# COVID-19 Outbreak Prediction with Machine Learning
## 3 Results
In general, it can be claimed that GWO, by suggesting the best parameter values for the functions presented in Equations (6)-(13), increases outbreak prediction accuracy for COVID-19 in comparison with PSO and GA. Therefore, the functions derived by GWO were selected as the best predictors for this research. Tables 11-15 present the description and coefficients of the linear, logarithmic, quadratic, cubic, compound, power, exponential, and logistic equations estimated by GWO. Tables 11-15 also present the RMSE and \(r\)-square values for each equation fitted to data for China, Italy, Iran, Germany, and USA, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Model** & **POP. SIZE** & **Iteration** & **Processing Time** & **RMSE** & **Correlation Coefficient** \\ \hline \multirow{3}{*}{Italy} & GA & 300 & 500 & 79 s & 8163.1 & 0.995 \\  & PSO & 1000 & 500 & 48 s & 52,075,925.37 & 0.839 \\  & GWO & 500 & 1000 & 18 s & 12,585.79 & 0.951 \\ \hline \multirow{3}{*}{China} & GA & 300 & 500 & 71 s & 68,991.73 & 0.866 \\  & PSO & 1000 & 500 & 45 s & 80,104.27 & 0.865 \\  & GWO & 500 & 1000 & 17 s & 24,987.34 & 0.895 \\ \hline \multirow{3}{*}{Iran} & GA & 300 & 500 & 89 s & 1,436,025.84 & 0.767 \\  & PSO & 1000 & 500 & 70 s & 3,745,673.26 & 0.744 \\  & GWO & 500 & 1000 & 21 s & 13,635.01 & 0.864 \\ \hline \multirow{3}{*}{USA} & GA & 300 & 500 & 84 s & 457,051.4 & 0.974 \\  & PSO & 1000 & 500 & 30 s & 982.37 & 0.932 \\ \cline{1-1}  & GWO & 500 & 1000 & 15 s & 364.87 & 0.988 \\ \hline \multirow{3}{*}{Germany} & GA & 300 & 500 & 87 s & 8176.54 & 0.981 \\ \cline{1-1}  & PSO & 1000 & 500 & 74 s & 3278.55 & 0.998 \\ \cline{1-1}  & GWO & 500 & 1000 & 19 s & 431.97 & 0.998 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Accuracy statistics for the exponential model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Model** & **Pop. Size** & **Iteration** & **Processing Time** & **RMSE** & **Correlation Coefficient** \\ \hline \multirow{3}{*}{Italy} & GA & 300 & 500 & 72 s & 7063.4 & 0.983 \\  & PSO & 1000 & 500 & 40 s & 6150.52 & 0.982 \\  & GWO & 500 & 1000 & 13 s & 3450.96 & 0.991 \\ \hline \multirow{3}{*}{China} & GA & 300 & 500 & 65 s & 39,669.92 & 0.976 \\  & PSO & 1000 & 500 & 39 s & 19,365.58 & 0.987 \\  & GWO & 500 & 1000 & 12 s & 4078.99 & 0.989 \\ \hline \multirow{3}{*}{Iran} & GA & 300 & 500 & 83 s & 2,343,032.5 & 0.951 \\  & PSO & 1000 & 500 & 65 s & 92,755.53 & 0.975 \\  & GWO & 500 & 1000 & 15 s & 1031.6 & 0.991 \\ \hline \multirow{3}{*}{USA} & GA & 300 & 500 & 79 s & 1030.01 & 0.779 \\  & PSO & 1000 & 500 & 24 s & 1005.27 & 0.751 \\ \cline{1-1}  & GWO & 500 & 1000 & 11 s & 790.16 & 0.837 \\ \hline \multirow{3}{*}{Germany} & GA & 300 & 500 & 85 s & 1475.39 & 0.871 \\ \cline{1-1}  & PSO & 1000 & 500 & 69 s & 1387.94 & 0.916 \\ \cline{1-1}  & GWO & 500 & 1000 & 14 s & 1341.91 & 0.875 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Accuracy statistics for the power model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model Name** & **Description** & **RMSE** & **r-Square** \\ \hline Linear & \(\mathrm{R}=656.068\times\mathrm{x}-4527.69\) & 1981.97 & 0.891 \\ \hline Logarithmic & \(\mathrm{R}=-7921.009+5449.784\times\log(\mathrm{x})\) & 8995.52 & 0.574 \\ \hline Quadratic & \(\mathrm{R}=310.48-251.09\times\mathrm{x}+29.26\times\mathrm{x}^{2}\) & 310.027 & 0.997 \\ \hline Cubic & \(\mathrm{R}=902.33-463.02\times\mathrm{x}+46.07\times\mathrm{x}^{2}-0.36\times \mathrm{x}^{3}\) & 250.204 & 0.998 \\ \hline Compound & \(\mathrm{R}=13.26\times 1.33\mathrm{x}\) & 13,635.014 & 0.748 \\ \hline Power & \(\mathrm{R}=0.51\times\mathrm{x}^{3.09}\) & 1031.607 & 0.982 \\ \hline Exponential & \(\mathrm{R}=13.26\times\mathrm{EXP}(0.28\times\mathrm{x})\) & 13,635.014 & 0.748 \\ \hline Logistic & \(\mathrm{R}=21936.052/\left(1+\mathrm{EXP}(((4*1255.36)\times(14.66-\mathrm{x} )/21936.052)+2)\right)\) & 392.88 & 0.996 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Model description for Germany fitted by GWO.