## 3 Results and Discussion
### Discussion  
Based on the results of each case study, the following comments can be made:  
* Case of Saudi Arabia: From Table 3, the average MAPE of the three DL algorithms is around 25%, which is a moderate value. The higher the MAPE, the better the prediction. However, the three techniques' \(R^{2}\) is about 0.8 (1 is the ideal value). Other studies, such as [34; 35], have tackled the problem of predicting the number of COVID-19 infections in Saudi Arabia while covering different periods and datasets. Compared with other studies in the same territory, such as [35], our R-squared value can be considered good, since the period covered by our models is larger than the one covered by that study. This value can be considered good and reflects an interesting predictability of daily new infections in Saudi Arabia. The average RMSE is around 330 new infections per day. It can be observed also that RNN has been found to outperform GRU and LSTM, since it yielded the best MAPE, R2, and RMSE. Therefore, for the case study of Saudi Arabia, a less complex DL algorithm in terms of structure and training time is preferred for modeling daily new COVID-19 cases. Saudi Arabia's population is a mixture of nationalities, religions, and culture. In addition, Saudi Arabia is a host to two holy mosques at Makkah and Madinah, which are visited by Muslim people who perform Haji and Umrah, which may induce hidden features in terms of factors impacting new infections. The desert climate of Saudi Arabia may be one the factors negatively affecting daily new infections. From Figure 3a, it can be observed that the actual recorded new infections curve and the DL algorithms curves were almost the same during the first 100 days of the testing period (out-of-sample) and that there were some fluctuations during the remaining days of the same period, with a relatively small superiority for the RNN curve. * Case of Egypt: Based on Table 3's performance measures, the MAPE of the three algorithms is around 8%, which can be considered good. In addition, the values of RMSE are also good (around 160 cases per day). However, the values of \(R^{2}\) are around 0.75. This value can be considered moderate, which may be due to jumps in new infections recorded around days 55 and 82 during the out-of-sample testing period. As observed from Figure 3b, sudden high daily new infections were recorded and the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Country** & \multicolumn{3}{c}{**Saudi Arabia**} & \multicolumn{3}{c}{**Egypt**} \\ \hline DL model & MAPE (\%) & \(R^{2}\) & RMSE (case) & MAPE (\%) & \(R^{2}\) & RMSE (case) \\ \hline RNN & 12.09 & 0.9754 & 299 & 7.53 & 0.7984 & 164 \\ GRU & 13.30 & 0.9690 & 336 & 8.79 & 0.7609 & 179 \\ LSTM & 17.98 & 0.9438 & 453 & 8.44 & 0.7961 & 165 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance metrics of the RNN, GRU, and LSTM DL algorithms during the testing period (Saudi Arabia and Egypt). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Country** & \multicolumn{3}{c}{**Italy**} & \multicolumn{3}{c}{**India**} \\ \hline DL model & MAPE (\%) & \(R^{2}\) & RMSE (case) & MAPE (\%) & \(R^{2}\) & RMSE (case) \\ \hline RNN & 25.72 & 0.8245 & 2863 & 17.58 & 0.8747 & 3920 \\ GRU & 24.48 & 0.8499 & 2648 & 21.59 & 0.8759 & 3902 \\ LSTM & 25.86 & 0.8089 & 2987 & 26.27 & 0.8438 & 4378 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance metrics of RNN, GRU, and LSTM DL algorithms during the testing period (Italy and India). DL algorithms did not capture those jumps. As in the case of Saudi Arabia, the RNN has the best ability to capture the hidden features of the data for the case of Egypt. Therefore, an RNN can be recommended in this case study. * Case of Italy: The GRU was found to better model the dynamics of daily new infections since it yielded the lowest MAPE (24.4818%), the highest \(R^{2}\) (0.8499), and the lowest RMSE (2648 cases/day). However, the MAPE value can be considered high, which indicates bad predictability of the daily new infections using DL.