# Hybrid Deep Learning-Based Epidemic Prediction Framework of COVID-19: South Korea Case
## 3 Methodology of Hybrid Deep Learning Framework based on Meta-population
\[\Delta S_{j}(t)=-\frac{\beta_{j}(t)}{N_{j}^{s}(t)}I_{j}(t)S_{j}(t)-\frac{\alpha _{j}(t)}{N_{j}^{s}(t)}E_{j}(t)S_{j}(t)+\sum_{i=1}^{N}\left(S_{i}(t)m_{ij}(t) \right)-\left(S_{j}(t)\sum\
olimits_{i=1}^{N}m_{ji}(t)\right) \tag{21}\]  
\[\Delta R_{j}(t)=\gamma_{j}(t)I_{j}(t) \tag{22}\]  
The population of city \(j\) on day \(t\) increases or decreases owing to intercity migration, as shown in Equation (23), where \(\Delta P_{j}(t)=P_{j}(t+1)-P_{j}(t)\). \[\Delta P_{j}(t)=\sum_{i=1}^{N}\left(P_{i}(t)m_{ij}(t)-P_{j}(t)\sum\
olimits_{ i=1}^{N}m_{ji}(t)\right) \tag{23}\]  
Then, the instant susceptible population in city \(j\) at time \(t\) is defined in Equation (24), where \(\Delta N_{j}^{s}(t)=N_{j}^{s}(t+1)-N_{j}^{s}(t)\). \[ \begin{split}\Delta N_{j}^{s}(t)=k_{I}\left[\sum\limits_{i=1}^{N }\left(I_{i}(t)m_{ij}(t)\right)-\left(I_{j}(t)\sum\
olimits_{i=1}^{N}m_{ji}( t)\right)\right]\\ +\sum\limits_{i=1}^{N}\left(E_{i}(t)m_{ij}(t)\right)-\left(E_{j} (t)\sum\
olimits_{i=1}^{N}m_{ji}(t)\right)\\ +\sum\limits_{i=1}^{N}\left(S_{i}(t)m_{ij}(t)\right)-\left(S_{j} (t)\sum\
olimits_{i=1}^{N}m_{ji}(t)\right)\end{split}  \tag{24}\]  
As shown in Equation (25), the parameters in the provided meta-population model are estimated using the historical COVID-19 tracking data. \[\phi_{j(t)}=\left\{\alpha_{j}(t),\beta_{j}(t),\gamma_{j}(t),\lambda_{j}(t), \tau_{j}(t),I_{j}(t_{0})\right\} \tag{25}\]  
An estimated number of infected cases in each city is generated using the provided meta-population. However, it is difficult to capture accurate parameters using historical data. The wrong estimation may result in a biased erratic result. To overcome this issue, this study incorporates a meta-population model with a deep learning approach. Figure 4 shows the architecture of the hybrid approach using deep learning algorithms. As shown in Figure 4, the meta-population model with the estimated parameter generates two types of parameters: the time-dependent reproduction number, \(R_{t}\), and the number of susceptible-exposed-infected-recovered people. However, it is difficult to obtain accurate results compared to the real COVID-19 data at time \(t\). For this reason, the gap is minimized using a deep learning model; a general DNN or LSTM model is considered and tested. Two output data from the previous meta-population model and the infected number of people from the real COVID-19 data (at time \(t\)-1) are used as input sets in the deep learning model. Then, the output of the DNN model is the parameters of the meta-population model. The weight in the hybrid deep learning model is updated with the minimization of error. The error is the gap between the real infected people at time \(t\) and the estimated infected people from the meta-population model at time \(t\). The backpropagation method was used to minimize the error. The novelty of this hybrid deep learning method enhances accuracy in the parameter estimation of the SEIR-based meta-population model. The following section shows the effectiveness of the proposed hybrid deep learning model through numerical analysis, and the results will be compared with the existing LSTM and DNN methods. Numerical Analysis and Performance Evaluation Using the Meta-Population-Based Hybrid Deep Learning Framework  
To demonstrate the effectiveness of the proposed framework, this study deploys data of COVID-19 cases in South Korea. As the transmission of the disease is still ongoing, the parameter affecting the simulation result has been changed dynamically with time. This study focuses on observing how the established meta-population model leads to a higher accuracy for outbreak prediction using parametric analysis. The parameters were learned using the DNN model. The approach allows us to determine the real-time dynamics of the reproduction number and analyze its relationship with other factors directly affecting the epidemic spread, such as the number of daily infected cases and people's mobility levels.