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Comparison of individual-based modeling and population approaches for prediction of foodborne pathogens growth Jean-Christophe Augustin a, *, Rachel Ferrier a, b, Bernard Hezard b, Adrienne Lintz b, Valérie Stahl b a b

Université Paris-Est, Ecole Nationale Vétérinaire d’Alfort, Maisons-Alfort F-94704, France Aérial, Institut technique agro-industriel, Parc d’Innovation, 250 rue Laurent Fries, Illkirch F-67412, France

a r t i c l e i n f o

a b s t r a c t

Article history: Available online xxx

Individual-based modeling (IBM) approach combined with the microenvironment modeling of vacuumpacked cold-smoked salmon was more effective to describe the variability of the growth of a few Listeria monocytogenes cells contaminating irradiated salmon slices than the traditional population models. The IBM approach was particularly relevant to predict the absence of growth in 25% (5 among 20) of artiﬁcially contaminated cold-smoked salmon samples stored at 8 C. These results conﬁrmed similar observations obtained with smear soft cheese (Ferrier et al., 2013). These two different food models were used to compare the IBM/microscale and population/macroscale modeling approaches in more global exposure and risk assessment frameworks taking into account the variability and/or the uncertainty of the factors inﬂuencing the growth of L. monocytogenes. We observed that the traditional population models signiﬁcantly overestimate exposure and risk estimates in comparison to IBM approach when contamination of foods occurs with a low number of cells ( > > > dN 1 > > > ¼ $mmax $ð1 expðN Nmax ÞÞ < dt 1 þ expð Q Þ with Q0 ¼ ln expðKÞ 1 > dQ > > > > > dt ¼ mmax > :

observed that exposure and risk estimates were still highly dependent on the modeling approach and that population models

where K, the initial physiological state characteristic, is equal to: K ¼ mmax $lag

Please cite this article in press as: Augustin, J.-C., et al., Comparison of individual-based modeling and population approaches for prediction of foodborne pathogens growth, Food Microbiology (2014), http://dx.doi.org/10.1016/j.fm.2014.04.006

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J.-C. Augustin et al. / Food Microbiology xxx (2014) 1e11

The effect of storage temperature and food characteristics on

mmax and lag was described by the following multiplicative function with interactions derived from cardinal and square root models:

gðT; pH; aw Þ ¼ CM2 ðTÞCM1 ðpHÞSR1 ðaw ÞxðT; pH; aw Þ

where c ¼ 7.6, Tinf ¼ 3.6 C, Tsup ¼ 17.3 C, pHinf ¼ 4.34, pHsup ¼ 5.93, aw,inf ¼ 0.917, and aw,sup ¼ 0.988. Individual-cell lag times, lagi, were derived from individual physiological states k, following an extreme value type II with parameters a and b (Guillier and Augustin, 2006):

with

CMn ðXÞ ¼

; X Xmin

0

8 >

$ Xopt Xmin $ X Xopt Xopt Xmax $ ðn 1Þ$Xopt þ Xmin nX : Xopt Xmin

; Xmin < X < Xmax ; X Xmax

0

and SRn X ¼

(

0 X Xmin Xopt Xmin

n

; Xmin < X Xopt

8

< expðT=cÞ exp Tinf c . with p T ¼ > : exp Tsup c exp Tinf c

; T Tinf ; Tinf < T < Tsup ; ; T Tsup

0 ;pH pHinf 8 > < expðpHÞexp pHinf ;pHinf < pH < pHsup ; p pH ¼ > : exp pHsup exp pHinf 1 8 > > > 0 > > > > < aw a w;inf and p aw ¼ a aw;inf > w;sup > > > > > > 1 :

lnðE½kÞ ¼ 0:0103$lnðKÞ5 þ 0:0065$lnðKÞ4 0:039$lnðKÞ3 þ 0:0586$lnðKÞ2 þ 1:1941$lnðKÞ þ 0:1549 where E[k] and S[k] are the expected value and the standard deviation of k, respectively. K is the population initial physiological state characteristic. References

where Xmin, Xopt and Xmax are the minimal, optimal and maximal temperature, pH and water activity for growth. In the IBM approach, the following equations were used to describe the impact of growth conditions on the single-cell growth probability, p, of L. monocytogenes (Augustin and CzarneckaKwasiborski, 2012):

1

(10)

with S½k ¼ e1:004$lnðE½kÞ0:447 and

uðX Þ Q i and u X 2$ jsi 1 u Xj

Xopt X Xopt Xmin

1:1642 S½k $S½k and b ¼ 0:3658 0:3658

;pH pHsup

; aw aw;inf ; aw;inf < aw < aw;sup ; ; aw aw;sup

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Please cite this article in press as: Augustin, J.-C., et al., Comparison of individual-based modeling and population approaches for prediction of foodborne pathogens growth, Food Microbiology (2014), http://dx.doi.org/10.1016/j.fm.2014.04.006