## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Weibull–Mafart**} & \multicolumn{4}{c}{**Bigelow**} \\ \hline
**Group** & **T (\({}^{\circ}\)C)** & **RMSE \({}^{\ast}\)** & **Loglik** & **AIC** & **A/B\({}_{f}\)** & **RMSE** & **Loglik** & **AIC** & **A/B\({}_{f}\)** \\ \hline \multirow{4}{*}{Control} & 52 & 0.10 & 42.70 & \(-81.40\) & 1.01/0.99 & 0.20 & 22.36 & \(-42.72\) & 1.02/1.00 \\  & 54 & 0.16 & 24.40 & \(-44.80\) & 1.02/1.00 & 0.29 & 13.30 & \(-24.60\) & 1.04/1.00 \\  & 57.5 & 0.08 & 47.44 & \(-90.88\) & 1.01/1.00 & 0.37 & 11.92 & \(-21.84\) & 1.04/1.00 \\  & 63 & 0.06 & 46.21 & \(-88.42\) & 1.01/0.99 & 0.48 & 5.35 & \(-8.70\) & 1.07/1.00 \\ \hline \multirow{4}{*}{PEO} & 52 & 0.42 & 10.36 & \(-16.72\) & 1.07/1.00 & 0.55 & 7.57 & \(-13.14\) & 1.09/1.00 \\  & 54 & 0.18 & 22.73 & \(-41.46\) & 1.02/1.00 & 0.30 & 14.33 & \(-26.66\) & 1.05/1.01 \\  & 57.5 & 0.33 & 10.96 & \(-17.92\) & 1.07/1.00 & 0.62 & 6.47 & \(-10.94\) & 1.45/1.42 \\ \hline \multirow{4}{*}{FIV} & 63 & 0.34 & 11.06 & \(-18.12\) & 1.06/1.00 & 1.00 & 2.52 & \(-3.04\) & 1.26/0.99 \\  & 52 & 0.20 & 19.14 & \(-34.28\) & 1.06/1.03 & 0.61 & 6.22 & \(-10.44\) & 1.12/1.02 \\ \cline{1-1}  & 54 & 0.33 & 11.55 & \(-19.10\) & 1.05/1.01 & 0.51 & 8.35 & \(-14.70\) & 1.06/1.00 \\ \cline{1-1}  & 57.5 & 0.20 & 19.50 & \(-35.00\) & 1.10/0.98 & 1.04 & 4.14 & \(-6.28\) & 1.30/0.94 \\ \cline{1-1}  & 63 & 0.24 & 11.94 & \(-19.88\) & 0.99/1.07 & 1.11 & 2.28 & \(-2.56\) & 1.39/0.95 \\ \hline \hline \end{tabular}  
* RMSE—Root Mean Square Error, Loglik—Log-likelihood, AIC—Akaike Information Criteria, A—Accuracy factor, and B—Bias factor.  
\end{table} 
Table 1: Goodness-of-fit indices estimated by fitting the Weibull–Mafart and Bigelow primary models to the inactivation data obtained at different temperatures for PEO (Pure Oregona Essential Oil), FIV (Fractionated Oregona Essential Oil), and Control groups. Figure 1: Thermal inactivation curves In vitro of \(L\). _monocytogenes_ at 52, 54, 57.5 and 63 \({}^{\circ}\)C exposed to the PEO (Pure Oregona Essential Oil), FIV (Fractionated Oregona Essential Oil), and Control groups. The data points represent two independent replicates. effects by disrupting bacterial membranes, increasing their permeability and interfering with essential cellular processes [42; 67]. The \(p\) parameter of the Weibull-Mafart model was \(<\)1 in all cases (Table 2), indicating a concave survival curve shape (Figure 1). The presence of a tail in the curves as time progressed suggests either microbial adaptation or the existence of a more resistant subpopulation (Figure 1) [68; 69]. Such tailing effects are often associated with the induction of stress response mechanisms or the selection of subpopulations with increased resistance to sequential hurdles. [PERSON] et al. [68] demonstrated that \(L\). _monocytogenes_ exposed to mild bactericidal treatments can develop tolerance, leading to slower inactivation rates and persistent survival. Similarly, [PERSON] et al. [69] reported tailing in inactivation curves when \(L\). _monocytogenes_ was subjected to mild heat combined with thymol and carvacrol, which is consistent with the primary components of FIV, suggesting that sublethal damage and cellular repair processes may contribute to the observed kinetic behavior. The one-step procedure was applied to estimate the z-values from the inactivation data, calculated as the negative inverse of the slope obtained from the linear regression of Log \(\delta\)-value versus temperature (Table 3, Figure 2). The resulting z-values were 5.75 \({}^{\circ}\)C for the control, 5.20 \({}^{\circ}\)C for PEO, and 5.00 \({}^{\circ}\)C for FIV. These results are consistent with other studies reporting z-values around 5 \({}^{\circ}\)C when using OEO against \(L\). _monocytogenes_ in food matrices [43; 70; 71].