title: Development of a restricted state space stochastic differential equation model for bacterial growth in rich media.
abstract: In the present study, bacterial growth in a rich media is analysed in a Stochastic Differential Equation (SDE) framework. It is demonstrated that the SDE formulation and smoothened state estimates provide a systematic framework for data driven model improvements, using random walk hidden states. Bacterial growth is limited by the available substrate and the inclusion of diffusion must obey this natural restriction. By inclusion of a modified logistic diffusion term it is possible to introduce a diffusion term flexible enough to capture both the growth phase and the stationary phase, while concentration is restricted to the natural state space (substrate and bacteria non-negative). The case considered is the growth of Salmonella and Enterococcus in a rich media. It is found that a hidden state is necessary to capture the lag phase of growth, and that a flexible logistic diffusion term is needed to capture the random behaviour of the growth model. Further, it is concluded that the Monod effect is not needed to capture the dynamics of bacterial growth in the data presented.
authors.affiliation: DTU Informatics, Richard Pedersens Plads, Technical University of Denmark Building 321, DK-2800 Lyngby, Denmark. jkm@imm.dtu.dk
authors.forename: Jan Kloppenborg
authors.initials: JK
authors.lastname: Møller
authors.forename: Kirsten Riber
authors.initials: KR
authors.lastname: Bergmann
authors.forename: Lasse Engbo
authors.initials: LE
authors.lastname: Christiansen
authors.forename: Henrik
authors.initials: H
authors.lastname: Madsen
mesh_terms: D001419:Bacteria / Q000254:growth & development*; D003470:Culture Media; D016983:Enterococcus / Q000254:growth & development; D008954:Models, Biological; D012475:Salmonella / Q000254:growth & development; D013269:Stochastic Processes
chemical_list: D003470:Culture Media