# An Integrated Neural Network and SEIR Model to Predict COVID-19
## 6 Results  
The comparison between the SEIR model and the model combining SEIR with NN includes the Mean Square Error (MSE) and Root Mean Square Error (RMSE) plots in Figure 6a,b. In Figure 6a, we can see that the Mean Square Error (MSE) of predicted confirmed cases is 0.0312 in the SEIR model and 0.0277 in the model combining SEIR with NN on the first day. After that, the error gradually increases over time. Although the error increases greatly on day 4 to day 7 in the SEIR model, the rate decreases in the model combining SEIR with NN. Again from Figure 6b, it can be observed that the Root Mean Square Error (RMSE) of predicted confirmed cases in the model combining SEIR with NN is always lower than that of the SEIR model. Therefore, the performance of our integrated model is better than the SEIR model.  
The cross-validation result (mean accuracy) for the model combining SEIR with a neural network is shown in Table 3.  
According to Table 3, the best-testing mean accuracy was 91.7%, which was achieved in the last fold. However, the training and validation mean accuracies were achieved in the third fold and they were 97.7% and 95.3%, respectively.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Fold** & **Training Accuracy** & **Validation Accuracy** & **Testing Accuracy** \\ \hline Fold 1 & 0.974 & 0.931 & 0.915 \\ Fold 2 & 0.925 & 0.915 & 0.881 \\ Fold 3 & 0.977 & 0.953 & 0.911 \\ Fold 4 & 0.958 & 0.912 & 0.897 \\ Fold 5 & 0.947 & 0.935 & 0.917 \\ Average & 0.956 & 0.929 & 0.904 \\ Best & 0.977 & 0.953 & 0.917 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Cross validation result (mean) of the SEIR model with a neural network.  
Figure 6: (**a**) Mean Squear Error (MSE) and (**b**) Root Mean Squeare Error (RMSE).  
The dataset was trained using the SEIR, SIR, SEIR with NN, and SIR with NN models with the same parameters. The comparison between these models is shown in Table 4. From this table, it can be observed that the performance of our proposed model is better than previously implemented models from the perspective of Bangladesh.  
Figure 6(a) shows the change in Normalized Root Mean Square Error (NRMSE) over epochs. From Figure 6(a), it can be observed that the validation error decreases from 1.99 to 0.68 while the training error decreases from 2.00 to 0.66 after the first 100 epochs. After 100 epochs, both the validation and training error decrease gradually. For example, the validation error becomes 0.51, while the training error becomes 0.35 in the last epoch, which is 173.  
Figure 6(b) illustrates a comparison between the actual confirmed cases (which is shown using a blue line) and predicted confirmed cases by using the SEIR model, which is shown using a yellow line. Figure 6(b) presents a comparison between actual confirmed cases and predicted cases using the combined SEIR and NN model. The predicted confirmed cases using our combined SEIR and NN model are shown using a green line. From this figure, it can be concluded that the prediction of cases by using our combined SEIR and NN model is better than the SEIR model alone.  
The neural network is trained using the dataset. It generated a pattern while predicting the number of quarantined patients. Since the number of quarantined patients was deducted from the number of confirmed cases, the prediction of the integrated model was better than that of the normal SEIR model. Thus, the neural network helps the integrated model achieve a higher accuracy than the SEIR model. While the actual confirmed cases depend on the action taken by law-makers, the neural network works on the parameters of trained neurons. Hence, there is some fluctuation in the accuracy of this integrated model.