# Hybrid Deep Learning-Based Epidemic Prediction Framework of COVID-19: South Korea Case
## 3 Methodology of Hybrid Deep Learning Framework based on Meta-population
The two datasets [4] used for numerical testing are detailed in Table 4. The datasets are provided by Korea Centers for Disease Control and Prevention (KCDC). The datasets include incidence types and relevant human mobility information of COVID-19. This study analyzes its human mobility with the viewpoint of inner/intra-city mobility. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data Characteristics** & **Seoul** & **Daegu** \\ \hline Time period & 12 March 2020–14 August 2020 & 8 April 2020–4 September 2020 \\ Characteristics of the basic reproduction number (\(R_{t}\)) & Highest value is 2.65 on 18 August 2020 & Highest value is 7.25 on 26 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Datasets of COVID-19 cases in Seoul and Daegu. Figure 4: Framework of a meta-population network based on deep learning. The basic reproduction number, \((R_{t})\), in both cities follows the patterns shown in Figure 5.  
Then, the proposed framework is compared with a general LSTM model and a general deep neural network model. The LSTM and DNN models are trained using the same dataset. Moreover, this study uses two different modules in the deep learning core of the proposed method. Table 5 shows the characteristics of the compared methods. As shown in Table 5, the architecture and hyper-parameters of the methods are determined using the COVID-19 dataset in South Korea. Figure 6a shows the training errors (general loss and Root Mean Square Error (RMSE)) of the proposed hybrid deep learning framework incorporating the meta-population model and LSTM model. The loss is calculated as the gap between the actual reproduction rate of COVID-19 and the estimated reproduction rate using the proposed method. The architecture and relevant hyper-parameters such as the number of layers, the used optimizer, and learning are determined with experimental analyses. Figure 6b shows performance comparison with methods with different numbers of layers. Using the experimental tests, the number of layers and other hyper-parameters are determined. Figure 5: Patterns of the basic reproduction number in **(a)** Seoul and **(b)** Daegu. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{2}{c}{**Proposed Hybrid Deep Learning Framework**} & \multirow{2}{*}{**LSTM**} & \multirow{2}{*}{**DNN**} \\ \cline{2-2} \cline{4-5}  & **Core Deep Learning** & & & \\  & **Module (LSTM)** & & & \\ \hline \multirow{3}{*}{Input} & ODE-based epidemic & ODE-based epidemic & & \\  & estimation and & estimation and & historical data of & \\  & historical data of & & COVID-19 at t-1 & \\  & COVID-19 at t-1 & & COVID-19 at t-1 & \\ \hline \multirow{3}{*}{Output} & Parameters of & Parameters of & Parameters of & Parameters of & \\  & meta-population & meta-population & meta-population & meta-population \\  & model & model & model & model \\ \hline Number of layers & 4 & 4 & 4 & 4 \\ \hline Activation & tanh, sigmoid & ReLU & tanh, sigmoid & ReLU \\ \hline Number of epochs & 300 & 300 & 300 & 300 \\ \hline Optimizer & Adam & Adam & Adam & Adam \\ \hline Learning rate & 0.001 & 0.001 & 0.001 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Characteristics of the compared methods. Table 6 illustrated in Figure 7 show several \(R_{t}\) values estimated using the different frameworks. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Target Date**} & \multirow{2}{*}{**Actual Value**} & **Proposed** & **Proposed** & \multirow{2}{*}{**LSTM**} & \multirow{2}{*}{**DNN**} \\  & & **Framework** & **with LSTM** & **with DNN** & \\ \hline
17 March & 1.36 & 1.49 & 1.75 & 1.45 & 1.29 \\
13 April & 0.89 & 0.98 & 0.87 & 1.02 & 0.73 \\
15 May & 1.31 & 1.20 & 1.77 & 1.11 & 1.31 \\
4 June & 1.26 & 1.20 & 1.64 & 1.16 & 1.31 \\
4 July & 0.93 & 0.96 & 0.92 & 0.97 & 0.73 \\
6 August & 0.94 & 0.95 & 0.93 & 0.96 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons of the estimated \(R_{t}\) value for Seoul.