# Hybrid Deep Learning-Based Epidemic Prediction Framework of COVID-19: South Korea Case
## 3 Methodology of Hybrid Deep Learning Framework based on Meta-population  
This paper proposes a new and effective framework, integrating an ODE-based meta-population model and deep neural network modeling [39, 40] to explain two hypotheses. The first hypothesis is that COVID-19 spread can be analyzed using an SEIR model. It is explained in the previous section. The second hypothesis is that a hybrid deep model can predict the COVID-19 spread considering human mobility. This section and the following section explain the second hypothesis and test it with relevant case studies. The prediction of disease propagation is achieved using an extended SEIR model. Meta-population [41, 42, 43] refers to a group of separated sub-populations of the same species, which are connected by an interaction network. Large-scale epidemic outbreaks, such as global pandemics, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Research Studies** & **Application** & **Deep Learning Method** \\ \hline [PERSON] et al. [31] & - Observation of structural patterns of & \\  & amino acids & CNN \\  & - Interactions between local sequence motifs & \\  & using a CNN & \\ \hline [PERSON] et al. [32] & - DNN-based classifier for cancer prediction & DNN \\  & using DNA methylation data & \\ \hline [PERSON] et al. [33] & - Predicting phenotypic traits and diseases from & DNN \\  & omics data & \\ \hline [PERSON] et al. [34] & - Estimation of infectious pattern of & \\  & hand–foot–mouth disease data & LSTM \\ \hline [PERSON] et al. [35] & - Prediction of Alzheimer’s disease based on & CNN and recurrent neural \\  & neuroimaging data & network (RNN) \\ \hline [PERSON] et al. [36] & - Malaria prediction using ensemble algorithms & LSTM \\ \hline [PERSON] et al. [37] & - Forecasting air quality time series & Multitask learning pre-trained by \\  & & a deep-belief network. \\ \hline [PERSON] et al. [38] & - Detection of coronary artery disease based on & CNN \\  & facial photo & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Deep learning-based infection modeling and the related framework. can be modeled using the propagation of pathogens through a meta-population network. Intra-cities in a country are modeled as sub-populations, and their human mobility is modeled with the network connecting the sub-populations, as shown in Figure 2. Individual movements among intra-cities can be considered as disease carriers. This research focuses on two cities in South Korea: Daegu and Seoul. Daegu is the city where the outbreak started in South Korea, and Seoul is the capital city with the highest trend of ongoing transmission. A susceptible individual of sub-population \(i\) may contact infectious individuals from two sources: infectious individuals from the same sub-population, \(i\), or infectious visitors from sub-population \(j\). The system in the meta-population model is divided into several connected sub-populations, along which individuals travel via transportation. Inside each sub-population, homogeneous mixing is assumed. This indicates that the mathematical modeling can capture the travel flows among sub-populations. The epidemic process of an infectious disease can be decomposed into different timelines of each sub-population, which can be represented as spatial and temporal processes. Figure 3 shows the SEIR-based meta-population model considering human mobility. Equations (5)-(12) represent sets of ODEs of disease transmission between two sub-populations in the meta-population model. \[\frac{dS_{1}^{i}(t)}{dt}=\xi\cdot S_{1}^{i}(t)-a_{11}^{j}\cdot S_{1}^{i}(t)- \delta_{S}\cdot S_{1}^{i}(t)+\theta\cdot R_{1}^{i}(t)-\beta_{ji}\cdot I_{1}^{j }(t)\cdot S_{1}^{i}(t)+m_{ij}\cdot S_{1}^{i}(t)-m_{ji}\cdot S_{1}^{j}(t) \tag{5}\]  
Figure 3: SEIR compartment-based meta-population model considering human mobility. Figure 2: SEIR-based meta-population network in South Korea.