## 3 Results and Discussion  
In nine different cake samples, including sponge cake, mousse cakes, cheesecake, brownnie, and triamisu, which had different \(\mathrm{a_{w}}\) and proximate compositions, _Salmonella_ spp. adequately survived. Cell numbers of _Salmonella_ spp. were maintained at 2-3 log CFU/g for 9 d in all cake samples, except A (sponge cake) and H (brownnie) cake (Table 1), where the density of _Salmonella_ spp. decreased. In contrast, the growth of _S. aureus_ was observed in all cake samples, except for cake A and H. Sample A was marble sponge cake with an \(\mathrm{a_{w}}\) of 0.86 \(\pm\) 0.00, which dried more rapidly than other sponge cake samples B and C during storage (data not shown). Sample H showed significantly lower \(\mathrm{a_{w}}\) (0.70 \(\pm\) 0.01) and moisture content (12.4 \(\pm\) 0.1%) than other samples. After storage for 7 d, _S. aureus_ grew up to 7.5-7.9 log CFU/g in D, E, F (mousse), G (Cheese), and I (tiramisu) cakes, and their \(\mathrm{a_{w}}\) values were significantly higher (0.90-0.91) than those of the other samples (Table 1). Growth of _S. aureus_ was slightly lower in samples B and C (sponge) than in samples D, E, and F (mousse) because of their low \(\mathrm{a_{w}}\) and moisture contents, indicating that _Salmonella_ spp. and _S. aureus_ growth in cake samples is associated with the \(\mathrm{a_{w}}\) and moisture content of the samples. These results suggest that if bakery products, including cake, have a high \(\mathrm{a_{w}}\), the growth and survival of _Salmonella_ spp. and _S. aureus_ are feasible, causing foodborne diseases upon temperature abuse [22]. Cake sample D reflected the worst growth conditions for _Salmonella_ spp. and _S. aureus_ because they were expected to grow well, considering favorable conditions including \(\mathrm{a_{w}}\), moisture content, and bacterial growth. Hence, cake sample D was selected for developing mathematical models. Before bacteria inoculation, total bacteria, _Salmonella_ spp. and _S. aureus_ cell counts were measured, but no colony was detected in any of the tested cake samples (data not shown). To develop a primary model to determine the kinetic parameters (\(\mu_{\rm max}\) and LPD), bacterial growth patterns in cake samples were examined at 4, 10, 15, 20, 25, and 30 \({}^{\circ}\)C for _Salmonella_ spp., and 4, 10, 15, 25, and 30 \({}^{\circ}\)C for _S. aureus_, respectively. Only at 20, 25, and 30 \({}^{\circ}\)C, _Salmonella_ spp. grew in cake samples (data not shown). For _S. aureus_, growth was observed at 15, 25, and 30 \({}^{\circ}\)C (data not shown). Growth data observed herein were fitted to the Baranyi model to develop the primary model. The values of \(\mu_{\rm max}\) for cake contaminated with _Salmonella_ spp. were 0.10 \(\pm\) 0.00, 0.19 \(\pm\) 0.00, and 0.35 \(\pm\) 0.05 log CFU/g/h at 20, 25, and 30 \({}^{\circ}\)C, respectively. In the case of _S. aureus_, the values of \(\mu_{\rm max}\) were 0.05 \(\pm\) 0.02, 0.29 \(\pm\) 0.07, and 0.33 \(\pm\) 0.02 log CFU/g/h at 15, 25, and 30 \({}^{\circ}\)C, respectively. \(\mu_{\rm max}\) significantly increased (_p_ < 0.05) with an increase in the temperature for both bacteria, indicating that \(\mu_{\rm max}\) is temperature-dependent (Table 2). In the case of _S. aureus_, LPD significantly decreased (_p_ < 0.05) with an increase in temperature, while no significant differences were observed in the LPD of _Salmonella_ spp. above 20 \({}^{\circ}\)C, where the growth of _Salmonella_ spp. was observed. \(R^{2}\) values of 0.942 to 0.996 indicate that the primary model was appropriate. Secondary models describing the effect of storage temperature on kinetic parameters (\(\mu_{\rm max}\) and LPD) were developed, using a polynomial model (Figure 1). For temperatures at which no growth was observed, \(\mu_{\rm max}\) was considered zero, and LPD was estimated on the basis of the maximum storage time.