Corresponding authors: Subhasish Basak (
Academic editor: Hernán Gómez Redondo
The aim of this quantitative risk assessment model is to estimate the risk of Haemolytic Uremic Syndrome (HUS) caused by Shigatoxin producing
This work is part of the ArtiSaneFood project (grant number:
This section summarises the metadata of the concerning QMRA model.
Microbiological food safety is a major challenge for the food sector (
The French partners of the ArtiSaneFood project, a European initiative aimed at improving the microbial safety of artisanal fermented foods in the Mediterranean Region, seek to optimise control measures to reduce the risk of foodborne illness from consuming soft cheese made from raw milk. While cheese is generally considered safe and nutritious, there are instances of foodborne illnesses related to its consumption, as noted by
The QMRA model is implemented as a stochastic simulator that is composed of several hierarchical levels that will be called modules. The simulator is divided into two parts—namely, the batchlevel simulator and the output module. In the batch level, the simulator is composed of a farm module followed by a preharvest intervention step, a cheese production module, a consumer module and a postharvest sampling module. This corresponds to the fabrication of a single batch of cheeses, that is produced from a single batch of milk coming from a fixed number of farms. Fig.
The model is made available in Food Safety Knowledge Markup Language (FSKML) format to facilitate its reuse. This open format is based on predefined terms, metadata and controlled vocabulary to harmonise annotations of risk assessment models (
In this section, we describe the different modules of the simulator that represent the farmtofork continuum in the cheese fabrication process. It starts with a farm module which computes the STEC concentration (CFU/ml) in the aggregated milk tank that is used for cheesemaking. This module includes a preharvest intervention step which performs "farm milk sorting" or, more precisely, rejecting the contaminated tankers of milk with a concentration in
The outcome of the farm module is the STEC concentration (CFU/ml) in the aggregated milk tank that collects milk from all the farms after preharvest milk sorting. The inputs of this module are denoted by
The set of inputs parameters of the farm module denoted by
The concentration of STEC in farm milk is usually too low to be assessed quantitatively through microbiological methods (because of their limit of detection). For this reason, we rely on the "relative" approach proposed by
For each farm
where
Preharvest intervention*
Bulk tank milk coming from each farm is tested for
For the
The number of cows infected with MPSSTEC in the
Remark: If we are interested to compute the concentration of MPSSTEC in the aggregated milk, we use
The concentration of
The STEC concentration
The quantities of interest from the farm module are
The cheese module begins with the input of the initial concentration
The inputs of the cheese module are the initial concentration
The evolution of STEC involves six steps, with milk storage and moulding taking place during the liquid growth phase and draining and salting occurring during the solid growth phase. Ripening and cheese storage represent the (solid) decline phase of STEC.
In all the growth steps, the concentration
where
The milk storage step starts with initial concentration
Remark: The factor
Starting from the draining phase, the evolution of the size of colony, stemming for one immobilised STEC cell, is studied. The draining phase commences with an initial colony size of 1 CFU and growth continues until the salting phase. It is assumed that the evolution of each colony inside each cheese (weighing 250 g) is identical during these phases, since they have the same environmental conditions. The output of the draining and salting steps are called
The growth in colony size stops after the salting phase. Then starts the decline phase, which is composed of two steps—namely, ripening and cheese storage. The ripening phase lasts until the 14^{th} day of cheese production and the cheese storage phase duration depends on the consumption time
where
The expected number of colonies
The outputs of interest for the cheese module are the average number of colonies
In this section, we describe the module of the batch level simulator that computes the risk of HUS for a particular batch. Given the outputs of the cheese module, i.e. the average number of colonies
The dose
where
where
The average number of colonies
where
where
The inputs of the consumer module are the average number of colonies
For a given set of input parameters
Alternatively, the batch risk can be computed by approximation of the integral
where
where
is monotone (nonincreasing) in
The choice of the method for computating the batch risk is determined through the parameter value
The current implementation also allows the user to compute the conditional batch risk
For STEC, due to the inactivation during the postripening storage phase,
The output of the consumer module is the estimated batch risk of HUS. For a given set of input parameters, Fig.
The postharvest step, also known as the sampling step, can be carried out at various stages of cheese production, depending on the type of bacteria. For STEC, this step is conducted at the end of the ripening phase, more precisely at the 14^{th} day of production by default. However the current implementation allows us to change this parameter with a minimum value of 3 days and a maximum value of 14 days. During this step, the batch of cheese produced is examined for MPSSTEC contamination by taking small portions of cheese samples from the batch. Once a single sample unit tests positive, the entire batch of cheese is rejected, meaning that the specific batch does not enter into the calculation of the overall risk of HUS.
The inputs of the postharvest module are initial STEC concentration in milk
We assume that the colonies are homogeneously distributed inside a cheese, a colony contains at least one MPSSTEC cell and the test is accurate enough to detect a colony with a single MPSSTEC cell. We observe that probability of a sample unit testing positive is
The output of the postharvest module is the probability of rejection. Fig.
The output module computes the overall risk of HUS from MPSSTEC and other quantities required to assess the analytical cost corresponding to the intervention steps. This module is outside the batchlevel simulator that computes the quantities of interest corresponding to the fabrication of a particular batch of cheese (see Fig.
The inputs of the output module are the outputs of the farm, consumer and postharvest module along with the parameters denoted by
The output module simulates several batches and produces estimates of the overall risk
with
where the batch risk is set to zero for rejected batches.
The overall risk of HUS is conditional on the event that the batch actually goes into the market, i.e. not rejected. It is computed by dividing
The quantities are estimated using simple Monte Carlo with sample size
The current implementation of the output module computes the relative risk of HUS with respect to a baseline scenario with no intervention steps. This quantity is obtained by dividing
The output module returns the relative risk of HUS
The R implementation proposed in this article differs in several respects from the QMRA model originally proposed by
In the farm module, the hyperparameters of the distribution of the concentration of
The proportion of MPS infected cows is considered to be
As an additional metric of cost of intervention, this model computes the average quantity of milk lost due to preharvest milk sorting.
The variable
The volume of milk used to produce a single cheese is taken (default value) as 2.2 litres instead of 2.5 litres. However, this value can be changed depending on the production scenario.
In the current implementation, the batch risk is computed at the time of consumption which includes the inactivation (decline in concentration) during the cheese storage phase. This is different from the batch risk computed at the end of production which does not take into account the decline in bacteria population during the cheese storage. The duration of this phase is modelled as a Triangular distribution with more recent and updated values of the parameters as shown in Table
The FSKX implementation (Suppl. material
This article presents a QMRA model that offers a scientific approach to simulate the reallife scenarios encountered during the production of raw milk soft cheese. The model builds upon the work of
According to
Subhasish Basak: Writing  Original Draft, Writing  Review & Editing
Janushan Christy, Laurent Guillier, Fanny TenenhausAziza, Julien Bect, Emmanuel Vazquez: Methodology, Writing Reviewing and Editing
Fanny TenenhausAziza: Project coordinator
Moez Sanaa, Frédérique AudiatPerrin: Writing Reviewing and Editing
No conflict of interest to declare
Disclaimer: This article is (co)authored by any of the EditorsinChief, Managing Editors or their deputies in this journal.
The Shigatoxin producing
The integral inside
ACTALIA SAS Script: The SAS script used by CNIEL and developed by ACTALIA uses a set of parameter values for the implementation. In our work, we have considered it as a reference for several parameter values.
We have used a Bayesian approach to estimate the values of the hygiene parameters in the farm module: this uses a Gibbs sampler to estimate posterior distribution of alpha and sigma, based on the
Number of cows: In the current implementation, the number of cows per each farm is sampled from the cow distribution data provided by ACTALIA/CNIEL and used by
The preharvest intervention step does not implement the reintegration procedure of farms in the production process, once a particular farm is rejected. The typical process of reintegration involves conducting repeated tests on the milk from the farm over several days until it consistently shows no signs of contamination, ensuring the production of uncontaminated milk from the farm.
Schematic diagram of the batch level simulator of the risk assessment model. Modules are denoted by pink coloured boxes with the blue boxes denoting the set of corresponding input parameters
Histogram of STEC (main pathogenic serotypes MPSSTEC) concentration (log_{10} (CFU/ml)) in milk put into production.
Evolution of STEC (main pathogenic serotypes MPSSTEC) in log_{10} CFU/ml during the storage and moulding step. The blue vertical line shows the end of the storage phase.
Evolution of STEC colony size during draining, salting and ripening of cheese fabrication. The decline rate for the MPS O157:H7 strain and nonMPS strains are equal (orange line) and significantly higher than the decline rate of MPS nonO157:H7 strain (red line). The three phases, namely, draining, salting and ripening are separated by vertical blue dotted lines.
Batch rejection probability as a function of the initial STEC (main pathogenic serotypes MPSSTEC) concentration (CFU/ml).
The relative batch risk (with respect to a baseline risk value) is plotted as a function of the initial STEC (main pathogenic serotypes MPSSTEC) concentration (CFU/ml).
Output module.
Inputs of farm module
Symbol  Description  default values/references 
N_farms  Number of farms  31 (see * 
N_cow_i  Number of cows in ith farm  see * 
alpha_i  Parameter for distribution of 
1.3 (see * 
sigma_i  Parameter for distribution of 
2.9 (see * 
a_weibull  Parameter for distribution of STEC in faecal matter  0.264 
b_weibull  Parameter for distribution of STEC in faecal matter  16.288 
mu_ecoli  Parameter for distribution of 
6 
tau_ecoli  Parameter for distribution of 
0.3 
mu_u  Parameter for distribution of probability infected cows  0.927 
tau_u  Parameter for distribution of probability infected cows  1.47411 
q_milk  Average quantity of milk from a cow  25 litres 
sorting_frequency  Milk testing frequency  10 
sorting_lim  Max. limit of 
50 
p_MPS_STEC  Proportion of pathogenic STEC in cows  0.025 
Parameters of cheese module
Symbol  Description  Values/reference 
Parameters for mu_max  Parameters to compute mu_max  Table I in 
mu_opt  Optimal growth rate  1.85 (average from Table II in 
y_max_milk  Hypothetical maximum population in milk  10^{9} CFU/ml 
y_max_cheese  Hypothetical maximum population in cheese  10^{5} CFU/g 
p_O157H7  Class probability of O157:H7  0.76 (taken from * 
p_MPS_STEC  Proportion of main pathogenic STEC  0.025 
rho_O157H7  Parameter for decline phase of O157:H7  0.14 log_{10} CFU/day 
rho_otherMPS  Parameter for decline phase of other MPS  0.033 log_{10} CFU/day 
a_w  Water activity parameter  0.99 
w_loss  Proportion of water loss  0.9 
v_cheese  Milk used in a single cheese  2200 
t_consum  Consumption time  Triangular (22,30,60) 
d  Duration of a step  Table III in 
pH  pH of a step  Table III in 
T  Temperature of a step  Table III in 
NA  Absolute tolerance of ode solver  10^{6} 
NA  Maximal step size of ode solver  0.01 
Parameters of the consumer module
Symbol  Description  Values/references 
k  Parameter for risk computation  0.38 
r_0  Parameter for risk computation  10^{2.33} 
wt_cheese  weight of a single cheese  250 gm 
wt_serving  weight of a single serving  25 gm 
g(a)  Proportion of cheese consumed by age group a  taken from * 
tau_eps_O157H7  Parameter for inter cheese variability  0.000279659 (taken from * 
tau_eps_otherMPS  Parameter for inter cheese variability  0.000065399 (taken from * 
a_max  Maximum age group  15 
N_dose  Monte Carlo sample size  0 
Inputs of output module
Symbol  Description  Values/reference 
N_batch  Monte Carlo sample size  1 
p_test  Proportion of cheese batch tested  0.5 
Default simulation settings.


fm_N_farms  31 
fm_q_milk  25 
fm_sorting_freq  10 
fm_sorting_lim  50 
fm_mu_u  0.927 
fm_tau_u  1.47411 
fm_a_weibull  0.264 
fm_b_weibull  16.288 
fm_mu_ecoli  6 
fm_tau_ecoli  0.3 
cm_mu_max_T_min  5.5 
cm_mu_max_T_opt  40.6 
cm_mu_max_T_max  48.1 
cm_mu_max_pH_min  3.9 
cm_mu_max_pH_opt  6.25 
cm_mu_max_pH_max  14 
cm_mu_max_aw_min  0.9533 
cm_mu_max_aw_opt  0.999 
cm_mu_max_mu_opt  2.03 
cm_w_activity  0.99 
cm_rho_O157H7  0.14 
cm_rho_otherMPS  0.033 
cm_y_max_milk  1e+09 
cm_y_max_cheese  1e+05 
cm_storage_duration  12 
cm_storage_duration_min  1 
cm_storage_duration_max  40 
cm_storage_duration_mode  12 
cm_storage_temperature  5 
cm_storage_temperature_min  1 
cm_storage_temperature_max  6 
cm_p_O157H7  0.76 
cm_p_MPS_STEC or fm_p_MPS_STEC  0.025 
cm_mu_eps_O157H7  0 
cm_tau_eps_O157H7  0.000279659 
cm_mu_eps_otherMPS  0 
cm_tau_eps_otherMPS  6.5399e05 
cm_molding_duration  3 
cm_draining_duration  17 
cm_salting_duration  4.5 
cm_consumption_time_min 
22 
cm_v_cheese  2200 
cm_w_loss  0.9 
cm_wt_cheese 
250 
cm_m_sample  25 
cm_n_sample  5 
cm_k  0.38 
cm_r0  1e2.33 
cm_age_max  14 
cm_p_test 
0.5 
cm_n_dose 
0 
flag_consum 
TRUE 
Parameters of the postharvest module \(\theta^{\rm post}\). Unless specified, the parameter values are taken from *
Symbol  Descrtption  Values/reference 
n_sample  Number of test portions  5 
m_sample  Mass of each test portion  25 gm 
d_test  Postharvest sampling day  14 days 
QMRA model assumptions
Assumptions  Significance  Comments 
Homogeneous distribution of colonies inside a cheese.  The distribution of colonies inside a cheese impacts the postharvest sampling step. This assumption is used to simplify the cheese testing step, which assures that, if the cheese is contaminated, it is always tested positive.  This overestimates the detection probability when colonies are clustered. 
Identifying MPSSTEC as the unique HUScausing hazard.  It was not taken into account that certain nonMPSSTEC strains can also cause HUS and that, within MPSSTEC, some of the strains maybe less virulent.  Some recent publications, see, for example, 
STEC and 
The preharvest intervention step is based on this assumption. The milk sorting is carried out using the 
This assumption is based on 
No intracheese variability.  All the colonies inside a single cheese are of same colony size. 
QRA simulator
fsk file
File: oo_877273.fskx