## 3 Results and Discussion
The \(R^{2}\) values of the secondary models were 0.968-0.988, indicating that the secondary models were appropriate to describe the effects of temperature on the kinetic parameters. To evaluate the performance of the models developed for _Salmonella_ spp. and _S. aureus_ in cake samples at a constant temperature, \(B_{f}\), \(A_{f}\), and RMSE were determined. The values of 0 for RMSE indicate perfect concurrence between the predicted data and the observed data, and when the \(B_{f}\) and \(A_{f}\) values were closer to 1, the performance of the developed model was considered a good fit [23]. In this study, \(B_{f}\), \(A_{f}\), and RMSE values of the model for _Salmonella_ spp. were 0.98, 1.11, and 0.78, respectively, and those of _S. aureus_ were 0.97, 1.07, and 0.54, for _Salmonella_ spp., respectively. These validation data indicate that the model developed herein successfully describes the behavior of _Salmonella_ spp. and _S. aureus_ in cake samples and can be used to develop risk management alternatives to control the risk of foodborne diseases. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Type of Cake**} & \multirow{2}{*}{\(\mathbf{a}_{w}\)} & \multicolumn{4}{c}{**Proximate Composition (\%)**} & \multicolumn{4}{c}{**Bacterial Density**} \\  & & & **Moisture** & **Fat** & **Protein** & **Carbohydrate** & _Salmonella_ & _S. aureus_ \\ \hline \multirow{4}{*}{Sponge} & A & 0.86 \(\pm\) 0.00 \({}^{\rm B}\) & 27.7 \(\pm\) 0.0 \({}^{\rm F}\) & 16.6 \(\pm\) 0.4 \({}^{\rm DE}\) & 8.6 \(\pm\) 0.1 \({}^{\rm A}\) & 45.9 \(\pm\) 0.6 \({}^{\rm B}\) & 1.5 \(\pm\) 0.0 \({}^{\rm C}\) & \textless{LOD}\({}^{\rm 2D}\) \\  & B & 0.82 \(\pm\) 0.02 \({}^{\rm C}\) & 20.4 \(\pm\) 0.1 \({}^{\rm G}\) & 31.0 \(\pm\) 0.6 \({}^{\rm B}\) & 6.6 \(\pm\) 0.0 \({}^{\rm C}\) & 41.3 \(\pm\) 0.6 \({}^{\rm C}\) & 2.9 \(\pm\) 0.1 \({}^{\rm A}\) & 5.8 \(\pm\) 0.4 \({}^{\rm B}\) \\  & C & 0.80 \(\pm\) 0.02 \({}^{\rm C}\) & 27.7 \(\pm\) 0.0 \({}^{\rm F}\) & 17.2 \(\pm\) 0.1 \({}^{\rm D}\) & 7.2 \(\pm\) 0.0 \({}^{\rm B}\) & 47.1 \(\pm\) 0.1 \({}^{\rm A}\) & 3.1 \(\pm\) 0.1 \({}^{\rm A}\) & 5.5 \(\pm\) 0.4 \({}^{\rm B}\) \\ \hline \multirow{4}{*}{Mousse} & D & 0.92 \(\pm\) 0.01 \({}^{\rm A}\) & 43.9 \(\pm\) 0.1 \({}^{\rm B}\) & 14.1 \(\pm\) 0.4 \({}^{\rm F}\) & 6.3 \(\pm\) 0.0 \({}^{\rm D}\) & 35.0 \(\pm\) 0.2 \({}^{\rm E}\) & 3.4 \(\pm\) 0.9 \({}^{\rm A}\) & 7.7 \(\pm\) 0.0 \({}^{\rm A}\) \\  & E & 0.90 \(\pm\) 0.01 \({}^{\rm A}\) & 40.1 \(\pm\) 0.0 \({}^{\rm D}\) & 14.2 \(\pm\) 0.2 \({}^{\rm F}\) & 5.9 \(\pm\) 0.0 \({}^{\rm E}\) & 39.1 \(\pm\) 0.2 \({}^{\rm D}\) & 2.6 \(\pm\) 0.2 \({}^{\rm AB}\) & 7.5 \(\pm\) 0.1 \({}^{\rm A}\) \\  & F & 0.90 \(\pm\) 0.01 \({}^{\rm A}\) & 45.1 \(\pm\) 0.0 \({}^{\rm A}\) & 10.0 \(\pm\) 0.1 \({}^{\rm G}\) & 3.9 \(\pm\) 0.1 \({}^{\rm G}\) & 40.6 \(\pm\) 0.1 \({}^{\rm C}\) & 2.6 \(\pm\) 0.2 \({}^{\rm AB}\) & 7.8 \(\pm\) 0.1 \({}^{\rm A}\) \\ \hline Cheese & G & 0.90 \(\pm\) 0.00 \({}^{\rm A}\) & 32.1 \(\pm\) 0.1 \({}^{\rm E}\) & 23.8 \(\pm\) 0.6 \({}^{\rm C}\) & 8.6 \(\pm\) 0.1 \({}^{\rm A}\) & 34.7 \(\pm\) 0.8 \({}^{\rm E}\) & 2.6 \(\pm\) 0.2 \({}^{\rm AB}\) & 7.6 \(\pm\) 0.1 \({}^{\rm A}\) \\ \hline Brownie & H & 0.70 \(\pm\) 0.01 \({}^{\rm D}\) & 12.4 \(\pm\) 0.1 \({}^{\rm H}\) & 34.1 \(\pm\) 0.1 \({}^{\rm A}\) & 5.7 \(\pm\) 0.1 \({}^{\rm F}\) & 46.4 \(\pm\) 0.3 \({}^{\rm AB}\) & 1.9 \(\pm\) 0.1 \({}^{\rm BC}\) & 3.5 \(\pm\) 0.0 \({}^{\rm C}\) \\ \hline Tiramisu & I & 0.91 \(\pm\) 0.01 \({}^{\rm A}\) & 43.3 \(\pm\) 0.3 \({}^{\rm C}\) & 16.0 \(\pm\) 0.5 \({}^{\rm E}\) & 7.4 \(\pm\) 0.1 \({}^{\rm B}\) & 32.3 \(\pm\) 0.3 \({}^{\rm F}\) & 3.0 \(\pm\) 0.7 \({}^{\rm A}\) & 7.9 \(\pm\) 0.1 \({}^{\rm A}\) \\ \hline \hline \end{tabular}  
\({}^{\rm A-H}\) Means within the same column with different superscript letters are significantly different (_p_ < 0.05), \({}^{\rm 1}\) bacterial density in cake after inoculation with _Salmonella_ spp. (9 days) and _S. aureus_ (7 days), \({}^{\rm 2}\) limits of detection (<1.5 Log CFU/g).  
\end{table}