# Hybrid Deep Learning-Based Epidemic Prediction Framework of COVID-19: South Korea Case
## 3 Methodology of Hybrid Deep Learning Framework based on Meta-population
Figure 6: Training progress and performance tests, (**a**) Training progress with respect to RMSE and general loss, and (**b**) Performance comparison with different number of the hidden layers using the Seoul dataset. The value of the basic reproduction number obtained using the four methods are also compared with the actual number of infected people, as shown in Figure 8.  
Figure 8: Estimation of the \(R_{t}\) for Seoul, (**a**) the proposed meta-population + long short-term memory (LSTM) model, (**b**) the proposed meta-population + deep neural network (DNN) model, (**c**) LSTM only, and (**d**) DNN only. Figure 7: Actual and estimated value of reproduction number using the proposed method and conventional machine learning methods. A comparison between the frameworks presented in Table 7 is illustrated in Figure 9. Figure 9 proves experimentally that the proposed method, incorporating the meta-population model and LSTM, has the best performance compared to the other three methods. The number of infected people obtained using the four methods are also compared with the actual number of infected people, as shown in Figure 10. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Target Date** & **Actual Value** & \
\begin{tabular}{c} **Proposed** \\ **Framework** \\ **with LSTM** \\ \end{tabular} &
\begin{tabular}{c} **Proposed** \\ **Framework** \\ **with DNN** \\ \end{tabular} & **LSTM** & **DNN** \\ \hline
17 March & 12 & 12 & 9 & 8 & 1 \\
13 April & 8 & 8 & 4 & 6 & 1 \\
15 May & 14 & 14 & 11 & 8 & 1 \\
4 June & 14 & 14 & 11 & 14 & 2 \\
4 July & 7 & 7 & 5 & 11 & 1 \\
6 August & 9 & 9 & 7 & 9 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Estimated number of infected people on target dates using the proposed method and conventional machine learning methods. Figure 10: _Cont._  
Figure 9: Actual and estimated numbers of infected people using the proposed method and conventional machine learning methods. The numerical tests indicate that the proposed method has better performance than other methods. In particular, the hybrid deep learning framework using the meta-population model and LSTM is more accurate than that using the meta-population model and DNN, as indicated by obtaining the least error value. Similar tests were performed for the cases in Daegu; the results are shown in Table 8, which is illustrated in Figure 11.  
The actual and predicted value of the reproduction number for Daegu using the proposed method are illustrated in Figure 12.  
Figure 11: Actual and estimated value of reproduction number. Figure 10: Estimation of the \(l_{t}\) for Seoul using (**a**) the proposed meta-population + LSTM model, (**b**) the proposed meta-population + DNN model, (**c**) LSTM only, and (**d**) DNN only. The actual and predicted numbers of infected people using the four methods shown in Table 9 are illustrated in Figure 13.  
Figure 12: Estimation of the \(R_{t}\) for Daegu using (**a**) the proposed meta-population + LSTM model, (**b**) the proposed meta-population + DNN model, (**c**) LSTM only, and (**d**) DNN only. Figure 13: Actual and estimated number of infected people. The actual and predicted numbers of infected people in Daegu using the four methods are illustrated in Figure 10:0 The numerical tests indicate that the proposed method has better performance than other methods. In particular, the hybrid deep learning framework using the meta-population model and LSTM is more accurate than that using the meta-population model and DNN considering the lowest error achieved. The overall performances are provided in Figure 10:1 The comparison results are calculated as the averages of 50 repetitions. The averages are provided in Table 10, and their standard deviations are less than 2.28 in \(I_{t}\) and 0.20 in \(R_{t}\), respectively. The effectiveness of hybrid deep learning for predicting the COVID-19 epidemic pattern is proven experimentally by achieving the least RMSE error compare with the other three methods.