COVID-19 Spatio-Temporal Evolution Using Deep Learning at a European Level
<p>A non-linear sequential model to predict daily confirmed cases and deaths due to the COVID-19 pandemic.</p> "> Figure 2
<p>Daily hospitalization and intensive care unit submissions due to the COVID-19 pandemic.</p> "> Figure 3
<p>Comparison between the LSTM and GRU structures.</p> "> Figure 4
<p>Deep learning architectures for COVID-19 predictions. The notation <span class="html-italic">n</span> is used for the <span class="html-italic">n</span>-th input that is ingested into the model.</p> "> Figure 5
<p>Austria new cases per million QQ-Plot for each method.</p> "> Figure 6
<p>Austria’s new cases per million real (blue line) and predicted (green line) values for each method, using training, validation and test datasets. The red line divides the train-validation (right size) and the test (left side) datasets.</p> "> Figure 7
<p>France new cases per million QQ-Plot for each method.</p> "> Figure 8
<p>France new cases per million real (blue line) and predicted (green line) values for each method, using the training, validation, and test datasets. The red line divides the train-validation (right size) and the test (left side) datasets.</p> "> Figure 9
<p>Italy’s new deaths per million QQ-Plot for each method.</p> "> Figure 10
<p>Italy’s new deaths per million real (blue line) and predicted (green line) values for each method, using the training, validation and test datasets. The red line divides the train-validation (right size) and the test (left side) datasets.</p> "> Figure 11
<p>Romania’s new deaths per million QQ-Plot for each method.</p> "> Figure 12
<p>Romania’s new deaths per million real (blue line) and predicted (green line) values for each method, using the training, validation, and test datasets. The red line divides the train-validation (right size) and the test (left side) datasets.</p> "> Figure 13
<p>Denmark ICU-Patients per million QQ-Plot for each method.</p> "> Figure 14
<p>Denmark ICU-Patients per million real (blue line) and predicted (green line) values for each method, using the training, validation, and test datasets. The red line divides the train-validation (right size) and the test (left side) datasets.</p> "> Figure 15
<p>Estonia ICU-Patients per million QQ-Plot for each method.</p> "> Figure 16
<p>Estonia ICU-Patients per million real (blue line) and predicted (green line) values for each method, using the training, validation and test datasets. The red line divides the train-validation (right size) and the test (left side) datasets.</p> "> Figure 17
<p>Austria HOSP-Patients per million QQ-Plot for each method.</p> "> Figure 18
<p>Austria’s HOSP-Patients per million real (blue line) and predicted (green line) values for each method, using the training, validation, and test datasets. The red line divides the train-validation (right size) and the test (left side) datasets.</p> "> Figure 19
<p>France HOSP-Patients per million QQ-Plot for each method.</p> "> Figure 20
<p>France HOSP-Patients per million real (blue line) and predicted (green line) values for each method, using the training, validation, and test datasets. The red line divide the train-validation (right size) and the test (left side) datasets.</p> ">
Abstract
:1. Introduction
- Implementing a robust deep learning model with global coverage that approximates the non-linear character of the multi-variable model of COVID-19 evolution. Each country has different timeseries data related to the COVID-19 pandemic. These timeseries do not follow the same distribution, and it is thus challenging to create a unique model that incorporates all this information into a unique model, achieving good performance for every single country. The contribution of our model is that except for the timeseries cases per country, we have added additional features in our analysis to help the model gain the domain knowledge for each country and boost the performance of the deep learning model;
- Aiding policy makers and researchers in understanding the evolution of the COVID-19 pandemic and thus acting as a supporting tool for health management. In literature, there are various techniques for COVID-19 cases and deaths predictions, however, techniques that are applied for hospitalizations and ICU management are limited, yet they are the most important for crisis management scenarios. This study proposes models that predict all the above information at the EU level;
- Assessing the impact of the policy measures on the COVID-19 progression. Policy measures are incorporated as input variables into the model. Their variability and the different response strategies are included in the model and affect the COVID-19 progression.
2. Related Work
3. Sequential Models for COVID-19 Evolution
3.1. Mathematical Formulation
3.1.1. A Non-Linear Sequential Model to Predict Daily Confirmed Cases and Deaths Due to COVID-19 Pandemic
3.1.2. A Non-Linear Sequential Model to Predict Intensive Care Admissions and Hospitalizations due to COVID-19
3.2. Approximating Non-Linear Relationships Using Deep Learning Architectures
3.2.1. Recurrent Neural Networks
3.2.2. Long Short Term Memory Networks
3.2.3. Gated Recurrent Networks
3.2.4. Hybrid Networks
3.3. The Proposed Deep Learning Architectures
4. Experimental Results
4.1. Dataset Description and Performance Evaluation Metrics
4.2. Case Study 1: New Cases per Million and New Deaths per Million
4.2.1. New Cases per Million Analysis
4.2.2. Daily Deaths per Million Analysis
4.3. Case Study 2: ICU Patients Admissions and Hospitalizations per Million of People
4.3.1. ICU-Patients per Million Results
4.3.2. HOSP-Patients per Million Results
4.4. Average Global European Model Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ARIMA | Autoregressive Integrated Moving Average |
Conv1D | One Dimension Convolution |
LSTM | Long Short Term Memory |
GRU | Gated Recurrent Units |
SimpleRNN | Simple Recurrent Neural Network |
MAE | Mean Absolute Error |
RMSE | Root Mean Square Error |
ICU | Intensive Care Unit |
HOSP | Hospitalized |
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Index | Variable | Column Data |
---|---|---|
1 | School Closures | |
2 | Workplace Closures | |
3 | Cancel Public Events | |
4 | Restriction in Gatherings | |
5 | Close Public Transport | |
6 | Stay Home Requirements | |
7 | Public Information Campaigns | |
8 | Restrictions Internal Movements | |
9 | International Travel Controls | |
10 | Facial Coverings | |
11 | New Cases per Million | |
12 | New Deaths per Million |
Index | Variable | Column Data |
---|---|---|
1 | School Closures | |
2 | Workplace Closures | |
3 | Cancel Public Events | |
4 | Restriction in Gatherings | |
5 | Close Public Transport | |
6 | Stay Home Requirements | |
7 | Public Information Campaigns | |
8 | Restrictions Internal Movements | |
9 | International Travel Controls | |
10 | Facial Coverings | |
11 | ICU-Patients per Million | |
12 | HOSP-Patients per Million |
New Cases per Million | ||||||
---|---|---|---|---|---|---|
Methods | RMSE | MAE | RMSE | MAE | RMSE | MAE |
Austria | Belgium | Denmark | ||||
Conv1D-LSTM | 22.25 | 16.23 | 99.31 | 75.02 | 59.71 | 46.60 |
GRU | 20.49 | 14.85 | 90.62 | 69.98 | 60.32 | 46.72 |
LSTM | 18.80 | 13.32 | 91.76 | 70.94 | 64.50 | 49.93 |
SimpleRNN | 22.67 | 17.02 | 93.38 | 66.95 | 46.20 | 32.51 |
Methods | RMSE | MAE | RMSE | MAE | RMSE | MAE |
Estonia | Finland | France | ||||
Conv1D-LSTM | 76.43 | 55.75 | 36.17 | 26.10 | 121.99 | 82.83 |
GRU | 61.25 | 44.80 | 33.45 | 22.81 | 108.13 | 73.20 |
LSTM | 72.71 | 54.37 | 34.46 | 23.75 | 111.92 | 76.21 |
SimpleRNN | 41.90 | 32.10 | 35.85 | 24.22 | 101.62 | 67.71 |
Germany | Ireland | Italy | ||||
Conv1D-LSTM | 35.97 | 21.93 | 62.89 | 46.35 | 32.14 | 24.77 |
GRU | 33.22 | 19.25 | 56.96 | 41.64 | 27.20 | 21.20 |
LSTM | 33.16 | 18.79 | 62.25 | 45.02 | 26.75 | 20.66 |
SimpleRNN | 37.67 | 24.71 | 34.93 | 25.76 | 21.53 | 16.83 |
The Netherlands | Portugal | Romania | ||||
Conv1D-LSTM | 138.46 | 101.10 | 68.83 | 47.10 | 26.59 | 18.73 |
GRU | 119.79 | 88.70 | 59.81 | 41.86 | 17.83 | 14.15 |
LSTM | 140.93 | 102.03 | 60.46 | 41.34 | 16.52 | 12.20 |
SimpleRNN | 85.96 | 61.99 | 46.16 | 32.48 | 17.22 | 13.35 |
New Deaths per Million | ||||||
---|---|---|---|---|---|---|
Methods | RMSE | MAE | RMSE | MAE | RMSE | MAE |
Austria | Belgium | Denmark | ||||
Conv1D-LSTM | 0.42 | 0.33 | 0.56 | 0.43 | 0.61 | 0.56 |
GRU | 0.41 | 0.32 | 0.48 | 0.37 | 0.50 | 0.45 |
LSTM | 0.45 | 0.38 | 0.50 | 0.39 | 0.60 | 0.55 |
SimpleRNN | 0.43 | 0.34 | 0.49 | 0.38 | 0.49 | 0.44 |
Estonia | Finland | France | ||||
Conv1D-LSTM | 0.99 | 0.80 | 0.43 | 0.37 | 0.77 | 0.60 |
GRU | 0.96 | 0.77 | 0.44 | 0.37 | 0.63 | 0.48 |
LSTM | 1.00 | 0.81 | 0.45 | 0.39 | 0.67 | 0.53 |
SimpleRNN | 0.97 | 0.74 | 0.39 | 0.30 | 0.64 | 0.50 |
Germany | Ireland | Italy | ||||
Conv1D-LSTM | 0.57 | 0.39 | 1.08 | 0.77 | 0.40 | 0.28 |
GRU | 0.54 | 0.36 | 1.02 | 0.66 | 0.36 | 0.25 |
LSTM | 0.55 | 0.38 | 1.08 | 0.67 | 0.39 | 0.30 |
SimpleRNN | 0.58 | 0.43 | 1.03 | 0.69 | 0.41 | 0.31 |
The Netherlands | Portugal | Romania | ||||
Conv1D-LSTM | 0.75 | 0.62 | 0.46 | 0.35 | 2.47 | 1.44 |
GRU | 0.68 | 0.54 | 0.39 | 0.29 | 2.31 | 1.30 |
LSTM | 0.69 | 0.58 | 0.46 | 0.37 | 2.36 | 1.38 |
SimpleRNN | 0.75 | 0.61 | 0.46 | 0.37 | 2.29 | 1.33 |
Intensive Care Unit Patients per Million | ||||||
---|---|---|---|---|---|---|
Methods | RMSE | MAE | RMSE | MAE | RMSE | MAE |
Austria | Belgium | Denmark | ||||
Conv1D-LSTM | 1.44 | 1.08 | 2.16 | 1.59 | 0.62 | 0.46 |
GRU | 1.33 | 1.01 | 1.82 | 1.47 | 0.74 | 0.60 |
LSTM | 1.50 | 1.17 | 3.33 | 2.72 | 0.74 | 0.63 |
SimpleRNN | 1.57 | 1.27 | 2.76 | 2.46 | 1.34 | 1.26 |
Estonia | Finland | France | ||||
Conv1D-LSTM | 2.48 | 1.76 | 0.90 | 0.66 | 2.31 | 1.80 |
GRU | 2.17 | 1.65 | 1.01 | 0.85 | 1.89 | 1.60 |
LSTM | 2.91 | 2.27 | 0.79 | 0.64 | 3.43 | 2.66 |
SimpleRNN | 2.74 | 2.13 | 2.35 | 2.26 | 2.91 | 2.43 |
Germany | Ireland | Italy | ||||
Conv1D-LSTM | 1.92 | 1.51 | 0.92 | 0.71 | 1.24 | 0.91 |
GRU | 1.24 | 1.05 | 1.03 | 0.73 | 1.52 | 1.12 |
LSTM | 1.21 | 0.94 | 0.91 | 0.72 | 1.49 | 1.17 |
SimpleRNN | 1.54 | 1.32 | 1.45 | 1.34 | 1.45 | 1.20 |
The Netherlands | Portugal | Romania | ||||
Conv1D-LSTM | 1.49 | 1.22 | 0.94 | 0.74 | 3.19 | 2.44 |
GRU | 1.33 | 1.12 | 1.48 | 1.24 | 2.19 | 1.72 |
LSTM | 1.54 | 1.32 | 1.16 | 0.87 | 3.38 | 2.99 |
SimpleRNN | 1.32 | 1.09 | 1.18 | 0.99 | 2.76 | 2.48 |
Hospitalized Patients per Million | ||||||
---|---|---|---|---|---|---|
Methods | RMSE | MAE | RMSE | MAE | RMSE | MAE |
Austria | Belgium | Denmark | ||||
Conv1D-LSTM | 9.29 | 8.18 | 13.23 | 11.30 | 10.67 | 10.05 |
GRU | 10.25 | 9.15 | 16.57 | 14.18 | 10.67 | 10.14 |
LSTM | 4.18 | 3.52 | 5.41 | 3.94 | 5.68 | 4.72 |
SimpleRNN | 8.71 | 7.87 | 7.03 | 6.20 | 6.55 | 5.82 |
Estonia | Finland | France | ||||
Conv1D-LSTM | 12.25 | 10.02 | 17.89 | 17.48 | 17.21 | 14.54 |
GRU | 9.15 | 7.35 | 19.54 | 18.10 | 18.00 | 13.00 |
LSTM | 15.26 | 11.85 | 4.45 | 3.63 | 13.14 | 10.95 |
SimpleRNN | 13.28 | 8.03 | 4.39 | 3.04 | 10.18 | 9.33 |
Germany | Ireland | Italy | ||||
Conv1D-LSTM | 11.01 | 9.74 | 15.65 | 15.16 | 17.26 | 15.49 |
GRU | 16.56 | 15.19 | 15.18 | 14.70 | 13.60 | 12.13 |
LSTM | 3.79 | 3.50 | 5.05 | 3.49 | 8.62 | 6.69 |
SimpleRNN | 8.77 | 7.22 | 8.09 | 7.08 | 9.78 | 8.46 |
The Netherlands | Portugal | Romania | ||||
Conv1D-LSTM | 10.25 | 8.11 | 16.31 | 15.42 | 10.23 | 8.41 |
GRU | 12.57 | 9.84 | 14.69 | 13.24 | 11.87 | 9.42 |
LSTM | 7.63 | 6.50 | 7.30 | 6.01 | 12.03 | 10.25 |
SimpleRNN | 8.33 | 7.29 | 8.26 | 7.35 | 10.02 | 7.32 |
Global European Model Average Errors | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Country | Conv1D-LSTM | GRU | LSTM | SimpleRNN | ARIMA | |||||
RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE | RMSE | MAE | |
New Cases per Million | 384.70 | 214.86 | 264.03 | 150.66 | 332.36 | 184.50 | 365.94 | 191.47 | 645.13 | 536.47 |
New Deaths per Million | 6.08 | 3.26 | 4.89 | 2.60 | 4.13 | 2.28 | 5.39 | 2.91 | 12.22 | 11.01 |
ICU-Patients per Million | 8.62 | 5.94 | 6.92 | 4.80 | 11.90 | 8.35 | 10.80 | 7.23 | 41.09 | 36.75 |
HOSP-Patients per Million | 89.05 | 57.46 | 87.53 | 56.05 | 85.28 | 50.81 | 104.44 | 60.11 | 318.92 | 282.08 |
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Kavouras, I.; Kaselimi, M.; Protopapadakis, E.; Bakalos, N.; Doulamis, N.; Doulamis, A. COVID-19 Spatio-Temporal Evolution Using Deep Learning at a European Level. Sensors 2022, 22, 3658. https://doi.org/10.3390/s22103658
Kavouras I, Kaselimi M, Protopapadakis E, Bakalos N, Doulamis N, Doulamis A. COVID-19 Spatio-Temporal Evolution Using Deep Learning at a European Level. Sensors. 2022; 22(10):3658. https://doi.org/10.3390/s22103658
Chicago/Turabian StyleKavouras, Ioannis, Maria Kaselimi, Eftychios Protopapadakis, Nikolaos Bakalos, Nikolaos Doulamis, and Anastasios Doulamis. 2022. "COVID-19 Spatio-Temporal Evolution Using Deep Learning at a European Level" Sensors 22, no. 10: 3658. https://doi.org/10.3390/s22103658