# A Hybrid Model Based on Improved Transformer and Graph Convolutional Network for COVID-19 Forecasting

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## Abstract

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## 1. Introduction

## 2. Literature Reviews

## 3. Datasets

#### 3.1. Confirmed Cased and Deaths Datasets

- Date: Observation date in mm/dd/yyyy.
- State: State of the USA.
- Cases: Cumulative counts of coronavirus cases till that date.
- Deaths: Cumulative counts of coronavirus deaths till that date.

#### 3.2. Vaccinations Dataset

- Date.
- State name.
- Daily count of vaccinations.

## 4. Methods

#### 4.1. Data Preprocessing

#### 4.2. Model

#### 4.2.1. Encoder

#### 4.2.2. Decoder

#### 4.3. Training Data

#### 4.4. Prediction Accuracy Measurement

## 5. Experimental Results

#### 5.1. Model Comparison

#### 5.2. Forecasting the Number of Confirmed Cases

#### 5.3. Forecasting the Number of Deaths

#### 5.4. Forecasting the Number of Administrated Vaccine Doses

## 6. Discussions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Paterlini, M. Closing borders is ridiculous’: The epidemiologist behind Sweden’s controversial coronavirus strategy. Nature
**2020**, 580, 574. [Google Scholar] - Roda, W.C.; Varughese, M.B.; Han, D.; Li, M.Y. Why is it difficult to accurately predict the COVID-19 epidemic? Infect. Dis. Model.
**2020**, 5, 271–281. [Google Scholar] - Ma, N.; Ma, W.; Li, Z. Multi-Model Selection and Analysis for COVID-19. Fractal Fract.
**2021**, 5, 120. [Google Scholar] - Scarpino, S.V.; Petri, G. On the predictability of infectious disease outbreaks. Nat. Commun.
**2019**, 10, 898. [Google Scholar] - Yang, Z.; Zeng, Z.; Wang, K.; Wong, S.S.; Liang, W.; Zanin, M.; He, J. Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions. J. Thorac. Dis.
**2020**, 12, 165. [Google Scholar] - Längkvist, M.; Karlsson, L.; Loutfi, A. A review of unsupervised feature learning and deep learning for time-series modeling. Pattern Recognit. Lett.
**2014**, 42, 11–24. [Google Scholar] - Benvenuto, D.; Giovanetti, M.; Vassallo, L.; Angeletti, S.; Ciccozzi, M. Application of the ARIMA model on the COVID-2019 epidemic dataset. Data Brief
**2020**, 29, 105340. [Google Scholar] - Hua, Y.; Zhao, Z.; Li, R.; Chen, X.; Liu, Z.; Zhang, H. Deep learning with long short-term memory for time series prediction. IEEE Commun. Mag.
**2019**, 57, 114–119. [Google Scholar] - Hwang, W.; Lei, W.; Katritsis, N.M.; MacMahon, M.; Chapman, K.; Han, N. Current and prospective computational approaches and challenges for developing COVID-19 vaccines. Adv. Drug Deliv. Rev.
**2021**, 172, 249–274. [Google Scholar] - Haiyan, W.; Nao, Y. Using a partial differential equation with google mobility data to predict COVID-19 in arizona. Math. Biosci. Eng.
**2020**, 17, 4891–4904. [Google Scholar] - Sarah, T.; Helmut, B.; Matthias, E. A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics. Math. Biosci. Eng.
**2022**, 19, 1213–1238. [Google Scholar] - Khubchandani, J.; Sharma, S.; Price, J.H.; Wiblishauser, M.J.; Sharma, M.; Webb, F.J. COVID-19 vaccination hesitancy in the United States: A rapid national assessment. J. Community Health
**2021**, 46, 270–277. [Google Scholar] - Shafiq, A.; Çolak, A.B.; Sindhu, T.N.; Lone, S.A.; Alsubie, A.; Jarad, F. Comparative Study of Artificial Neural Network versus Parametric Method in COVID-19 data Analysis. Results Phys.
**2022**, 38, 105613. [Google Scholar] - Pinter, G.; Felde, I.; Mosavi, A.; Ghamisi, P.; Gloaguen, R. COVID-19 pandemic prediction for Hungary; a hybrid machine learning approach. Mathematics
**2020**, 8, 890. [Google Scholar] - Torres, J.F.; Hadjout, D.; Sebaa, A.; Martínez-Álvarez, F.; Troncoso, A. Deep learning for time series forecasting: A survey. Big Data
**2021**, 9, 3–21. [Google Scholar] - Ma, W.; Zhao, Y.; Guo, L.; Chen, Y. Qualitative and quantitative analysis of the COVID-19 pandemic by a two-side fractional-order compartmental model. ISA Trans.
**2022**, 124, 144–156. [Google Scholar] - Kim, T.H.; Hong, K.J.; Do Shin, S.; Park, G.J.; Kim, S.; Hong, N. Forecasting respiratory infectious outbreaks using ED-based syndromic surveillance for febrile ED visits in a Metropolitan City. Am. J. Emerg. Med.
**2019**, 37, 183–188. [Google Scholar] - Chimmula, V.K.R.; Zhang, L. Time series forecasting of COVID-19 transmission in Canada using LSTM networks. Chaos Solitons Fractals
**2020**, 135, 109864. [Google Scholar] - Chandra, R.; Jain, A.; Singh Chauhan, D. Deep learning via LSTM models for COVID-19 infection forecasting in India. PLoS ONE
**2022**, 17, e0262708. [Google Scholar] - Roy, S.; Bhunia, G.S.; Shit, P.K. Spatial prediction of COVID-19 epidemic using ARIMA techniques in India. Modeling Earth Syst. Environ.
**2021**, 7, 1385–1391. [Google Scholar] - Alabdulrazzaq, H.; Alenezi, M.N.; Rawajfih, Y.; Alghannam, B.A.; Al-Hassan, A.A.; Al-Anzi, F.S. On the accuracy of ARIMA based prediction of COVID-19 spread. Results Phys.
**2021**, 27, 104509. [Google Scholar] - Shahid, F.; Zameer, A.; Muneeb, M. Predictions for COVID-19 with deep learning models of LSTM, GRU and Bi-LSTM. Chaos Solitons Fractals
**2020**, 140, 110212. [Google Scholar] - Rahimi, I.; Chen, F.; Gandomi, A.H. A review on COVID-19 forecasting models. Neural Comput. Appl.
**2021**, 1–11. [Google Scholar] - Li, Y.; Wang, Y.; Ma, K. Integrating Transformer and GCN for COVID-19 Forecasting. Sustainability
**2022**, 14, 10393. [Google Scholar] - Miralles-Pechuán, L.; Jiménez, F.; Ponce, H.; Martínez-Villaseñor, L. A methodology based on deep q-learning/genetic algorithms for optimizing covid-19 pandemic government actions. In Proceedings of the 29th ACM International Conference on Information Knowledge Management, New York, NY, USA, 19–23 October 2020; pp. 1135–1144. [Google Scholar]
- Shorten, C.; Khoshgoftaar, T.M.; Furht, B. Deep Learning applications for COVID-19. J. Big Data
**2021**, 8, 1–54. [Google Scholar] - Farsani, R.M.; Pazouki, E. A transformer self-attention model for time series forecasting. J. Electr. Comput. Eng. Innov. (JECEI)
**2021**, 9, 1–10. [Google Scholar] - La Gatta, V.; Moscato, V.; Postiglione, M.; Sperli, G. An epidemiological neural network exploiting dynamic graph structured data applied to the covid-19 outbreak. IEEE Trans. Big Data
**2021**, 7, 45–55. [Google Scholar] - Nytimes. Coronavirus (COVID-19) Data in the United States. Available online: https://github.com/nytimes/covid-19-data (accessed on 20 August 2022).
- Srk. Novel Corona Virus 2019 Dataset. Available online: https://www.kaggle.com/sudalairajkumar/novel-corona-virus-2019-dataset (accessed on 20 August 2022).
- Edouard, M. State-by-State Data on COVID-19 Vaccinations in the United States. Available online: https://ourworldindata.org/us-states-vaccinations (accessed on 20 August 2022).
- Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A.N.; Polosukhin, I. Attention is all you need. arXiv
**2017**, arXiv:1706.03762. [Google Scholar] - Bresson, X.; Laurent, T. Residual gated graph convnets. arXiv
**2017**, arXiv:1711.07553. [Google Scholar] - Yang, W.; Zhibin, C. Dynamic graph Conv-LSTM model with dynamic positional encoding for the large-scale traveling salesman problem. Math. Biosci. Eng.
**2022**, 19, 9730–9748. [Google Scholar] - Kipf, T.N.; Welling, M. Semi-supervised classification with graph convolutional networks. arXiv
**2016**, arXiv:1609.02907. [Google Scholar] - Ibrahimi, K.; Cherif, O.O.; Elkoutbi, M.; Rouam, I. Model to Improve the Forecast of the Content Caching based Time-Series Analysis at the Small Base Station. In Proceedings of the 7th International Conference on Wireless Networks and Mobile Communications (WINCOM’19), Fez, Morocco, 29 October–1 November 2019. [Google Scholar]
- Ibrahimi, K.; Serbouti, Y. Prediction of the Content Popularity in the 5G Network: Auto-Regressive, Moving-Average and Exponential Smoothing Approaches. In Proceedings of the International Conference on Wireless Networks and Mobile Communications (WINCOM’17), Rabat, Morocco, 1–4 November 2017. [Google Scholar]
- Adil, B.; Lhazmir, S.; Ghogho, M.; Benbrahim, H. COVID-19-Related Scientific Literature Exploration: Short Survey and Comparative Study. Biology
**2022**, 11, 1221. [Google Scholar]

Date | State | Cases | Deaths |
---|---|---|---|

2021/4/22 | Ohio | 1,060,119 | 19,033 |

2021/4/22 | Oklahoma | 446,246 | 6716 |

2021/4/22 | Oregon | 178,110 | 2484 |

2021/4/22 | Pennsylvania | 1,128,144 | 25,934 |

2021/4/22 | Puerto Rico | 158,827 | 2238 |

2021/4/22 | Rhode Island | 146,028 | 2660 |

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**MDPI and ACS Style**

Li, Y.; Ma, K.
A Hybrid Model Based on Improved Transformer and Graph Convolutional Network for COVID-19 Forecasting. *Int. J. Environ. Res. Public Health* **2022**, *19*, 12528.
https://doi.org/10.3390/ijerph191912528

**AMA Style**

Li Y, Ma K.
A Hybrid Model Based on Improved Transformer and Graph Convolutional Network for COVID-19 Forecasting. *International Journal of Environmental Research and Public Health*. 2022; 19(19):12528.
https://doi.org/10.3390/ijerph191912528

**Chicago/Turabian Style**

Li, Yulan, and Kun Ma.
2022. "A Hybrid Model Based on Improved Transformer and Graph Convolutional Network for COVID-19 Forecasting" *International Journal of Environmental Research and Public Health* 19, no. 19: 12528.
https://doi.org/10.3390/ijerph191912528