Table 1.
Simulation model and formulas in the Excel® spreadsheet used to calculate the risk of B. cereus in packaged tofu with @RISK
| Symbol | Unit | Definition | Formula | References |
|---|---|---|---|---|
| Product at market | ||||
| Pathogens contamination level | ||||
| PR | Prevalence of B. cereus in Tofu | RiskBeta (12, 75) | This research, Vose (1998) | |
| CL | CFU/g | Contamination level of B. cereus | − LN(1 − PR)/25 | Sanaa et al. (2004) |
| IC | Log CFU/g | Initial contamination level | Log(CL) | |
| Market | ||||
| Market storage | ||||
| Mark-Time | h | Storage time in the market | RiskPert (0.17, 48, 168) | This research |
| Mark-Temp | °C | Food temperature during storage in the market | RiskUniform (4, 11.1) | Lee et al. (2008) |
| Growth | ||||
| T1 | IF(MarkTemp ≥ 10, 1, 0) | |||
| SGR1 | Log CFU/h | Specific growth rate | IF(T1 = 1, − 0.722 + (0.0720 * MarkTemp) + (− 0.0008 * MarkTemp2), 0) | This research, McMeekin et al. (1993) |
| LT1 | h | Lag time | IF(T1 = 1, 18.07 + (− 1015/MarkTemp) + (16,071/MarkTemp2), 0) | This research, Davey (1989) |
| C | Fixed | Difference between initial and final cell numbers | 5.026 | This research |
| G1 | Log CFU/g | Growth model | IC + C * EXP(− EXP((2.718 * SGR1/C) * (LT1-MarkTime) + 1)) | This research |
| Survival | ||||
| Delta1 | h | Average of 4 °C and 9 °C, fixed | 281.08 | This research |
| p | Fixed | Average of 4 °C and 9 °C, fixed | 0.55 | This research |
| S1 | Log CFU/g | Survival model | IC − (MarkTime/Delta1)p | This research, Geeraerd et al. (2005) |
| C1 | Log CFU/g | IF(T1 = 1, G1, S1) | ||
| Transportation | ||||
| Trans-Time | h | Time (market to home) | RiskPert(0.325, 0.984, 1.643) | Jung (2011) |
| Trans-Temp | °C | Storage temperature during transportation | RiskPert(10, 18, 25) | Jung (2011) |
| Growth | ||||
| SGR2 | Log CFU/h | Specific growth rate | − 0.722 + (0.072 * TransTemp) + (− 0.0008 * TransTemp2) | This research, McMeekin et al. (1993) |
| LT2 | h | Lag time | 18.07 + (−1015/TransTemp) + (16,071/TransTemp2) | This research, Davey (1991) |
| C | Fixed | Difference between initial and final cell number | 5.026 | This research |
| G2 (C2) | Log CFU/g | Growth model | C1 + C * EXP(− EXP((2.718 * SGR2/C) * (LT2-TransTime) + 1)) | This research |
| Home | ||||
| Home storage | ||||
| Home-Time | h | Storage time until consumption | RiskPert (1,24,168) | MFDS (2012) |
| Home-Temp | °C | Storage temperature until consumption | RiskLoglogistic (− 10.407, 13.616, 8.611) | Bahk (2010) |
| Growth | ||||
| T3 | IF(HomeTemp ≥ 10, 1, 0) | |||
| SGR3 | Log CFU/h | Specific growth rate | IF(T3 = 1, − 0.722 + (0.072 * HomeTemp) + (− 0.0008 * HomeTemp2), 0) | This research, McMeekin et al. (1993) |
| LT3 | h | Lag time | IF(T3 = 1, 18.07 + (− 1015/HomeTemp) + (16,071/HomeTemp2), 0) | This research, Davey (1991) |
| C | Fixed | Difference between initial and final cell numbers | 5.026 | This research |
| G3 | Log CFU/g | Growth model | C2 + C * EXP(− EXP((2.718 * SGR3/C) * (LT3-HomeTime) + 1)) | This research |
| Survival | ||||
| Delta3 | h | Average of 4 °C and 9 °C, fixed | 281.08 | This research |
| p | Fixed | Average of 4 °C and 9 °C, fixed | 0.55 | This research |
| S3 | Log CFU/g | Survival model | C2 – (Home time/delta3)p | This research, Geeraerd et al. (2005) |
| C3 | Log CFU/g | IF(T3 = 1, G3, S3) | ||
| Consumption | ||||
| Consum | g | Daily consumption average amount | RiskInvgauss (101.66, 261.75, RiskShift(− 12.247)), 4.707, 23.985, 175.84) | MFDS (2012) |
| ConFre | %, fixed | Daily consumption frequency | 13.62 | MFDS (2012) |
| CF(0) | Daily non-consumption frequency (rate) | 1 − ConFre/100 | MFDS (2012) | |
| CF(1) | Daily consumption frequency (rate) | ConFre/100 | MFDS (2012) | |
| CF | Distribution for consumption frequency | RiskDiscrete({0, 1}, {CF(0), CF(1)}) | MFDS (2012) | |
| Amount | Daily consumption average amount considered frequency | IF(CF = 0, 0, Consum) | ||
| Hazard characterization (minimum infective dose) | ||||
| Final dose (D) | B. cereus amount | 10C3 × Amount | MFDS (2016) | |
| Risk characterization | ||||
| Risk | Probability of illness/person/day | IF(D ≥ 100,000, 1, 0) | MFDS (2016) | |