54
0.0 0.5
1.0 1.5
2.0
log
10
cfu g
-1
day
-1
P r
o ba
bi li
ty de
ns it
y Core
Rind
Figure 9: Marginal density functions for single Camembert cheese rind EGR
20
blue and single Camembert cheese core EGR
20
black, when EGR
20
greater than 0.
Normal Gamma distribution, at Table 12 m.l.e.
Maximum Population Density
The maximum population density y
max
logcfug in milk and cheese was set using values from FDAFSIS 2003. These values are a function of the temperature and the media as shown in
Table 14. It was assumed that there are no among L. monocytogenes strain and among cheese effects and that temperature alone accounts for all variability in the maximum population
density.
Table 14: Maximum population density logcfug as a function of temperature and medium. Medium
5°C 5-7°C
7°C
Milk 7
7.5 8
Soft-ripened cheese 5
6.5 8
FDAFSIS 2003.
Following the procedure used in FDAFSIS 2003, a range of one logcfug was used to represent the uncertainty around these point estimates, specifically
= fT + X, X ~ uniform-0.5, 0.5 and fT from Table 14.
T
y
max
Lag
There were no data available to derive the lag time or the number of relative generations that occur following the incorporation of bacteria into milk or cheese from the environment. In a
55 meta-analysis of 74 publications, Augustin and Carlier 2000 derived a median value of
K
ξ
= 3.09 for this lag. Most of their data came from studies using bacteria in good physiological condition, i.e. this value for K is probably lower than would be expected for bacterial transfer in
milk or during cheese-making. Ross and McMeekin 2003 showed that K for many bacterial pathogens appears to have a pronounced peak in the range 3–6 under a very wide range of
experimental conditions. Mellefont et al. 2003 found that most relative lag times were in the range of 4–6 and that relative lag times greater than 8 could not be found with the experimental
system used. Ross et al. 2009 used a logNormal distribution with a mean of 5.29 and a standard deviation of 5.72 equivalent to a distribution such as lnx ~ Normal1.28, 0.88
2
for K in a model of L monocytogenes in ready-to-eat meat. This distribution, lnK
ξ
~ Normal1.28, 0.88
2
, was used here to model the lag time. The uncertainty for the
µ
ξ
and σ
2 ξ
parameter estimates was specified as
284 88
. ,
28 .
1 ~
ˆ
2
Normal
ξ
µ and
[ ]
1 2
88 .
88 .
283 5
. ,
2 283
~ ˆ
− −
× ×
× Gamma
ξ
σ .
Note that Sanaa et al. 2004 modeled the growth lag in cheese using lag ~ Triangular14, 32, 54 in days based on unpublished data. This lag period leads to an absence of growth during a
large part or all of the process. There is no published literature that supports using such a long lag period.
6.1.2. Growth in Cheese During Processing
During cheese processing, the bacterial environment is characterized by complex changes of temperature, pH and a
w
Liu and Puri 2004. Measurements of L. monocytogenes levels during Camembert cheese-making have shown that bacterial populations decrease due to low pH values
during the first 12 days. After these 12 days, these populations increase for the remaining ripening period Ryser and Marth 1987; Ryser 2007; Liu et al. 2009. Some complex models
have been written that model growth in this environment Sanaa et al. 2004; Liu and Puri 2008; Schvartzman et al. 2011. We model the influence of the temperature, the pH, the water activity
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