Source: RISK ASSESSMENTS: Risk assessments models

Identifier: QMRA_Salmonella_egg

Rights: Creative Commons Attribution-NonCommercial 4.0

Software: R

Product Name: Eggs Chicken

Product Unit: Piece

Hazard Name: Salmonella

Hazard Description: Salmonella Enteritidis

Study Title: QMRA for Salmonella Enteritidis in eggs

Study Description: This QMRA assesses the risk to consumers posed by Salmonella Enteritidis associated with the consumption of table eggs. The model estimates (a) the number of illnesses per million servings of egg (uncooked, lightly or well-cooked) and (b) the probability of illness when ingesting a random serving of egg.

The exposure assessment model is composed of six steps. The evolution of the contamination along theses steps is assessed with the model equations described below. It takes into account the time and temperature conditions described in default simulation settings. Three scenarios of egg cooking are defined to assess the probability of illness: uncooked, lightly and well-cooked. The reduction of concentrations is applied to the initial concentration of S. Enteritidis in egg. Risk is evaluated when a random serving is ingested (i.e. either lightly or well-cooked egg).

The beta-Poisson dose response model was used to characterise the relationship between the ingested dose and the probability of salmonellosis. In this model, the variability in host-pathogen interaction is assumed to be beta distributed. The parameterisation of Thomas et al. (2006) was chosen.

Risk was estimated through different metrics (risk per serving or number of illnesses per millions of serving) for the different cooking modes of the eggs. The default number of simulations to explore variability was set to 2,000.

In this model, we only considered the internal contamination of egg with S. Enteritidis. Growth models of S. Enteritidis are different in egg yolk and albumen. While the yolk membrane does not break down, we consider the growth of S. Enteritidis albumen as insignificant. However, the resistance of the yolk membrane can decrease, for example, with the vibrations during the transport phase. At the storage phase, the resistance of the membrane depends on the time and temperature. At ambient temperature, the yolk membrane is rapidly damaged, leading to the yolk diffusion in egg albumen and contamination with S. Enteritidis. After the breakdown of the yolk membrane, the distribution of S. Enteritidis is considered to be uniform in the egg.

\((log_{10} TRMV=a+b \times T)\)

where \(TRMV\) is the time of the yolk membrane breakdown (day), \(a\) is the intercept of the equation (\(a\)= 2.0872 hours) (Thomas et al. 2006), \(b\) is the slope of the equation (\(b\) = -0.042579 hours/°C) (Thomas et al. 2006) and \(T\) is the temperature (°C).

The estimation of the time required for the yolk membrane breakdown becomes more complicated because the temperature is no longer constant and changes over time. The calculation of the breakdown time is, therefore, done step by step at each temperature change. In order to determine whether or not there is a rupture, the \(TRMV\) is calculated hourly as a function of temperature and the cumulative sum of the inverse of the different previous \(TRMVs\). If the sum of the inverses of the \(TRMVs\) is less than 1, then the membrane is considered still intact, otherwise (cumulative sum greater than or equal to 1), the yolk membrane is no longer intact and Salmonella growth then becomes possible.

Using the Rosso growth rate equation (Delignette-Muller and Rosso 2000, Rosso et al. 1993, Rosso et al. 1995, Whiting et al. 2000), in particular \(\mu_{opt}\) also called kopt in the model script:

\((\mu_{max}=\mu_{opt} \times \gamma(T))\)

with \(\gamma(T) = \begin{cases}0 & \quad T < T_{min}\\\frac{(T-T_{max})(T-T_{min})^{2} }{(T_{opt}-T_{min})[(T_{opt}-T_{min})(T-T_{opt})-(T_{opt}-T_{max})(T_{opt}+T_{min}-2T)]} & \quad T_{min} \leq T \leq T_{max}\\0 & \quad T > T_{max}\end{cases}\)

where \(\mu_{max}\) is the growth rate (log₁₀CFU/g per hour) at temperature \(T\) (°C), \(\mu_{opt}\) is the optimal growth rate (1.6) and \(\gamma(T)\) is the growth mitigation factor, \(T_{min}\) is the minimal growth temperature (6.29°C), \(T_{opt}\) is the optimum growth temperature (40.11°C) and \(T_{max}\) is the maximum growth temperature (43.46°C) (EFSA BIOHAZ Panel (EFSA Panel on Biological Hazards) 2014).

The temperature of a laid egg is 41.2°C (Thomas et al. 2006) and then this temperature decreases progressively, according to the environmental conditions of the different process steps like production, transport and storage. The formula of the temperature decrease (EFSA BIOHAZ Panel (EFSA Panel on Biological Hazards) 2014) is:

\(T = T_{s} +(T_{i}-T_{s})\space exp(-kr_{s}t_{s})\)

where \(T\) is th egg temperature (°C), \(T_{s}\) is the storage temperature in stage \(s\), \(T_{i}\) is the internal temperature at the start of the time interval, \(kr_{s}\) is the cooling rate constant in stage \(s\) and \(t_{s}\) is the time spent in stage \(s\). \(T_{s}\) follows a Pert distribution with \(minT\), \(modeT\) and \(maxT\) as parameters, which vary at each step of the process (Tables 1, 3). The rapidity of internal tempearture decreasing depends on the storage place, in particular, on the ventilation systems and air humidity. Pert distributions were used to describe this variability of the cooling rate due to the conditions of storage. The values of Pert distributions differ according to the process step (Table 2). \(t_{s}\) follows a Pert distribtuion with \(minD\), \(modeD\) and \(maxD\) as parmeters, which vary at each process step (Tables 1, 3)

From the moment that growth becomes possible, the growth rate is re-assessed hourly according to the \(\gamma\) model already presented. The growth rates calculated hourly until the end of egg storage are then cumulated. At the end, a number of ten-fold increase (\(NCD\)) is obtained for each egg. In order to determine the concentration before the egg's preparation, data on the initial concentration, i.e. at the time of laying, must be available.

The number of bacteria at the end of the storage is estimated by:

\(NSS=C_{0} \times 10^{NCD}\),

where \(NSS\) is the number of Salmonella per egg (CFU), \(C_{0}\) is the initial concentration which follows a Poisson law with a mean value at 7 and a minimum value at 1 cell per egg and \(NCD\) is the number of ten-fold increase; after that, the different process steps (log₁₀ CFU/h). \(NCD\) are estimated by:

\(NCD = \sum_{s = 1}^6 \mu_{max,s}.t_{TRMV}\),

where \(t_{TRMV}\) is the duration of the step after the complete deterioration of the yolk membrane is observed (TRMV).

The number of bacteria ingested is calculated as follows:

\(NSC = NSS \times 10^{-NRD}\)

where \(NSC\) is the number of Salmonella per egg after cooking and \(NRD\) is the number of log₁₀ reductions, according to the conditions of cooking. \(NRD\) follows a normal distribution with a mean value at 2 and a standard deviation at 0.5 when eggs are lightly-cooked and a normal distribution with a mean value at 12 and a standard deviation at 1 when eggs are well-cooked (Thomas et al. 2006).

The beta-Poisson dose-response model from (FAO/WHO 2002) was used:

\(P_{ill \space | \space cont \space serving} = 1-(1+ \frac {NSC}{\beta})^{- \alpha}\)

\(P_{ill | \text{cont serving} | \text{w}}\) and \(P_{ill | \text{cont serving} | \text{l}}\) are the probability of illness per S. Enteritidis-contaminated serving for well or lightly cooked eggs, respectively. The coefficients of the dose-response model are \(\alpha\) (0.1345) and \(\beta\) (53.33) which were taken from (Thomas et al. 2006).

The potential risk for humans of becoming infected via egg consumption is estimated by:

\(R_{lightly-cooked} = (1-fq_{cooking}) \times prevalence \times P_{ill \space | \space cont \space serving | \space l} \times 10^{6}\)

\(R_{well-cooked} = fq_{cooking} \times prevalence \times P_{ill \space | \space cont \space serving | \space w} \times 10^{6}\)

where \(R_{lightly-cooked}\) is the number of illnesses per million servings of cooked egg, \(fq_{cooking}\) is the percentage of people who well cook eggs (set to 0.9), \(prevalence\) is the prevalence (set to 10% for illustration purposes) and \(P_{ill \space | \space cont \space serving}\), the probability of illness per S. Enteritidis-contaminated serving of egg.

Execute with default simulation parameters: https://data.d4science.org/analytics/get/FMJ_Lab?dim=https://data.d4science.org/shub/E_MklUWkdmZmp6eW56LzhDSXRxRk9QeXl2YXA1a0tNMUorbXhEVUMvcFJMVzNFRS83ZHBqSDZ6TW1pZ1hmbmprdA==

Execute with new simulation parameters: https://data.d4science.org/knime/get/FMJ_Lab?pm:file_ID=E_VEtmWmx2VTRVc2hHSXFSUElaWi9BK1VVUnpRUXVQcDd6RWNORG42Z3kxL3RidUpVNVNMSlNyOFlwWW9CbVBVWQ==