## 2 Results and Discussion
### Antibacterial Study
These findings suggest that Et-DVB-AN is more effective against both pathogens, as it achieved a greater reduction in microbial counts within shorter treatment periods. This observation aligns with the improved inactivation results seen in the experimental data, indicating that the material's structure affects its efficiency. Additionally, the  
Figure 11: First-order kinetic model of _E. coli_ and _S. aureus_ reduction by treatment with Bz-DVB-AN and Et-DVB-AN. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Time, h** & **0** & **3** & **6** & **9** & **12** & **18** \\ \cline{2-7}  & \multicolumn{7}{c}{**Log N\({}_{t}\)/N\({}_{0}\) ***} \\ \hline  & \multicolumn{7}{c}{_E. coli_} \\ \hline Bz-DVB-AN & 0 & \(-\)0.0732 & \(-\)0.1417 & \(-\)0.2429 & \(-\)0.3316 & \(-\)0.5562 \\ Et-DVB-AN & 0 & \(-\)0.1240 & \(-\)0.3518 & \(-\)0.4884 & \(-\)0.5052 & \(-\)0.8095 \\ \hline  & \multicolumn{7}{c}{_S. aureus_} \\ \hline Bz-DVB-AN & 0 & \(-\)0.0777 & \(-\)0.1505 & \(-\)0.3410 & \(-\)0.4134 & \(-\)0.6090 \\ Et-DVB-AN & 0 & \(-\)0.1560 & \(-\)0.4179 & \(-\)0.4227 & \(-\)1.0087 & \(-\)1.2839 \\ \hline \hline \end{tabular}  
* N\({}_{t}\) is the number of germs at time t (h); N\({}_{0}\) is the initial number of germs.  
\end{table} 
Table 3: The logarithmic surviving fraction (log(N\({}_{t}\)/N\({}_{0}\)) for both Bz-DVB-AN and Et-DVB-AN vs. the interval time of contact (h). decimal reduction in _S. aureus_ for both materials showed a better effectiveness, indicating that the dynamics of bacterial inactivation differ between species. The first-order kinetic model is typically only applicable to log-linear inactivation patterns. Since microbial inactivation curves frequently show non-log-linear relationships, the Weibull model is typically used to analyze non-log-linear survival curves and is describe by Equation (2) [25; 26; 27; 28]. \[log\frac{N_{t}}{N_{0}}=-bt^{n} \tag{2}\]  
where \(n\) is the dimensionless shape parameter and \(b\) is the distinctive slope or scale parameter (min\({}^{-1}\)). Inactivation resistance can be interpreted using concavity; downward concavity (\(n>1\)) indicates shoulder or decreasing resistance, while upward concavity (\(n<1\)) indicates tailing or growing resistance [27]. Therefore, variations in the resistance of the bacteria to the treatment are shown by the Weibull inactivation curve. The Weibull model representations of _E. coli_ and _S. aureus_ reduction by treatment with Bz-DVB-AN and Et-DVB-AN samples are presented in Figure 12, and the obtained kinetic parameters are summarized in Table 5. \begin{table}
\begin{tabular}{c c c c} \hline
**Antimicrobial Materials** & **Kinetic Parameters \({}^{*}\)** & _E. coli_ & _S. aureus_ \\ \hline \multirow{2}{*}{Bz-DVB-AN} & R\({}^{2}\) & 0.99525 & 0.99216 \\  & D\({}_{\text{T}}\), h & 32.4 & 28.4 \\ \hline \multirow{2}{*}{Et-DVB-AN} & R\({}^{2}\) & 0.98512 & 0.97158 \\  & D\({}_{\text{T}}\), h & 22.6 & 13.4 \\ \hline \end{tabular} \({}^{*}\)R\({}^{2}\) is regression coefficient; D\({}_{\text{T}}\) is decimal regression time.  
\end{table} 
Table 4: First-order kinetic model parameters for _E. Coli_ and _S. aureus_ reduction by treatment with Bz-DVB-AN and Et-DVB-AN. Figure 12: Weibull model of _E. coli_ and _S. aureus_ reduction by treatment with Bz-DVB-AN and Et-DVB-AN. The Weibull model suggests a good fit of the experimental data obtained in all cases, with chi-square values less than 0.003. It could be observed that the obtained graphics present a downward concave curve (\(n>1\)) for _E. coli_ and _S. aureus_ pathogens treated with Bz-DVB-AN and for _S. aureus_ on Et-DVB-AN. This indicates that the _S. aureus_ bacteria are more vulnerable to the materials under study. In the case of _E. coli_ treated with Et-DVB-AN, the fitted model presents an upward concavity (\(n<1\)), assuming that the less-sensitive microorganisms were deactivated at a relatively fast rate but with survivors possibly being unaffected by the treatment.