# COVID-19 Outbreak Prediction with Machine Learning
## 4 Discussion  
The parameters of several simple mathematical models (i.e., logistic, linear, logarithmic, quadratic, cubic, compound, power, and exponential) were fitted using GA, PSO, and GWO. The logistic model outperformed other methods and showed promising results based on training for 30 days. Extrapolation of the prediction beyond the original observation range of 30 days should not be expected to be realistic considering the new statistics. The fitted models generally showed low accuracy and also weak generalization ability for the five countries. Although the prediction for China was promising, the model was insufficient for extrapolation, as expected. In turn, the logistic GWO outperformed the PSO and GA, and the computational cost for GWO was reported as satisfactory. Consequently, for further assessment of the ML models, the logistic model fitted with GWO was used for comparative analysis. In the next step, for introducing the machine learning methods for time-series prediction, two scenarios were proposed. Scenario 1 considered four data samples from the progress of the infection from previous days, as reported in Table 2. The sampling for data processing was done weekly for scenario 1. However, scenario 2 was devoted to daily sampling for all previous consecutive days. Providing these two scenarios expanded the scope of this study. Training and test results for the two machine learning models (MLP and ANFIS) were considered for the two scenarios. A detailed investigation was also carried out to explore the most suitable number of neurons. For the MLP, the performances of using 8, 12, and 16 neurons were analyzed throughout the study. For the ANFIS, the membership function (MF) types of Tri, Trap, and Gauss were analyzed throughout the study. The five counties of Italy, China, Iran, Germany, and USA were considered. The performance of both ML models for these countries varied between the two different scenarios. Given the observed results, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Logistic** & **Linear by** & **Logarithmic** & **Quadratic** & **Power by** & **MLP** & **ANFIS** \\  & **by GWO** & **GWO** & **by GWO** & **GWO** & **GWO** & **MLP** & **ANFIS** \\ \hline Day 20 th & 431.027 & 1438.128 & \(-\)279.772 & 763.1467 & 400.0548 & 432.8991 & 431.8119 \\ \hline Day 40 th & 35,356.27 & 4006.551 & 9.199328 & 10,492.96 & 1624.405 & 35,355.14 & 35,355.72 \\ \hline Day 60 th & 55,043.44 & 6574.974 & 178.2366 & 30,100.56 & 3687.126 & 55,036.14 & 55,044.03 \\ \hline Day 80 th & 55,179.07 & 9143.397 & 298.1705 & 59,585.93 & 6595.829 & 55,179.05 & 55,178.88 \\ \hline Day 100 th & 55,179.67 & 11,711.82 & 391.1984 & 98,949.09 & 10,355.87 & 55,179.9 & 55,179.47 \\ \hline Day 120 th & 55,179.67 & 14,280.24 & 467.2078 & 148,190 & 14,971.42 & 55,179.92 & 55,179.42 \\ \hline Day 140 th & 55,179.67 & 16,848.66 & 531.4728 & 207,308.7 & 20,445.86 & 55,179.94 & 55,179.37 \\ \hline Day 150 th & 55,179.67 & 18,132.88 & 560.2357 & 240,572.3 & 23,506.09 & 55,179.96 & 55,179.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 20: The outbreak prediction for Germany through 150 days.