2.1. Overview and Fundamental Concepts of the Model
Four main phases of the cheese process were taken into consideration and each phase is composed of different steps (Table I):
- The cheese-making phase, during which the milk is pasteurized and shared out in milk basins, and rennet is added. The resulting curd is then molded and young cheeses are transferred to the draining room, during which time whey drains out. Before salting with brine salting or dry salt, cheeses may go through different maturation rooms to continue acidification and for chilling. After salting, they may go through a drying room and/or yeast maturation room.
- The ripening phase is made up of several cycles of maturation steps in the ripening room followed by a smearing step in the smearing room and ending with a final phase of maturation, before packaging, in a room devoted to this. During smearing, cheeses are salted and washed with brine to develop flavor and remove molds that could develop on the surfaces.
- The packaging phase during which the product is packed, using a packaging machine.
- The distribution phase consisting of transport, retailing, and consumption, from the cheese leaving the factory to the end of the shelf-life of the product.
For each step of the four phases, compartments were defined, inside which L. monocytogenes can be present. Compartments were divided into three categories:
- Production units: milk in basins before molding, and cheeses after molding,
- Machine: surfaces of a machine in contact with the production units,
- Environment: surfaces of a room that are not in contact with production units (e.g., floor).
Table I. Phases and Steps of the Cheese Process, with Associated Events and Compartments Involved in the Step
|Phase||Step Code||Step||Impact of Physical and Chemical Conditions on the Microorganism||Secondary Contaminations||Compartments Involved in the Step|
|Cheese Making||St1||Prereneting|| ||Recontamination of the pasteurized milk||Milk basins containing milk|
| ||St2||Postreneting|| || || |
| ||St3||Molding||Stress|| || |
| ||St4||Drainage|| || || |
| ||St5||Acidification|| || || |
| ||St6||Chilling|| ||Recontamination of product's surface|| |
| ||St7||Salting|| || ||Cheeses|
| ||St8||Dry stir step|| || || |
| ||St9||Drying step||Growth|| || |
| ||St10||Yeast maturation|| || || |
|Ripening||–||Smearing||Stress||Cross-contaminationTransfer from the smearing to the ripening room||CheesesEnvironment of the smearing roomSmearing machine|
| ||–||Maturation in a||Growth||Recontamination of product's||Environment of the|
| || ||ripening room||Stress||surface||ripening roomCheeses|
|Packaging||–||Packaging|| ||Cross-contamination||CheesesPackaging machine|
|Transport and Retailing||–||Transport and retailing||Growth||–||Cheeses|
The ripening phase was modeled with a single ripening room inside which there is a smearing room containing a smearing machine. During packaging, we considered the surfaces of the packaging machine. During transport, retailing, and conservation, we only considered production units. Environments of each phase of the process were considered to be independent, meaning that they cannot contaminate each other (Fig. 1).
Figure 1. Evolution of the level of contamination in the different compartments resulting from secondary contamination events.
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The level of contamination of a milk basin is given by the concentration of L. monocytogenes in cells per liter. For the other compartments (cheese, machine surfaces, and environment surfaces), the level of contamination is given by the number of colonies of L. monocytogenes in the compartment, each colony being characterized by its size, i.e., the number of cells that form the colony.
Cells present in a milk basin or in a colony are also characterized by their physiological state, also called “work to be done.” The “work to be done” depends on the successive stresses undergone by the cells during their life. The physiological state of the cells that are transferred to an environment where growth is possible can be translated to the length of the adaptation to the new environment, also called “lag time,” in hours or days, defined as the time before cells can start to grow exponentially.[6, 7] This “lag time” is often expressed with the so called work to be done, equal to the product of the exponential growth rate and the lag time,[8, 9] or the “relative lag time,” the ratio of the lag time to the doubling time, and it is therefore proportional to the quantity of work to be done.[10, 11]
The evolution of the contamination level of one compartment over time can result from the environmental physical and chemical conditions of the compartment and/or from the transfer of colonies between compartments, inducing secondary contaminations. In the first case, the possible events considered were (1) if the environmental conditions in the compartment allow for growth of L. monocytogenes, the population of pathogenic bacteria present in a compartment can increase; (2) if they are under stress, the population can decrease or remain stable. In the second case, two main types of secondary contamination events were considered and defined as follows: (1) cross-contamination, corresponding to a systematic transfer of cells or colonies between the surface of several products from the same batch, by indirect (machine or people) or direct contact; (2) recontamination, corresponding to the sudden transfers of cells or colonies from the environment to products’ surfaces, through aerosols or people, for instance (Fig. 1). In both events, a colony or part of a colony can move from one compartment to another with a probability of transfer depending on the step of the process and the colony's capacity to adhere to the initial surface.
For one given step, the majority of the events identified in the HACCP system were included in the model. Table I identifies the events modeled for each step of the process.
In order to track the presence of L. monocytogenes over time and space, the following assumptions were made:
- Cells present in a compartment are submitted to the same physical and chemical conditions, allowing for growth or inducing a stress or the destruction, partial or not, of the population.
- Cells present in the same milk basin or in the same colony have the same physiological state due to their physical proximity. As a consequence, they have the same quantity of work to be done.
- Cells present in the same compartment are all viable and have the same capacity to grow and to resist any destructive treatment.
- When a colony reaches its maximum size, growth of the cells of the colony stops.
- Spatial interactions between colonies in the same compartment are not taken into account since colonies are assumed to be far enough away from each other.
- Because of a lack of information on the consequences of a succession of environmental stresses on cells, a stress resulting in a new physiological state of the cells of a colony cancels out the previous physiological state, except when data on succession of stresses are available.
The model simulates the dispersion and the evolution of all the colonies over space and time following an initial contamination by L. monocytogenes of one compartment after pasteurization (primo-contamination event). A primo-contamination event is initialized in one of the compartments. If said compartment is a milk basin, it is defined by a concentration of L. monocytogenes in cells per milliliter of milk, and by the physiological state of the cells. In the case of the compartment being the core or the surface of a product, a machine, or the environment, it has the following components: the number of colonies, their corresponding sizes, and the physiological state of the cells. The evolution of the contamination level is assessed for all the compartments using different scales: “production” scale, “production process” scale, “batch” scale, and “process step” scale (Table II).
Table II. Scales Used in the Model
|Name of the Scale||Origin of the Scale||Unit of the Scale|
|Production||Day of primo-contamination event||Day|
|Production Process||Pasteurization step||Hour|
|Batch||First product of a batch||Rank of one product within a batch|
|Process Step||Beginning of a step||Hour|
Management options considered in the model were (i) sampling plans of the environment and of the products after packaging, characterized by the frequency of sampling and the number of samples; (ii) hygienic operations applied in the workplace environment and to the machines, characterized by their frequency and their intensity. Management options are applied under two different regimes: (1) standard regime, when no previous contamination of the environment or the product is detected; and (2) reinforced regime, when corrective actions are applied after a positive sample.
Application of management options is based on the definition of a batch, which varies in accordance with the regime. In the standard regime, a batch is defined as a set of products manufactured the same day; in the reinforced regime, a batch is a set of products not separated by hygienic operations during a given step. This is the case, for instance, during the smearing step when products from the same day are separated into four or five groups of products between which a hygienic operation is performed in the environment and on the smearing machine to prevent cross-contamination.
A stochastic approach was adopted using Monte Carlo simulations, by considering uncertainty and variability arising from process parameters (e.g., cross-contamination parameters during smearing), biological variability (e.g., lag time distribution), and random processes (e.g., binomial and Poisson processes used for the transfer of colonies and the repartition of colonies between cheeses). The model was implemented using MATLAB software (V7.0.4). The program allows the parameterization of primo-contamination scenario, cheese process, microbiological behavior, hygienic operations, and sampling plans (Table III).
Table III. Parameters and Equations of the Model
|Event or Management||Parameter||Value for the|| |
|Option||Name||Reference Scenario||Description of the Parameter|
|Primo-Contamination Event at the Cheese-Making Phase||Reconth||0||Indice equal to 1 if the contamination occurs at step Sth, 0 if not, h = 1 to 10|
| ||I(Sth)||–||Set of indices of contaminated milk basins at step Sth, h = 1 or 2|
| ||C(Sth)||–||Concentration in a milk basin at step Sth, h = 1 or 2, in number of cells per liter|
| ||I’(Sth)||–||Set of indices of products contaminated on the surface at step Sth, h = 4 to 10|
| ||C’(Sth)||–||Number of contaminant cells on the surface of the product at step Sth, h = 4 to 10|
| ||Q(Sth)||–||Quantity of work to be done of the contaminant cells at step Sth, h = 1 to 10|
| ||IJ||–||Frequency at which the contamination occurs described by the indices of days where the primo-contamination scenario is applied (scale “production”)|
|Primo-Contamination Event at the Ripening Phase||NCrip_env||2,000||Number of cells initially present in the environment of the ripening room|
| ||NCsmear_mac||0||Number of cells initially present in the environment of the smearing machine|
|Transfer of the Colonies from the Smearing Room to the Ripening Room||psr||0.05*||Probability of a colony to be transferred from E2 to the environment of the ripening room|
| ||pgrowth||0.7*||Proportion of colony growing in the environment of the ripening room|
|Recontamination During the||pdetach||0.5*||Proportion of cells detached and transferred from a colony|
|Ripening Phase||pcont||10−6**||Probability of contact between a colony and a product|
|Growth in the Environment||GT||24***||Generation time of a cell in the environment of the ripening room (hours)|
|Hygienic Operations||Nhyg_rip||50||Frequency of hygienic operation in the ripening room (number of days)|
| ||DRhyg_env||2**||Number of decimal reductions during hygienic operation in the environment|
| ||DRhyg_mach||3**||Number of decimal reductions during hygienic operation on a machine|
| ||DRadd||1||Number of additional decimal reductions in reinforced regime|
|Sampling||Nsamp_env_stand||25||Number of samples in the environment of the ripening room randomly dispatched during one week and in standard regime|
| ||Nsamp_env_reinf||5||Number of additional samples in reinforced regime|
| ||Stot||2,000||Area of the surface of the environment of the ripening room (m2)|
| ||Ssamp||0.003||Area of the surface of the sample in the environment of the ripening room (m2)|
| ||Nsamp_prod_stand||5||Number of products sampled in one batch|
| ||Nsamp_prod_reinf||3||Number of additional samples by batch in reinforced regime|
We assessed the risk of listeriosis for a reference scenario and for 17 alternative scenarios (what-if scenarios). Graphical results illustrating a selected set of outputs of the simulation model are given for the reference scenario and the impact of the 17 alternative scenarios on the risk of listeriosis was simulated.
The cheese process considered here is one of a typical soft cheese with a characteristic drop in pH after renetting, generating stress for L. monocytogenes. Parameters relative to the cheese production process and to management options were based on the industrial reality. When a parameter value was not available, scientific literature was used and quality managers from cheese factories were consulted. Four degree polynomial models were adjusted on the basis of data collected, for pH and aw, as a function of time, for core and rind separately, from the end of brine salting to the end of the shelf-life.
Table VI. Parameters of the Polynomial Function f Describing the Evolution of pH and aw as a Function of Time, for Core and Rind Separately, from the End of Brine Salting to the End of the Shelf-Life; , Where t Is in Hours. Corresponds to the End of Brine Salting, and to the End of the Shelf-Life
|a||5.40E + 00||5.41E + 00||9.59E − 01||9.63E − 01|
|b||1.38E − 03||−3.10E − 03||−6.93E − 05||−4.82E − 05|
|c||3.05E − 06||6.97E − 06||1.19E − 07||5.48E − 08|
|d||−2.74E − 09||−3.85E − 09||−9.61E − 11||−5.08E − 11|
|e||6.00E − 13||7.09E − 13||2.60E − 14||1.51E − 14|
Values of the parameters of the model for the reference scenario are given in Table III. In this scenario, the primo-contamination event occurred in the environment of the ripening room with 2,000 contaminant colonies, each colony containing one cell. This scenario, which is theoretical, allows visualizing the evolution of the contamination over space and time. All the parameters of the alternative scenarios were identical to the parameters of the reference scenario, with the exception of one or two parameters (Table VII).
Table VII. Initial and New Values of the Parameters Varying Between the Reference and the Alternative Scenarios and Results of the 20 Iterations Performed for Each Scenario
|Event and Management Options||Modifed Parameter||New Value||Initial Value||Average Concentration of Contaminated Products c180d (log10 cells/g)||Average Prevalence p180d (%)||Average Risk of Listeriosis r180d|
|Primo-Contamination Event at the Ripening Phase||NCrip_env||500||2000||2.504||0.009||7.348.10−11*,**|
| ||NCsmear_mac||500||0|| || || |
| || ||2.319||0.00014||7.800.10−13*,**|
| ||NCrip_env||0||2000|| || || |
|Primo-Contamination Event at the Cheese-Making Phase||Recont3||1||0|| || || |
| ||NCrip_env||0||2000|| || || |
| ||C’(St3)||10 cells/product||–|| || || |
| ||I’(St3)||Every 10 products among the first 100 products of the batch||–||2.324||0.00065||3.428.10−12*,**|
| ||IJ||Every three days||–|| || || |
| ||Q(St3)||Calculated using protocol S = “hyg” (Table V)||–|| || || |
| ||Recont6||1||0|| || || |
| ||NCrip_env||0||2,000|| || || |
| ||C’(St6)||10 cells/product||–|| || || |
| ||I’(St6)||Every 10 products among the first 100 products of the batch||–||2.422||0.001||6.653.10−12*,**|
| ||IJ||Every three days||–|| || || |
| ||Q(St6)||Calculated using protocol P4 (Table V)||–|| || || |
| ||Recont2||1||0|| || || |
| || || || || |
| ||NCrip_env||0||2,000|| || || |
| ||C(St2)||5 cells/L||–|| || || |
| ||I(St2)||Every 10 basins among the first 100 basins of the batch||–||1.178||1.064||4.015.10−10*,**|
| ||IJ||Every three days||–|| || || |
| ||Q(St2)||Calculated using protocol S = “hyg” (Table V)||–|| || || |
| ||Nsamp_env_stand||35||25|| || || |
| || ||2.478||0.036||2.728.10−10|
| ||Nsamp_prod_stand||8||5|| || || |
| ||Nsamp_env_stand||15||25|| || || |
| || ||2.492||0.036||2.832.10−10|
| ||Nsamp_prod_stand||3||5|| || || |
|Growth in the Environment||pgrowth||0.3||0.7||2.490||0.021||1.630.10−10*,**|
For one scenario, 20 iterations were performed, assessing the consequences of a primo-contamination event after 180 days of production. For each iteration, we calculated the percentage of contaminated products during the 180 days p180d, the average concentration of contaminated products c180d, in cells per gram, and the final risk of listeriosis r180d for one individual, having ingested 25 g of a product, 100 times over the course of the 180 days. The average individual risk of listeriosis r, caused by the ingestion of one cell of L. monocytogenes, was equal to 10−12, corresponding to a sensitive population (children, pregnant women). The dose-response model based on the “single hit” hypothesis was used to assess the expected risk of illness for one random sensitive individual after 180 days' intake of the considered food product r180d (Equation (2)).[26, 27]
Equalities of the empirical distribution and of the median of the 20 values of r180d, between one alternative scenario and the reference scenario, were tested using the Kolmogorov-Smirnov test and the Wilcoxon test, respectively.