Ej. Dens et Jf. Van Impe, On the importance of taking space into account when modeling microbial competition in structured food products, MATH COMP S, 53(4-6), 2000, pp. 443-448
Most of the models discussed up till now in predictive microbiology do not
take into account the variability of microbial growth with respect to space
. In structured (solid) foods, microbial growth can strongly depend on the
position in the food and the assumption of homogeneity can thus, not be acc
epted: space must be considered as an additional independent variable. In t
he current paper, a continuous time - two species competition model (propos
ed in previous work by the authors) is extended to take space into account.
The spatio-temporal behavior of the spatially extended model is observed o
n a coupled map lattice. The smaller motility of the micro-organisms in sol
id foods allows spatial segregation which causes pattern formation. Evidenc
e is given for the fact that taking space into account indeed has an influe
nce on the behavior (coexistence/extinction) of the populations, which is v
ery important in the field of predictive microbiology, where microbial safe
ty is of major interest. (C) 2000 IMACS. Published by Elsevier Science B.V.
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