Microbial Risk Assessment of Non-Enterohemorrhagic Escherichia coli in Natural and Processed Cheeses in Korea.

This study assessed the quantitative microbial risk of non-enterohemorrhagic Escherichia coli (EHEC). For hazard identification, hazards of non-EHEC E. coli in natural and processed cheeses were identified by research papers. Regarding exposure assessment, non-EHEC E. coli cell counts in cheese were enumerated, and the developed predictive models were used to describe the fates of non-EHEC E. coli strains in cheese during distribution and storage. In addition, data on the amounts and frequency of cheese consumption were collected from the research report of the Ministry of Food and Drug Safety. For hazard characterization, a dose-response model for non-EHEC E. coli was used. Using the collected data, simulation models were constructed, using software @RISK to calculate the risk of illness per person per day. Non-EHEC E. coli cells in natural- (n=90) and processed-cheese samples (n=308) from factories and markets were not detected. Thus, we estimated the initial levels of contamination by Uniform distribution × Beta distribution, and the levels were -2.35 and -2.73 Log CFU/g for natural and processed cheese, respectively. The proposed predictive models described properly the fates of non-EHEC E. coli during distribution and storage of cheese. For hazard characterization, we used the Beta-Poisson model (α=2.21×10-1, N50=6.85×107). The results of risk characterization for non-EHEC E. coli in natural and processed cheese were 1.36×10-7 and 2.12×10-10 (the mean probability of illness per person per day), respectively. These results indicate that the risk of non-EHEC E. coli foodborne illness can be considered low in present conditions.

Introduction

Cheese consumption has been increasing gradually in Korea since the 1990s (KDC, 2016), but the cases of contamination with Listeria monocytogenes, Staphylococcus aureus, and Escherichia coli have been reported (Jo ; Tekinsen and Özdemir, 2006; Thayer ). Especially, E. coli has been isolated from various cheeses in many countries (Haran ; Zinke ).

E. coli, a facultative anaerobic Gram-negative bacillus, is commonly found in the intestinal flora of humans and animals, and certain strains are pathogenic (MFDS, 2010; Olsvik ). According to infection symptoms and pathogenesis, pathogenic E. coli strains are classified e.g., enteropathogenic E. coli (EPEC), enteroinvasive E. coli (EIEC), enterotoxigenic E. coli (ETEC), enterohemorrhagic E. coli (EHEC), and enteroaggregative E. coli (EAEC) (Nataro and Kaper, 1998; Yoon, 2009). Among the pathogenic E. coli strains, E. coli O157:H7 is one of the major concerns in the dairy industry, and the survival of the pathogens in various cheeses has been well documented (Griffin and Tauxe, 1991; Reitsma and Henning, 1996). Thus, several countries (EU, USA, and Canada) have a quantitative standard or “zero tolerance” policy for control of the pathogens in cheese (EC, 2005; FDA, 2009; Health Canada, 2008); several microbiological risk assessments for E. coli O157:H7 in cheese have also been conducted (FSANZ, 2009; Perrin ). However, microbial risk assessment for non-EHEC E. coli in cheese has not been conducted. Hence, there is a lack of scientific evidence to determine microbial risk of non-EHEC E. coli.

EPA (2012) recommends microbiological risk assessment to evaluate the risk posed by bacteria, to prevent foodborne illnesses, and to identify environmental factors influencing microbial growth. The microbiological risk assessment should include hazard identification, exposure assessment, hazard characterization, and risk characterization (Codex, 1999).

The objective of this study was to conduct microbial risk assessment for non-EHEC E. coli in natural cheese which is manufactured from milk fermentation by adding start culture enzyme, and salt and processed cheeses which are manufactured from natural cheese using emulsifiers in Korea.

Materials and Methods

Hazard identification

To identify the hazards of E. coli, the general characteristics and foodborne-illness outbreaks linked to E. coli in cheese were collected from other studies.

Exposure assessment

Prevalence of E. coli

To evaluate non-EHEC E. coli prevalence and the contamination level, natural- (n=90) and processed-cheese samples (n=308) were collected from various cheese factories and markets. At two factories, samples were collected throughout the manufacturing process from raw milk to packaged cheese. Natural-cheese samples were collected from raw milk, pasteurized milk, cheese before ripening, cheese after packaging, cheese before shipping, and markets. Processed-cheese samples were also collected after packaging, before shipping, and in markets. In addition, distributed cheeses were collected from local markets in five cities in Korea. Cheese samples were evaluated in both summer and winter to reduce the effect of external environmental factors such as temperature, humidity and contamination levels of the pathogen. The collected samples were placed in an ice cooler and were transported to a laboratory. One-milliliter samples of raw milk and pasteurized milk were serially diluted with 0.1% buffered peptone water (BPW; Becton, Dickinson, and Company, USA). The diluents were then surface-plated on tryptic soy agar (TSA; Becto, Dickinson, and Company) and E. coli /Coliform Count petrifilm (3M™, USA) to quantify total bacteria, and non-EHEC E. coli and coliform counts, respectively. In addition, 25 g or 1 slice of cheese was aseptically transferred into a sample bag (3M™), and 25 mL of BPW was added, and the mixture was homogenized for 120 s with a pummeler (Bag-Mixer®, Interscience, France). One milliliter of the homogenate was serially diluted with BPW, and 0.1-mL diluents for TSA and 1-mL diluents for non-EHEC E. coli / Coliform Count petrifilm (3M™) were then surface-plated, respectively. The plates and petrifilms were incubated at 35°C for 24 h, and then the colonies were manually counted.

Initial level of contamination with non-EHEC E. coli

Beta distribution is a continuous probability distribution parametrized by two shape parameters (α1 and α2), and the interval of the distribution is zero to one (Johnson ). When the number of positive samples is low, beta distribution can be used to estimate bacterial prevalence. The data on non-EHEC E. coli prevalence in cheese were fitted to a Beta distribution (α1, α2), where α1 is the number of positive samples + 1, and α2 is the number of all tested samples - positive samples + 1 (Vose, 1998). Uniform distribution is also a continuous probability distribution defined by the two parameters (a and b), and the distribution indicates equal probability in the range of two parameters. Because non-EHEC E. coli were detected under detection limit, initial concentration was assumed in the range of zero to detection limit. Thus, the data on the non-EHEC E. coli contamination level in cheese from cheese factory storage were fitted to a Uniform distribution (a, b), where a is the minimal contamination level, and b is the maximal contamination level. Finally, the initial contamination level (Log CFU/g) was calculated by prevalence × contamination level using the @RISK software, version 5.7 (Palisade Corp., USA).

Non-EHEC E. coli growth during distribution and storage

To calculate non-EHEC E. coli growth during distribution and storage, predictive models for natural and processed cheeses from a study by MFDS (2013) were used as follows.

The μmax (Log CFU/g) is the maximum specific growth rate, LPD (h) is lag phase duration, and T (°C) is temperature. In addition, to simulate non-EHEC E. coli growth under changing temperature and time, probabilistic distributions for temperature and time from a study by Lee were used.

Cheese consumption

Data on cheese consumption and intake frequency of cheese were taken from the study of Lee to calculate the non-EHEC E. coli risk as a result of cheese consumption in Korea. According to a study by Lee , the mean consumption amounts of natural cheese and processed cheese are 12.40±19.43 g/d (95% confidence interval: 0.915−34.90 g/d) and 19.46±14.39 g/d (95% confidence interval: 2.6−40.0 g/d), respectively, and the consumption frequencies of cheese are 0.0389 and 0.0232 for natural and processed cheese, respectively. The ratios were fitted to the Discrete distribution{(0,1), [1 − (daily frequency of consumption), daily frequency of consumption]} (Lee ). Finally, ingested E. coli cell counts were calculated as a result of consuming natural or processed cheese from the final concentration at the time of consumption taking into account the consumption amount and frequency.

The dose-response model

Twenty-eight dose-response models for E. coli infection were surveyed from other studies. Because about 90% of E. coli foodborne illness in Korea occurred by EPEC (Hong ), the following dose-response model developed by Powell for EPEC was used in this study.

Where P is the probability of illness, D is the ingested E. coli cell number (CFU/serving), N50 is the dose infecting 50% of the population with E. coli, and α is a coefficient.

Risk characterization

The results of the exposure assessment, dose-response model, and cheese consumption amount and frequency were used to estimate the risk of non-EHEC E. coli in cheese by means of a simulation in software @RISK according to the scheme of the simulation model in Fig. 1. In the simulation for risk characterization, the sampling type was Median Latin Hypercube, and the generator seed was random with settings for 10,000 iterations. Tables 1 and 2 show simulation models and formulas for calculating the risk of non-EHEC E. coli in natural and processed cheeses by means of @RISK. Sensitivity analysis to determine factors influencing the risk was also conducted in @RISK.

Fig. 1.

Fitted Beta distribution (A) and probability density (B) of the simulated initial level of contamination with Escherichia coli in natural cheese.

Table 1.

The simulation model and formulas in a Microsoft Excel® spreadsheet used to calculate the risk of illness of Escherichia coli in natural cheese by means of the @RISK software

Input Model	Unit	Code	Formula	References
PRODUCT
Product
Pathogen Contamination
level
Non-EHEC E. coli		PR	=RiskBeta(1,91)	Vose (1998)
prevalence
Concentration	CFU/g	C	=RiskUniform(0,2)	Vose (1998)
Initial contamination level	CFU/g	IC	=PR×C	Vose (1998)
	Log CFU/g	log(IC)	=log(PR×C)
TRANSPORTATION
Transportation time	h	timetrans	=RiskPert(1,3,6)	Personal communicationa
Food temperature	°C	temptrans	=RiskPert(0,4,10)	Personal communicationa
during transportation

Table 1.

The simulation model and formulas in a Microsoft Excel® spreadsheet used to calculate the risk of illness of Escherichia coli in natural cheese by means of the @RISK software

Input Model	Unit	Code	Formula	References
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 2.26	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.36	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 9.04	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	TransLt	=IF{Temptrans>4,	MFDS (2013)
			[1/(−0.0522+0.0142×Temptrans)]2, 1320}
Growth rate	Log CFU/g/h	TransGr	=IF{Temptrans>5.4235,	MFDS (2013)
			[0.0268×(Temptrans−5.4235)]2, 0}	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C1	=IC+1/{1+EXP[−ln(q)]}×	MFDS (2013)
E. coli growth			[1−10−|Y0−Yend|/LN(10)]×TransGr×timetrans	Baranyi and Roberts (1994)
MARKET
Market storage
Storage time	h	Mark-timest	=RiskPert(0,2,48)	Personal communicationb
Food temperature	°C	Mark-Tempst	=RiskUniform(2,4)	Personal communicationb
during storage
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 2.26	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.36	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 9.04	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	Markst−TimeLt	=IF{Mark−Tempst>4,	MFDS (2013)
			[1/(−0.0522+0.0142×Mark−Tempst)]2, 1320}
Growth rate	Log CFU/g/h	Markst−RGr	=IF{Mark−Tempst>5.4235,	MFDS (2013)
			[0.0268×(Mark−Tempst−5.4235)]2, 0}	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C2−1	=C1+1/{1+EXP[−ln(q)]}×[1−10−|Y0−end|/	MFDS (2013)
E. coli growth			LN(10)]×Markst−RGr×Mark−timest	Baranyi and Roberts (1994)
Market display
Storage time	h	Mark-timedis	=RiskPert(0,48,168)	Personal communicationb
Food temperature	°C	Mark-Tempdis	=RiskTriang(0.60703,4.1000,15.18)	Lee et al. (2015)
during storage
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 2.26	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.36	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 9.04	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	Markdis−TimeLt	=IF{Mark−Tempdis>4,	MFDS (2013)
			[1/(−0.0522+0.0142×Mark−Tempdis)]2, 1320}
Growth rate	Log CFU/g/h	Markdis−RGr	=IF{Mark−Tempdis>5.4235,	MFDS (2013)
			[0.0268×(Mark−Tempdis−5.4235)]2, 0}	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C2	=(C2−1)+1/{1+EXP[−ln(q)]}×[1−10−|Y0−end|/	MFDS (2013)
E. coli growth			LN(10)]×Markdis−RGr×Mark−timedis	Baranyi and Roberts (1994)

Results and Discussion

Hazard identification of E. coli in cheese

Pathogenic E. coli causes diarrhea in infants or acute enteritis in adults (MFDS, 2010). Although ground beef and fresh vegetables are considered major vectors for pathogenic E. coli (MFDS, 2010), there are several reports about E. coli isolated from various cheeses in many countries. The most frequently isolated E. coli serotype in cheese is E. coli O157:H7 in many countries (BCCDC, 2013; CDC, 2010; Honish ), but other pathotypes such as EPEC, ETEC, and EAEC were also isolated from various cheeses (Baranceli ; Bonyadian ; Najand and Ghanbarpour, 2006). In addition, the most frequently isolated pathotype in Korea in various foods is EPEC (Hong ). Thus, after non-EHEC E. coli was identified as a hazard in cheese, subsequent quantitative microbial risk assessment for natural and processed cheeses was conducted.

Initial level of non-EHEC E. coli

Non-EHEC E. coli cell counts were found to be below the detection limit (natural cheese: 2 CFU/g; processed cheese: 2.8 CFU/g) in all samples. Thus, it was assumed that non-EHEC E. coli cell counts in cheese to be above 0 CFU/g, but below the detection limit (2 CFU/g), and then we described contamination levels of the pathogen with Uniform distribution (0,2) and Uniform distribution (0,2.8) for natural and processed cheese, respectively (Figs. 2 and 3). Therefore, using the @RISK software, the initial contamination level of non-EHEC E. coli were calculated by Beta distribution(1,91) × Uniform distribution(0,2), and Beta distribution(1,309) × Uniform distribution(0,2.8) for natural and processed cheese, respectively. As a result of the simulation, the initial level of contamination with non-EHEC E. coli in cheese was 2.35 and −2.73 Log CFU/g for natural and processed cheese, respectively (Figs. 2 and 3).

Fig. 2.

Fitted Beta distribution (A) and probability density (B) of the simulated initial level of contamination with Escherichia coli in processed cheese.

Fig. 3.

The scatter plots of the initial concentration level versus the home consumption level in terms of Escherichia coli in natural (A) and processed cheese (B).

Non-EHEC E. coli growth and cheese consumption

The cumulative distributions of non-EHEC E. coli growth during distribution and storage (initial concentration, concentration after transportation, concentration after storage in a market, concentration at the time of purchase, concentration when at home, and concentration at the time of consumption) were analyzed. As a result of the simulation, in natural cheese, the initial concentration was −2.35 Log CFU/g, and concentration at the final stage (at the time of consumption) was −2.31 Log CFU/g (data not shown). This result indicates that non-EHEC E. coli in natural cheese may not grow during distribution and storage under the conditions in Korea. In addition, non-EHEC E. coli growth probability in processed cheese was similar to that in natural cheese (data not shown). Moreover, the results of comparison of the initial concentration with final concentration indicate that none of the 10,000 iterations could yield more than 0 Log CFU/g at the point of final concentration (Fig. 4).

Fig. 4.

The regression coefficient (A) and the correlation coefficient (B) values for the sensitivity risk factor affecting the probability of illness per person per day as a result of consumption of natural cheese.

The dose-response model and risk characterization

After cheese consumption, to estimate the probability of non-EHEC E. coli foodborne illness, the Beta-Poisson model (α = 2.21×10−1, N50 = 6.85×107) was used (Powell ). Subsequently, the simulation model was prepared with the values of input variables such as non-EHEC E. coli prevalence, temperature, and time for distribution and display in markets, and home storage, the amount of cheese consumption, and intake frequency as presented Tables 1 and 2. The simulations were conducted by random sampling from the distribution described above for 10,000 iterations, and the mean probabilities of a non-EHEC E. coli outbreak as a result of cheese consumption per person per day in Korea were 1.36×10−7 and 2.12×10−10 for natural and processed cheese, respectively (Table 3), which are higher than the risk (7.84×1010) of S. aureus foodborne illness per person per day as a result of natural cheese consumption and the risk (3.64×10−9 to 1.30×10−7) of listeriosis per person per day as a result of eating lettuce at a restaurant in Korea (Ding ; Lee ). These results indicate that natural cheese poses a high risk of a non-EHEC E. coli outbreak as compared to processed-cheese-related and S. aureus-related foodborne illnesses as a result of natural cheese consumption and listeriosis as a result of lettuce consumption in Korea. In addition, sensitivity analysis revealed that intake frequency was the most influential factor for this risk, whereas the other factors such as storage temperature and time were not obviously related (Fig. 5).

Table 1.

The simulation model and formulas in a Microsoft Excel® spreadsheet used to calculate the risk of illness of Escherichia coli in natural cheese by means of the @RISK software

Input Model	Unit	Code	Formula	References
TRANSPORTATION (CAR)
Transportation
(CAR) storage
Transportation time	h	timecar	=RiskPert(0.325,0.984,1.643)	Jung (2011)
Food temperature	°C	Tempcar	=RiskPert(10,18,25)	Jung (2011)
during transportation
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 2.26	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.36	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 9.04	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	Car-TimeLt	=IF{Tempcar>4,	MFDS (2013)
			[1/(−0.0522+0.0142×Tempcar)]2, 1320}
Growth rate	Log CFU/g/h	Car−RGr	=IF{Tempcar>5.4235,	MFDS (2013)
			[0.0268×(Tempcar−5.4235)]2, 0}	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C3	=C2+1/{1+EXP[−ln(q)]}×[1−10−|Y0−Yend|/	MFDS (2013)
E. coli growth			LN(10)]×Car−RGr×timecar	Baranyi and Roberts (1994)
HOME
Home storage
Storage time	h	Home-timest	RiskNormal[250.1742, 176.0175,	Lee et al. (2015)
			RiskTruncate(0,4320)]
Food temperature	°C	Home-Tempst	=RiskLogLogistic[-29.283, 33.227, 26.666,	Lee et al. (2015)
during storage			RiskTruncate(−5,20)]
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 2.26	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.36	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 9.04	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	Home−TimeLt	=IF{Home−Tempst>4,	MFDS (2013)
			[1/(−0.0522+0.0142×Home−Tempst)]2, 1320}
Growth rate	Log CFU/g/h	Home−RGr	=IF{Home−Tempst>5.4235,	MFDS (2013)
			[0.0268×(Home−Tempst−5.4235)]2, 0}	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C4	=C3+1/{1+EXP[−ln(q)]}×[1−10−|Y0−Yend|/	MFDS (2013)
E. coli growth			LN(10)]×Home−RGr×Home−timest	Baranyi and Roberts (1994)
CONSUMPTION
Daily consumption	g	Consump	=RiskPearson5[2.6488, 25.81,	MFDS (2013)
average amount			RiskTruncate(0,100),RiskShift(-3.2572)]
Daily consumption	%	ConFre	Fixed 3.894	MFDS (2013)
frequency
		CF(0)	=1−3.894/100	MFDS (2013),
		CF(1)	=3.894/100	MFDS (2013),
		CF	=RiskDiscrete[{0,1},{CF(0),CF(1)}]	MFDS (2013),
		ConFre	=IF(CF=0,0,Consump)	MFDS (2013),
DOSE-RESPONSE
Non-EHEC E. coli amount		D	=10C4×ConFre
Parameter of α		α	=Fixed 2.21×10−1	Powell (2000)
Parameter of N50		N50	=Fixed 6.85×107	Powell (2000)
RISK
Probability of		Risk	=1−(1+{D×[(21/α)−1]/N50})−α	Powell (2000)
illness/person/day

aWith a supervisor of a cheese manufacturing plant

bWith a manager in charge of cheese products at markets

Fig. 5.

The regression coefficient (A) and the correlation coefficient (B) values for the sensitivity risk factor affecting the probability of illness per person per day as a result of consumption of processed cheese.

Thus, our results indicate that non-EHEC E. coli cannot grow in natural and processed cheeses under the present distribution and storage conditions, and that a different factor is more important for the risk of illness. Consumption frequency of processed cheese is lower than that of natural cheese, if we assume that the consumption amount of natural and processed cheese is similar. Accordingly, processed cheese poses a lower risk than natural cheese for non-EHEC E. coli.

Conclusion

The risk of a non-EHEC E. coli outbreak via cheese consumption seems to be low for natural and processed cheese in Korea, and the intake frequency of cheese is the most influential factor for this risk. In addition, the microbial risk assessment model that we developed in this study can be useful for quantitative risk assessment.

Table 2.

The simulation model and formulas in a Microsoft Excel® spreadsheet used to calculate the risk of Escherichia coli in processed cheese by means of the @RISK software

Input Model	Unit	Code	Formula	References
PRODUCT
Product
Pathogen Contamination
level
Non-EHEC E. coli		PR	=RiskBeta(1,309)	Vose (1998)
prevalence
Concentration	CFU/g	C	=RiskUniform(0,2.8)	Vose (1998)
Initial contamination level	CFU/g	IC	=PR×C	Vose (1998)
	Log CFU/g	log(IC)	=log(PR×C)
TRANSPORTATION
Transportation time	h	timetrans	=RiskPert(1,3,6)	Personal communicationa
Food temperature	°C	Temptrans	=RiskPert(0,4,10)	Personal communicationa
during transportation
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 0.65	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.11	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 7.32	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	TransLt	=IF{Temptrans>4,	MFDS (2013)
			[1/(−0.0826+0.0275×Tempcar)]2, 1320}
Growth rate	Log CFU/g/h	TransGr	=IF(Temptrans>8.6,0.0036−0.0030×Temptrans+	MFDS (2013)
			0.0004×Temptrans2, 0)	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C1	=IC+1/{1+EXP[−ln(q)]}×[1−10−|Y0−Yend|/	MFDS (2013)
E. coli growth			LN(10)]×TransGr×timetrans	Baranyi and Roberts (1994)
MARKET
Market storage
Storage time	h	Market-timest	=RiskPert(0,2,48)	Personal communicationb
Food temperature	°C	Mark-Tempst	=RiskUniform(2,4)	Personal communicationb
during storage
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 0.65	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.11	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 7.32	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	Markst−TimeLt	=IF{Mark−Tempst>4,	MFDS (2013)
			[1/(−0.0826+0.0275×Mark−Tempst)]2, 1320}
Growth rate	Log CFU/g/h	Markst−RGr	=IF(Mark−Tempst>8.6,0.0036−0.0030×	MFDS (2013)
			Mark−Tempst+0.0004×Mark−Tempst2, 0)	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C2−1	=C1+1/{1+EXP[−ln(q)]}×[1−10−|Y0−Yend|/	MFDS (2013)
E. coli growth			LN(10)]×Mark−RGr×Mark−timest	Baranyi and Roberts (1994)
Market display
Storage time	h	Mark−timedis	=RiskPert(0,48,168)	Personal communicationb
Food temperature	°C	Mark−Tempdis	=RiskTriang(0.60703,4.1000,15.18)	Lee et al. (2015)
during storage
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 0.65	MFDS (2013),
				Baranyi and Roberts (1994)

Table 2.

The simulation model and formulas in a Microsoft Excel® spreadsheet used to calculate the risk of Escherichia coli in processed cheese by means of the @RISK software

Input Model	Unit	Code	Formula	References
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.11	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 7.32	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	Markdis−TimeLt	=IF{Mark−Tempdis>4,	MFDS (2013)
			[1/(−0.0826+0.0275×Mark−Tempdis)]2, 1320}
Growth rate	Log CFU/g/h	Markdis−RGr	=IF(Mark−Tempdis>8.6,0.0036−0.0030×	MFDS (2013)
			Mark−Tempdis+0.0004×Mark−Tempdis2, 0)	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C2	=(C2−1)+1/{1+EXP[−ln(q)]}×[1−10−|Y0−Yend|/	MFDS (2013)
E. coli growth			LN(10)]×Markdis−RGr×Mark−timedis	Baranyi and Roberts (1994)
TRANSPORTATION (CAR)
Transportation
(CAR) storage
Transportation time	h	timecar	=RiskPert(0.325,0.984,1.643)	Jung (2011)
Food temperature	°C	Tempcar	=RiskPert(10,18,25)	Jung (2011)
during transportation
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 0.65	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.11	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 7.32	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	Car−TimeLt	=IF{Tempcar>4,	MFDS (2013)
			[1/(−0.0826+0.0275×Tempcar)]2, 1320}
Growth rate	Log CFU/g/h	Car−RGr	=IF(Tempcar>8.6,	MFDS (2013)
			0.0036−0.0030×Tempcar+0.0004×Tempcar2, 0)	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C3	=C2+1/{1+EXP[−ln(q)]}×[1−10−|Y0−Yend|/	MFDS (2013)
E. coli growth			LN(10)]×Car−RGr×timecar	Baranyi and Roberts (1994)
HOME
Home storage
Storage time	h	Home−timest	=RiskNormal[250.1742, 176.0175,	Lee et al. (2015)
			RiskTruncate(0,4320)]
Food temperature	°C	Home−Tempst	=RiskLogLogistic[-29.283, 33.227, 26.666,	Lee et al. (2015)
during storage			RiskTruncate(−5,20)]
Growth
h0	Log CFU/g	h0	=average(growth rate×lag time), Fixed 0.65	MFDS (2013),
				Baranyi and Roberts (1994)
Y0	Log CFU/g	Y0	=average(Y0i), Fixed 3.11	MFDS (2013),
				Baranyi and Roberts (1994)
Yend	Log CFU/g	Yend	=average(Yendi), Fixed 7.32	MFDS (2013),
				Baranyi and Roberts (1994)
ln(q)		ln(q)	=LN{1/[EXP(h0)−1]}	MFDS (2013),
				Baranyi and Roberts (1994)
Lag time	h	Home−TimeLt	=IF{Home−Tempst>4,	MFDS (2013)
			[1/(−0.0826+0.0275×Home−Tempst)]2, 1320}
Growth rate	Log CFU/g/h	Home−RGr	=IF(Home−Tempst>8.6,0.0036−0.0030×	MFDS (2013)
			Home−Tempst+0.0004×Home−Tempst2,0)	Ratkowsky et al. (1982)
Non-EHEC	Log CFU/g	C4	=C3+1/{1+EXP[−ln(q)]}×[1−10−|Y0−Yend|/	MFDS (2013)
E. coli growth			LN(10)]×Home−RGr×Home−timest	Baranyi and Roberts (1994)

Table 2.

The simulation model and formulas in a Microsoft Excel® spreadsheet used to calculate the risk of Escherichia coli in processed cheese by means of the @RISK software

Input Model	Unit	Code	Formula	References
CONSUMPTION
Daily consumption	g	Consump	=RiskWeibull[1.3482, 20.932,	MFDS (2013),
average amount			RiskShift(0.26384),RiskTruncate(0,100)]
Daily consumption	%	ConFre	Fixed 2.323	MFDS (2013)
frequency
		CF(0)	=1−2.323/100	MFDS (2013)
		CF(1)	=2.323/100	MFDS (2013)
		CF	=RiskDiscrete{[0,1],[CF(0),CF(1)]}	MFDS (2013)
		ConFre	=IF(CF=0,0,Consump)	MFDS (2013)
DOSE-RESPONSE
Non-EHEC E. coli amount		D	=10C4×ConFre
Parameter of α		α	=Fixed 2.21×10−1	Powell (2000)
Parameter of N50		N50	=Fixed 6.85×107	Powell (2000)
RISK
Probability of		Risk	=1−(1+{D×[(21/α)−1]/N50})−α	Powell (2000)
illness/person/day

aWith a supervisor of a cheese manufacturing plant

bWith a manager in charge of cheese products at markets

Table 3.

Probability of foodborne illness caused by Escherichia coli per person per day as a result of consumption of natural and processed cheeses

Probability of illness/(person·d)	5%	25%	50%	95%	99%	Maximum	Mean
Natural cheese	0	0	0	0	3.34×10−6	2.26×10−4	1.36×10−7
Processed cheese	0	0	0	0	4.59×10−9	1.20×10−7	2.12×10−10