## 3 Computer Simulation and Results
#### Sensitivity Analysis  
For this model, a local analysis of sensitivity was performed, to identify the parameters that are more sensitive to the model. Table 3 are shown the results of changing \(\pm 50\%\) the value of the parameters was considered the decrease in tumor cell population for observing the behavior of the model parameters. It is noted that change values by \(\pm 50\%\) the most sensitive parameter is \(K\), however, decreasing the value parameters in \(-50\%\) are \(r\) with major changes in the population of tumor cells.  
It can be seen from Table 3, that the most sensitive parameters of the model are \(r_{T}\), \(K\), \(\mu_{D}\) and \(D_{inf}\). Additionally, it is worth mentioning that, when performing experiments by changing the CD number from \(10^{7}\) to \(10^{9}\), the sensitivity is around \(200\%\), showing that the decrease of tumor cell population depends strongly on the number of Dendritic cells infused, even when we use random conditions.The other parameters have a sensitivity of less than 0.3 percent, so they are not reported.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**HM** & **NDC** & **PI** & **\%G** & **RT** & **ST** & **SuT** & **RECIST** \\ \hline
1 & \(10^{3}\) & 48 & 0.99 & 100 & 0 & 0 & PD \\
2 & \(10^{3}\) & 96 & 0.99 & 100 & 0 & 0 & PD \\
3 & \(10^{3}\) & 144 & 0.99 & 100 & 0 & 0 & PD \\
4 & \(10^{3}\) & 192 & 0.99 & 100 & 0 & 0 & PD \\ \hline
5 & \(10^{7}\) & 48 & 0.49 & 50 & 0 & 50 & PR \\
6 & \(10^{7}\) & 96 & 0.53 & 54 & 0 & 46 & PR \\
7 & \(10^{7}\) & 144 & 0.55 & 56 & 0 & 44 & PR \\
8 & \(10^{7}\) & 192 & 0.50 & 51 & 0 & 49 & PR \\ \hline
9 & \(10^{9}\) & 48 & 0.011 & 0 & 0 & 100 & CR \\
10 & \(10^{9}\) & 96 & 0.007 & 0 & 0 & 100 & CR \\
11 & \(10^{9}\) & 144 & 0.010 & 0 & 0 & 100 & CR \\
12 & \(10^{9}\) & 192 & 0.009 & 0 & 0 & 100 & CR \\ \hline \end{tabular}  
* HM = Hypothetical immunotherapy, NDC = Number of DCs injected, PI = Period of infusion, %G = Percentage of growth, RT = Response tests, ST = Stable tests, SuT = Success tests, RECIST = Response evaluation criteria in solid tumors [21] (Complete Response: CR, Partial response: PR, Progressive Disease: PD, and Stable Disease: SE).  
\end{table}
Table 2: Hypothetical immunotherapy for ODEs model with different number of Dendritic cells (DCs) injected and different periods of infusion.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Param** & **PR1** & **S1** & **PR2** & **S2** \\ \hline \(r\) & \(2.10\times 10^{-15}\) & 2 & \(9.99\times 10^{10}\) & \(2.44\times 10^{-4}\) \\ \(K\) & \(4.99\times 10^{10}\) & 1.00 & \(1.49\times 10^{11}\) & 1.00 \\ \(\mu_{D}\) & \(9.95\times 10^{10}\) & 0.008 & \(9.99\times 10^{10}\) & \(6 In Figure 4 the results from varying the most sensitive model parameters are shown. In all simulations we infused \(10^{7}\) DCs every 168 h; except Figure 4E,F where the number of Dendritic cells injected varies.  
Figure 4A,B modify the value of parameter \(K\) in \(10^{6}\) and \(10^{11}\) respectively, it can be seen the larger the value of K, the less response there is from applied immunotherapy.  
In the case of Figure 4C,D the varied parameter now is \(r_{T}\), the rate of tumor growth with values of 0.001 and 0.1 respectively, observing that when using smaller values, the immunotherapy can be more effective. Finally, for graphs Figure 4E,F the number of dendritic cells injected is varied in \(10^{3}\) and \(10^{9}\) every 168 h. It can be seen that by increasing the amount of DCs, the success of the therapy increases dramatically having a sensitivity of 200% when \(10^{9}\) DCs is infused.