.
Figure 17
Forecasting Results for the Best LSTM Models. In (a) we show the forecasting results of the best LSTM model for Brazil daily COVID-19 cases. We show in (b) the forecasting results of the best LSTM model for India daily COVID-19 cases. For countries that have controlled the COVID-19 evolution, in (c) we show the forecasting China, and in (d) we show the results for New Zealand in both countries, the predictions show a progressive growth in the number of cases.
Figure 18
The different behaviors of COVID-19 evolution in Rio de Janeiro favelas, based on the time series of daily cases. (a) shows the entire series; (b) shows a window for the first 80 days since the first reported case, in this scenario it is possible to observe a progressive growth in the number of infections; (c) shows a window having an extreme peak of cases; and (d) shows a window that the time series presents similar behavior to the first 80 days, this shows that controlling the epidemic in the favelas is difficult, and this problem grows when there is an underreporting of cases and deaths.
Figure 19
Validation results for Daily cases predictions in Rio de Janeiro favelas. The validation results show that the model can predict the different epidemic scenarios shown in (a,b,c, and d) in cities and regions.
Figure 20
Forecasting Results for Daily COVID-19 cases in Rio favelas.
Figure 21
Result after statistical imputation for anomaly values identified at COVID daily cases from Brazil.
Figure 22
Prediction result for forecasting with treated data. In (a) we show the forecasting result for untreated data of daily COVID-19 cases in Brazil. In (b) we show the same prediction under-treated data using the statistical imputation method. Here it is observed that the prediction results obey the time series regime, since the unexpected seasonality was treated and removed from the time series. Thus, we observe that the application of this statistical imputation method allowed us to produce a more reliable prediction that obeys the natural evolution behavior of COVID-19.
Figure A1.
Basic Structure of a RNN.
Figure A2
LSTM networks with sequences of inputs generating the outputs. In (a) we show a 1 to 1 model, in (b) we show the 1 to N model, in (c) we show the N to 1 model, and in (d) we show the N to N model. In this work, all the LSTM prediction models work as a N to N model.