# Soft Computing Paradigms to Find the Numerical Solutions of a Nonlinear Influenza Disease Model
## 3 Simulations and Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(u\)} & \multicolumn{6}{c}{\(R(u)\)} \\ \cline{2-7}  & **Min** & **Max** & **Med** & **Mean** & **S.I.R** & **SD** \\ \hline
0 & \(6.2366\times 10^{-6}\) & \(1.4851\times 10^{-2}\) & \(1.8505\times 10^{-4}\) & \(2.1832\times 10^{-3}\) & \(3.8502\times 10^{-4}\) & \(2.9318\times 10^{-3}\) \\ \hline
0.1 & \(2.4607\times 10^{-3}\) & \(1.9038\times 10^{-1}\) & \(1.8634\times 10^{-1}\) & \(8.0571\times 10^{-2}\) & \(3.2715\times 10^{-2}\) & \(6.2894\times 10^{-2}\) \\ \hline
0.2 & \(2.3532\times 10^{-3}\) & \(1.7746\times 10^{-1}\) & \(1.7489\times 10^{-1}\) & \(8.2758\times 10^{-2}\) & \(2.4669\times 10^{-2}\) & \(5.9498\times 10^{-2}\) \\ \hline
0.3 & \(2.3392\times 10^{-3}\) & \(1.6039\times 10^{-1}\) & \(1.5817\times 10^{-1}\) & \(8.1157\times 10^{-2}\) & \(2.0756\times 10^{-2}\) & \(5.4314\times 10^{-2}\) \\ \hline
0.4 & \(1.7447\times 10^{-3}\) & \(1.4608\times 10^{-1}\) & \(1.4106\times 10^{-1}\) & \(7.9023\times 10^{-2}\) & \(1.8914\times 10^{-2}\) & \(4.8288\times 10^{-2}\) \\ \hline
0.5 & \(1.4329\times 10^{-3}\) & \(1.3259\times 10^{-1}\) & \(1.2623\times 10^{-1}\) & \(7.6406\times 10^{-2}\) & \(1.7328\times 10^{-2}\) & \(4.3191\times 10^{-2}\) \\ \hline
0.6 & \(6.3834\times 10^{-4}\) & \(1.1983\times 10^{-1}\) & \(1.1406\times 10^{-1}\) & \(7.3296\times 10^{-2}\) & \(1.5985\times 10^{-2}\) & \(3.9221\times 10^{-2}\) \\ \hline
0.7 & \(1.0809\times 10^{-3}\) & \(1.0806\times 10^{-1}\) & \(1.0395\times 10^{-1}\) & \(6.9938\times 10^{-2}\) & \(1.4990\times 10^{-2}\) & \(3.5981\times 10^{-2}\) \\ \hline
0.8 & \(9.6811\times 10^{-4}\) & \(9.7331\times 10^{-2}\) & \(9.4041\times 10^{-2}\) & \(6.6416\times 10^{-2}\) & \(1.3740\times 10^{-2}\) & \(3.3132\times 10^{-2}\) \\ \hline
0.9 & \(6.8779\times 10^{-4}\) & \(8.7620\times 10^{-2}\) & \(8.5302\times 10^{-2}\) & \(6.2713\times 10^{-2}\) & \(1.2596\times 10^{-2}\) & \(3.0469\times 10^{-2}\) \\ \hline
1 & \(3.8749\times 10^{-4}\) & \(7.8853\times 10^{-2}\) & \(7.7195\times 10^{-2}\) & \(5.8825\times 10^{-2}\) & \(1.0930\times 10^{-2}\) & \(2.7874\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical measures for the nonlinear influenza disease model based \(R(u)\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(u\)} & \multicolumn{6}{c}{\(C(u)\)} \\ \cline{2-7}  & **Min** & **Max** & **Med** & **Mean** & **S.I.R** & **SD** \\ \hline
0 & \(1.1372\times 10^{-5}\) & \(6.9224\times 10^{-3}\) & \(2.1165\times 10^{-4}\) & \(1.1227\times 10^{-3}\) & \(6.5694\times 10^{-4}\) & \(1.8441\times 10^{-3}\) \\ \hline
0.1 & \(1.5570\times 10^{-4}\) & \(1.5199\times 10^{-2}\) & \(7.0904\times 10^{-3}\) & \(7.0882\times 10^{-3}\) & \(3.7494\times 10^{-4}\) & \(2.5091\times 10^{-3}\) \\ \hline
0.2 & \(2.3633\times 10^{-3}\) & \(2.9209\times 10^{-2}\) & \(2.4420\times 10^{-2}\) & \(2.0540\times 10^{-2}\) & \(4.4120\times 10^{-3}\) & \(7.6724\times 10^{-3}\) \\ \hline
0.3 & \(2.5936\times 10^{-4}\) & \(4.1491\times 10^{-2}\) & \(3.9420\times 10^{-2}\) & \(3.2301\times 10^{-2}\) & \(7.0413\times 10^{-3}\) & \(1.3088\times 10^{-2